Receiving Helpdesk

cos^2x integration

by Yolanda Gulgowski Published 3 years ago Updated 3 years ago

The integral of cos 2x dx is written as ∫ cos 2x dx and ∫ cos 2x dx = (sin 2x)/2 + C, where C is the integration constant.

What is an indefinite integral?

Indefinite Integrals: It is an integral of a function when there is no limit for integration. It contains an arbitrary constant. Definite Integrals: An integral of a function with limits of integration. There are two values as the limits for the interval of integration. One is the lower limit and the other is the upper limit.

What is the difference between a definite integral and an indefinite integral?

The definite integral of the function gives the area while the indefinite integral gives the anti-derivative of the function, i.e. the function of which our given function is a derivative, and also the integral of sinx is -cosx, as the derivative of -cosx is equal to sinx.

What are the hyperbolic trig functions?

The hyperbolic trig functions sinh (, cosh (, and tanh ( are an analog of normal trig functions, but for a hyperbola, rather than a circle. They can be expressed in terms of real powers of e, and don’t depend on the Degree or Radian mode setting.

Popular Posts:

  • 1. is cone a long o sound
  • 2. can sperm go through 2 layers of clothing
  • 3. food to eat during fever
  • 4. how long is flight from texas to alaska
  • 5. who is charlie writing the letter to in perks of being a wallflower
  • 6. 42 kg to lbs
  • 7. does home depot have safety glasses
  • 8. sistemas contra incendios méxico
  • 9. xfinity stream nfl network
  • 10. onguard bike lock lost key
    • A B C D E F G H I J K L M N O P Q R S T U V W X Y Z 1 2 3 4 5 6 7 8 9
    Messages17TimelineExceptionsViews7RouteQueries7Models15Livewire0MailsGateSessionRequest
    8.3.21PHP Version2.95sRequest Duration2MBMemory UsageGET {post}Route
    • warninglog[04:48:24] LOG.warning: Creation of dynamic property Barryvdh\Debugbar\DataFormatter\QueryFormatter:...
    • warninglog[04:48:24] LOG.warning: Creation of dynamic property Barryvdh\Debugbar\DataFormatter\QueryFormatter:...
    • warninglog[04:48:24] LOG.warning: Callables of the form ["Swift_SmtpTransport", "Swift_Transport_EsmtpTranspor...
    • warninglog[04:48:24] LOG.warning: Creation of dynamic property Barryvdh\Debugbar\DataFormatter\SimpleFormatter...
    • warninglog[04:48:24] LOG.warning: Creation of dynamic property Barryvdh\Debugbar\DataFormatter\SimpleFormatter...
    • warninglog[04:48:24] LOG.warning: json_decode(): Passing null to parameter #1 ($json) of type string is deprec...
    • warninglog[04:48:24] LOG.warning: json_decode(): Passing null to parameter #1 ($json) of type string is deprec...
    • warninglog[04:48:24] LOG.warning: json_decode(): Passing null to parameter #1 ($json) of type string is deprec...
    • warninglog[04:48:24] LOG.warning: json_decode(): Passing null to parameter #1 ($json) of type string is deprec...
    • warninglog[04:48:24] LOG.warning: json_decode(): Passing null to parameter #1 ($json) of type string is deprec...
    • warninglog[04:48:24] LOG.warning: json_decode(): Passing null to parameter #1 ($json) of type string is deprec...
    • warninglog[04:48:24] LOG.warning: json_decode(): Passing null to parameter #1 ($json) of type string is deprec...
    • warninglog[04:48:24] LOG.warning: json_decode(): Passing null to parameter #1 ($json) of type string is deprec...
    • warninglog[04:48:24] LOG.warning: json_decode(): Passing null to parameter #1 ($json) of type string is deprec...
    • warninglog[04:48:24] LOG.warning: json_decode(): Passing null to parameter #1 ($json) of type string is deprec...
    • warninglog[04:48:24] LOG.warning: json_decode(): Passing null to parameter #1 ($json) of type string is deprec...
    • warninglog[04:48:24] LOG.warning: mt_rand(): Passing null to parameter #2 ($max) of type int is deprecated in ...
    warning
    • Booting (14.46ms)
    • Application (2.93s)
    • 1 x Application (99.49%)
      2.93s
      1 x Booting (0.49%)
      14.46ms
      7 templates were rendered
      • themes.DevBlog.content.post (resources/views/themes/DevBlog/content/post.blade.php)34blade
        Params
        0
        post
        1
        postContent
        2
        author
        3
        updated_at
        4
        bing_rich_snippet_text
        5
        bing_rich_snippet_link
        6
        bing_related_keywords
        7
        google_related_keywords
        8
        bing_news_title
        9
        bing_news_description
        10
        bing_videos
        11
        bing_images
        12
        bing_search_result_title
        13
        bing_search_result_description
        14
        bing_search_result_url
        15
        bing_paa_questions
        16
        bing_paa_answers
        17
        bing_slider_faq_questions
        18
        bing_slider_faq_answers
        19
        bing_pop_faq_questions
        20
        bing_pop_faq_answers
        21
        bing_tab_faq_questions
        22
        bing_tab_faq_answers
        23
        google_faq_questions
        24
        google_faq_answers
        25
        google_rich_snippet
        26
        google_search_result
        27
        indexedArray
        28
        total_images
        29
        total_videos
        30
        settings
        31
        url_current
        32
        menus
        33
        sidebar
      • themes.DevBlog.layouts.master (resources/views/themes/DevBlog/layouts/master.blade.php)41blade
        Params
        0
        __env
        1
        app
        2
        errors
        3
        post
        4
        postContent
        5
        author
        6
        updated_at
        7
        bing_rich_snippet_text
        8
        bing_rich_snippet_link
        9
        bing_related_keywords
        10
        google_related_keywords
        11
        bing_news_title
        12
        bing_news_description
        13
        bing_videos
        14
        bing_images
        15
        bing_search_result_title
        16
        bing_search_result_description
        17
        bing_search_result_url
        18
        bing_paa_questions
        19
        bing_paa_answers
        20
        bing_slider_faq_questions
        21
        bing_slider_faq_answers
        22
        bing_pop_faq_questions
        23
        bing_pop_faq_answers
        24
        bing_tab_faq_questions
        25
        bing_tab_faq_answers
        26
        google_faq_questions
        27
        google_faq_answers
        28
        google_rich_snippet
        29
        google_search_result
        30
        indexedArray
        31
        total_images
        32
        total_videos
        33
        settings
        34
        url_current
        35
        menus
        36
        sidebar
        37
        i
        38
        __currentLoopData
        39
        loop
        40
        item
      • themes.DevBlog.panels.head (resources/views/themes/DevBlog/panels/head.blade.php)41blade
        Params
        0
        __env
        1
        app
        2
        errors
        3
        post
        4
        postContent
        5
        author
        6
        updated_at
        7
        bing_rich_snippet_text
        8
        bing_rich_snippet_link
        9
        bing_related_keywords
        10
        google_related_keywords
        11
        bing_news_title
        12
        bing_news_description
        13
        bing_videos
        14
        bing_images
        15
        bing_search_result_title
        16
        bing_search_result_description
        17
        bing_search_result_url
        18
        bing_paa_questions
        19
        bing_paa_answers
        20
        bing_slider_faq_questions
        21
        bing_slider_faq_answers
        22
        bing_pop_faq_questions
        23
        bing_pop_faq_answers
        24
        bing_tab_faq_questions
        25
        bing_tab_faq_answers
        26
        google_faq_questions
        27
        google_faq_answers
        28
        google_rich_snippet
        29
        google_search_result
        30
        indexedArray
        31
        total_images
        32
        total_videos
        33
        settings
        34
        url_current
        35
        menus
        36
        sidebar
        37
        i
        38
        __currentLoopData
        39
        loop
        40
        item
      • themes.DevBlog.panels.header (resources/views/themes/DevBlog/panels/header.blade.php)41blade
        Params
        0
        __env
        1
        app
        2
        errors
        3
        post
        4
        postContent
        5
        author
        6
        updated_at
        7
        bing_rich_snippet_text
        8
        bing_rich_snippet_link
        9
        bing_related_keywords
        10
        google_related_keywords
        11
        bing_news_title
        12
        bing_news_description
        13
        bing_videos
        14
        bing_images
        15
        bing_search_result_title
        16
        bing_search_result_description
        17
        bing_search_result_url
        18
        bing_paa_questions
        19
        bing_paa_answers
        20
        bing_slider_faq_questions
        21
        bing_slider_faq_answers
        22
        bing_pop_faq_questions
        23
        bing_pop_faq_answers
        24
        bing_tab_faq_questions
        25
        bing_tab_faq_answers
        26
        google_faq_questions
        27
        google_faq_answers
        28
        google_rich_snippet
        29
        google_search_result
        30
        indexedArray
        31
        total_images
        32
        total_videos
        33
        settings
        34
        url_current
        35
        menus
        36
        sidebar
        37
        i
        38
        __currentLoopData
        39
        loop
        40
        item
      • themes.DevBlog.panels.navbar (resources/views/themes/DevBlog/panels/navbar.blade.php)41blade
        Params
        0
        __env
        1
        app
        2
        errors
        3
        post
        4
        postContent
        5
        author
        6
        updated_at
        7
        bing_rich_snippet_text
        8
        bing_rich_snippet_link
        9
        bing_related_keywords
        10
        google_related_keywords
        11
        bing_news_title
        12
        bing_news_description
        13
        bing_videos
        14
        bing_images
        15
        bing_search_result_title
        16
        bing_search_result_description
        17
        bing_search_result_url
        18
        bing_paa_questions
        19
        bing_paa_answers
        20
        bing_slider_faq_questions
        21
        bing_slider_faq_answers
        22
        bing_pop_faq_questions
        23
        bing_pop_faq_answers
        24
        bing_tab_faq_questions
        25
        bing_tab_faq_answers
        26
        google_faq_questions
        27
        google_faq_answers
        28
        google_rich_snippet
        29
        google_search_result
        30
        indexedArray
        31
        total_images
        32
        total_videos
        33
        settings
        34
        url_current
        35
        menus
        36
        sidebar
        37
        i
        38
        __currentLoopData
        39
        loop
        40
        item
      • themes.DevBlog.panels.footer (resources/views/themes/DevBlog/panels/footer.blade.php)41blade
        Params
        0
        __env
        1
        app
        2
        errors
        3
        post
        4
        postContent
        5
        author
        6
        updated_at
        7
        bing_rich_snippet_text
        8
        bing_rich_snippet_link
        9
        bing_related_keywords
        10
        google_related_keywords
        11
        bing_news_title
        12
        bing_news_description
        13
        bing_videos
        14
        bing_images
        15
        bing_search_result_title
        16
        bing_search_result_description
        17
        bing_search_result_url
        18
        bing_paa_questions
        19
        bing_paa_answers
        20
        bing_slider_faq_questions
        21
        bing_slider_faq_answers
        22
        bing_pop_faq_questions
        23
        bing_pop_faq_answers
        24
        bing_tab_faq_questions
        25
        bing_tab_faq_answers
        26
        google_faq_questions
        27
        google_faq_answers
        28
        google_rich_snippet
        29
        google_search_result
        30
        indexedArray
        31
        total_images
        32
        total_videos
        33
        settings
        34
        url_current
        35
        menus
        36
        sidebar
        37
        i
        38
        __currentLoopData
        39
        loop
        40
        item
      • themes.DevBlog.panels.scripts (resources/views/themes/DevBlog/panels/scripts.blade.php)41blade
        Params
        0
        __env
        1
        app
        2
        errors
        3
        post
        4
        postContent
        5
        author
        6
        updated_at
        7
        bing_rich_snippet_text
        8
        bing_rich_snippet_link
        9
        bing_related_keywords
        10
        google_related_keywords
        11
        bing_news_title
        12
        bing_news_description
        13
        bing_videos
        14
        bing_images
        15
        bing_search_result_title
        16
        bing_search_result_description
        17
        bing_search_result_url
        18
        bing_paa_questions
        19
        bing_paa_answers
        20
        bing_slider_faq_questions
        21
        bing_slider_faq_answers
        22
        bing_pop_faq_questions
        23
        bing_pop_faq_answers
        24
        bing_tab_faq_questions
        25
        bing_tab_faq_answers
        26
        google_faq_questions
        27
        google_faq_answers
        28
        google_rich_snippet
        29
        google_search_result
        30
        indexedArray
        31
        total_images
        32
        total_videos
        33
        settings
        34
        url_current
        35
        menus
        36
        sidebar
        37
        i
        38
        __currentLoopData
        39
        loop
        40
        item
      uri
      GET {post}
      middleware
      web, checkdate
      as
      post.show
      controller
      App\Http\Controllers\Frontend\json_data\PostController@show
      namespace
      where
      file
      app/Http/Controllers/Frontend/json_data/PostController.php:18-166
      7 statements were executed2.91s
      receivinghelpdeskask
      • select * from `posts` where `published_at` <= '2025-06-23 04:48:24' and `slug` = 'cos-2x-integration' and `posts`.`deleted_at` is null limit 1
        2.51ms/app/Providers/RouteServiceProvider.php:54receivinghelpdeskask
        Metadata
        Bindings
        • 0. 2025-06-23 04:48:24
        • 1. cos-2x-integration
        Backtrace
        • 15. /app/Providers/RouteServiceProvider.php:54
        • 18. /vendor/laravel/framework/src/Illuminate/Routing/Router.php:842
        • 19. Route binding:39
        • 20. /vendor/laravel/framework/src/Illuminate/Pipeline/Pipeline.php:167
        • 21. /vendor/laravel/framework/src/Illuminate/Foundation/Http/Middleware/VerifyCsrfToken.php:78
      • select * from `json_post_contents` where `json_post_contents`.`post_id` = 23780 and `json_post_contents`.`post_id` is not null and `rewrite_id` = 0
        2.62msmiddleware::checkdate:30receivinghelpdeskask
        Metadata
        Bindings
        • 0. 23780
        • 1. 0
        Backtrace
        • 19. middleware::checkdate:30
        • 20. /vendor/laravel/framework/src/Illuminate/Pipeline/Pipeline.php:167
        • 21. /vendor/laravel/jetstream/src/Http/Middleware/ShareInertiaData.php:61
        • 22. /vendor/laravel/framework/src/Illuminate/Pipeline/Pipeline.php:167
        • 23. /vendor/laravel/framework/src/Illuminate/Routing/Middleware/SubstituteBindings.php:50
      • select * from `nova_menu_menus` where `slug` = 'header' limit 1
        830μs/vendor/outl1ne/nova-menu-builder/src/helpers.php:32receivinghelpdeskask
        Metadata
        Bindings
        • 0. header
        Backtrace
        • 15. /vendor/outl1ne/nova-menu-builder/src/helpers.php:32
        • 17. /vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 18. /vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:45
        • 19. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:261
        • 20. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `nova_menu_menu_items` where `nova_menu_menu_items`.`menu_id` = 1 and `nova_menu_menu_items`.`menu_id` is not null and `parent_id` is null order by `parent_id` asc, `order` asc, `name` asc
        400μs/vendor/outl1ne/nova-menu-builder/src/Models/Menu.php:35receivinghelpdeskask
        Metadata
        Bindings
        • 0. 1
        Backtrace
        • 19. /vendor/outl1ne/nova-menu-builder/src/Models/Menu.php:35
        • 20. /vendor/outl1ne/nova-menu-builder/src/helpers.php:33
        • 22. /vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 23. /vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:45
        • 24. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:261
      • select * from `nova_menu_menu_items` where `nova_menu_menu_items`.`parent_id` in (1) order by `order` asc
        530μs/vendor/outl1ne/nova-menu-builder/src/Models/Menu.php:35receivinghelpdeskask
        Metadata
        Backtrace
        • 24. /vendor/outl1ne/nova-menu-builder/src/Models/Menu.php:35
        • 25. /vendor/outl1ne/nova-menu-builder/src/helpers.php:33
        • 27. /vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 28. /vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:45
        • 29. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:261
      • select `id`, `post_title`, `slug` from `posts` where `status` = 'publish' and `posts`.`deleted_at` is null order by RAND() limit 10
        2.9s/app/View/Composers/SidebarView.php:22receivinghelpdeskask
        Metadata
        Bindings
        • 0. publish
        Backtrace
        • 14. /app/View/Composers/SidebarView.php:22
        • 15. /app/View/Composers/SidebarView.php:12
        • 16. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:124
        • 17. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:162
        • 20. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:177
      • select * from `fake_users` where `fake_users`.`id` = 7233 limit 1
        650μsview::2dd102cf0462e89a4d4d8bc77355d767652bf9aa:15receivinghelpdeskask
        Metadata
        Bindings
        • 0. 7233
        Backtrace
        • 21. view::2dd102cf0462e89a4d4d8bc77355d767652bf9aa:15
        • 23. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:108
        • 24. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 25. /vendor/livewire/livewire/src/ComponentConcerns/RendersLivewireComponents.php:69
        • 26. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:61
      App\Models\FakeUser
      1
      Outl1ne\MenuBuilder\Models\MenuItem
      1
      Outl1ne\MenuBuilder\Models\Menu
      1
      App\Models\JsonPostContent
      1
      App\Models\Post
      11
          _token
          eOKGIXz1TL4cmRMTejkKL4F4r3cuNNvrE4AIq8cp
          _previous
          array:1 [ "url" => "https://receivinghelpdesk.com/ask/cos-2x-integration" ]
          _flash
          array:2 [ "old" => [] "new" => [] ]
          PHPDEBUGBAR_STACK_DATA
          []
          path_info
          /cos-2x-integration
          status_code
          200
          status_text
          OK
          format
          html
          content_type
          text/html; charset=UTF-8
          request_query
          []
          request_request
          []
          request_headers
            0 of 0   
          array:25 [▼
  "cookie" => array:1 [▶
    0 => "_pk_id.64.7c30=e60b1be82f1030ae.1750634289.; _pk_ses.64.7c30=1; XSRF-TOKEN=eyJpdiI6InZmZFp2Wkphd2kxWndIRGVJWW5XS1E9PSIsInZhbHVlIjoiQ0lvTzdOVFp0UHMrZlo4NXd3Rkx6WEd1Nko1QTIyY1MrVDF4dlQ2bUF0UU9xc1RZbHNQV3dOenZrMFcyUXVtcnB2bFYvQUNPYXYrVmJJaGVrNXBjRjdmYUxzSk5jM0ZDS1R1bUg4M1RkWUdOTFhPa3NWL01YZTJuU29Md0taclEiLCJtYWMiOiJkY2Q4YzFkYmI3MGNlNzZjNjZlMGFhZTkyM2IxZTc5MzJmN2Q2Y2IzMzA3NDlmZmE0Y2FlNTcwZDBmYWFjZDE2IiwidGFnIjoiIn0%3D; askhelpdesk_session=eyJpdiI6Ikx3cFE5WVdENjVONzd2cWoxOE9Tc1E9PSIsInZhbHVlIjoiR3A3cXpnSUg1aEJCTGc2cHA0MkRtbCtSYlQyMnhuV1p5RlorMXhxNjE0NU5tS1l6bGxrOGdUVFlzRDFCSXFxcXArcjhSQ2wwWS8yeUlsWnN4amFMOHBnUy93Wkc3S3hQWlZ0N2UyZ1ZoQUU2Q2NqdURIWGNDc3RiUzVsbkpjbHUiLCJtYWMiOiIxMGI3NTI3N2M4ZDBhOGZmYmMzMzRmMWRjNzE2MzZmMGFhZTczNTJhM2FlYTdiNjliYTAwY2UyNGY5ZmRlZTcwIiwidGFnIjoiIn0%3D ◀_pk_id.64.7c30=e60b1be82f1030ae.1750634289.; _pk_ses.64.7c30=1; XSRF-TOKEN=eyJpdiI6InZmZFp2Wkphd2kxWndIRGVJWW5XS1E9PSIsInZhbHVlIjoiQ0lvTzdOVFp0UHMrZlo4NXd3Rkx6W ▶"
  ]
  "cf-ipcountry" => array:1 [▶
    0 => "US"
  ]
  "cf-connecting-ip" => array:1 [▶
    0 => "216.73.216.130"
  ]
  "cdn-loop" => array:1 [▶
    0 => "cloudflare; loops=1"
  ]
  "sec-fetch-mode" => array:1 [▶
    0 => "navigate"
  ]
  "sec-fetch-site" => array:1 [▶
    0 => "none"
  ]
  "accept" => array:1 [▶
    0 => "text/html,application/xhtml+xml,application/xml;q=0.9,image/avif,image/webp,image/apng,*/*;q=0.8,application/signed-exchange;v=b3;q=0.7"
  ]
  "user-agent" => array:1 [▶
    0 => "Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)"
  ]
  "upgrade-insecure-requests" => array:1 [▶
    0 => "1"
  ]
  "sec-ch-ua-platform" => array:1 [▶
    0 => ""Windows""
  ]
  "sec-ch-ua-mobile" => array:1 [▶
    0 => "?0"
  ]
  "sec-ch-ua" => array:1 [▶
    0 => ""Chromium";v="130", "HeadlessChrome";v="130", "Not?A_Brand";v="99""
  ]
  "cache-control" => array:1 [▶
    0 => "no-cache"
  ]
  "pragma" => array:1 [▶
    0 => "no-cache"
  ]
  "accept-encoding" => array:1 [▶
    0 => "gzip, br"
  ]
  "cf-ray" => array:1 [▶
    0 => "953f76f05f46f501-ORD"
  ]
  "priority" => array:1 [▶
    0 => "u=0, i"
  ]
  "sec-fetch-dest" => array:1 [▶
    0 => "document"
  ]
  "sec-fetch-user" => array:1 [▶
    0 => "?1"
  ]
  "cf-visitor" => array:1 [▶
    0 => "{"scheme":"https"}"
  ]
  "connection" => array:1 [▶
    0 => "close"
  ]
  "x-forwarded-proto" => array:1 [▶
    0 => "https"
  ]
  "x-forwarded-for" => array:1 [▶
    0 => "216.73.216.130, 172.69.17.133"
  ]
  "x-server-addr" => array:1 [▶
    0 => "154.12.239.204"
  ]
  "host" => array:1 [▶
    0 => "receivinghelpdesk.com"
  ]
]
          request_server
            0 of 0   
          array:56 [▼
  "USER" => "runcloud"
  "HOME" => "/home/runcloud"
  "SCRIPT_NAME" => "/ask/index.php"
  "REQUEST_URI" => "/ask/cos-2x-integration"
  "QUERY_STRING" => ""
  "REQUEST_METHOD" => "GET"
  "SERVER_PROTOCOL" => "HTTP/1.0"
  "GATEWAY_INTERFACE" => "CGI/1.1"
  "REDIRECT_URL" => "/ask/cos-2x-integration"
  "REMOTE_PORT" => "52302"
  "SCRIPT_FILENAME" => "/home/runcloud/webapps/ReceivingHelpDesk/ask/index.php"
  "SERVER_ADMIN" => "you@example.com"
  "CONTEXT_DOCUMENT_ROOT" => "/home/runcloud/webapps/ReceivingHelpDesk/"
  "CONTEXT_PREFIX" => ""
  "REQUEST_SCHEME" => "http"
  "DOCUMENT_ROOT" => "/home/runcloud/webapps/ReceivingHelpDesk/"
  "REMOTE_ADDR" => "172.69.17.133"
  "SERVER_PORT" => "80"
  "SERVER_ADDR" => "127.0.0.1"
  "SERVER_NAME" => "receivinghelpdesk.com"
  "SERVER_SOFTWARE" => "Apache/2.4.63 (Unix) OpenSSL/1.1.1f"
  "SERVER_SIGNATURE" => ""
  "LD_LIBRARY_PATH" => "/RunCloud/Packages/apache2-rc/lib"
  "PATH" => "/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin"
  "HTTP_COOKIE" => "_pk_id.64.7c30=e60b1be82f1030ae.1750634289.; _pk_ses.64.7c30=1; XSRF-TOKEN=eyJpdiI6InZmZFp2Wkphd2kxWndIRGVJWW5XS1E9PSIsInZhbHVlIjoiQ0lvTzdOVFp0UHMrZlo4NXd3Rkx6WEd1Nko1QTIyY1MrVDF4dlQ2bUF0UU9xc1RZbHNQV3dOenZrMFcyUXVtcnB2bFYvQUNPYXYrVmJJaGVrNXBjRjdmYUxzSk5jM0ZDS1R1bUg4M1RkWUdOTFhPa3NWL01YZTJuU29Md0taclEiLCJtYWMiOiJkY2Q4YzFkYmI3MGNlNzZjNjZlMGFhZTkyM2IxZTc5MzJmN2Q2Y2IzMzA3NDlmZmE0Y2FlNTcwZDBmYWFjZDE2IiwidGFnIjoiIn0%3D; askhelpdesk_session=eyJpdiI6Ikx3cFE5WVdENjVONzd2cWoxOE9Tc1E9PSIsInZhbHVlIjoiR3A3cXpnSUg1aEJCTGc2cHA0MkRtbCtSYlQyMnhuV1p5RlorMXhxNjE0NU5tS1l6bGxrOGdUVFlzRDFCSXFxcXArcjhSQ2wwWS8yeUlsWnN4amFMOHBnUy93Wkc3S3hQWlZ0N2UyZ1ZoQUU2Q2NqdURIWGNDc3RiUzVsbkpjbHUiLCJtYWMiOiIxMGI3NTI3N2M4ZDBhOGZmYmMzMzRmMWRjNzE2MzZmMGFhZTczNTJhM2FlYTdiNjliYTAwY2UyNGY5ZmRlZTcwIiwidGFnIjoiIn0%3D ◀_pk_id.64.7c30=e60b1be82f1030ae.1750634289.; _pk_ses.64.7c30=1; XSRF-TOKEN=eyJpdiI6InZmZFp2Wkphd2kxWndIRGVJWW5XS1E9PSIsInZhbHVlIjoiQ0lvTzdOVFp0UHMrZlo4NXd3Rkx6W ▶"
  "HTTP_CF_IPCOUNTRY" => "US"
  "HTTP_CF_CONNECTING_IP" => "216.73.216.130"
  "HTTP_CDN_LOOP" => "cloudflare; loops=1"
  "HTTP_SEC_FETCH_MODE" => "navigate"
  "HTTP_SEC_FETCH_SITE" => "none"
  "HTTP_ACCEPT" => "text/html,application/xhtml+xml,application/xml;q=0.9,image/avif,image/webp,image/apng,*/*;q=0.8,application/signed-exchange;v=b3;q=0.7"
  "HTTP_USER_AGENT" => "Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)"
  "HTTP_UPGRADE_INSECURE_REQUESTS" => "1"
  "HTTP_SEC_CH_UA_PLATFORM" => ""Windows""
  "HTTP_SEC_CH_UA_MOBILE" => "?0"
  "HTTP_SEC_CH_UA" => ""Chromium";v="130", "HeadlessChrome";v="130", "Not?A_Brand";v="99""
  "HTTP_CACHE_CONTROL" => "no-cache"
  "HTTP_PRAGMA" => "no-cache"
  "HTTP_ACCEPT_ENCODING" => "gzip, br"
  "HTTP_CF_RAY" => "953f76f05f46f501-ORD"
  "HTTP_PRIORITY" => "u=0, i"
  "HTTP_SEC_FETCH_DEST" => "document"
  "HTTP_SEC_FETCH_USER" => "?1"
  "HTTP_CF_VISITOR" => "{"scheme":"https"}"
  "HTTP_CONNECTION" => "close"
  "HTTP_X_FORWARDED_PROTO" => "https"
  "HTTP_X_FORWARDED_FOR" => "216.73.216.130, 172.69.17.133"
  "HTTP_X_SERVER_ADDR" => "154.12.239.204"
  "HTTP_HOST" => "receivinghelpdesk.com"
  "HTTPS" => "on"
  "REDIRECT_STATUS" => "200"
  "REDIRECT_HTTPS" => "on"
  "FCGI_ROLE" => "RESPONDER"
  "PHP_SELF" => "/ask/index.php"
  "REQUEST_TIME_FLOAT" => 1750634304.0705
  "REQUEST_TIME" => 1750634304
]
          request_cookies
            0 of 0   
          array:4 [▼
  "_pk_id_64_7c30" => null
  "_pk_ses_64_7c30" => null
  "XSRF-TOKEN" => "eOKGIXz1TL4cmRMTejkKL4F4r3cuNNvrE4AIq8cp"
  "askhelpdesk_session" => "ILbMcPRxv56jAg42d3YFSUe0fPb7CFAJQdEeVJQt"
]
          response_headers
            0 of 0   
          array:7 [▼
  "content-type" => array:1 [▶
    0 => "text/html; charset=UTF-8"
  ]
  "cache-control" => array:1 [▶
    0 => "private, must-revalidate"
  ]
  "date" => array:1 [▶
    0 => "Sun, 22 Jun 2025 23:18:24 GMT"
  ]
  "pragma" => array:1 [▶
    0 => "no-cache"
  ]
  "expires" => array:1 [▶
    0 => -1
  ]
  "set-cookie" => array:2 [▶
    0 => "XSRF-TOKEN=eyJpdiI6IlI1TUhtZXU0aGJvNVB6WXM2dHlQRUE9PSIsInZhbHVlIjoiTHJnV1l2eTZiNHN1WjJSMXNsbVhGRDRMK0o1L0ZrOTB3Z3hTd01TTzM4WXhLZUlCa3Vmd2xNdFRHT3czNEpvbklsdE1FUm8xZXpPRUlNREdnM05RZGJsbSt1dHU2VFJzNzV2Q2Y2bVFBbHBHbGU5bHFTT09jbVZUNkpaYk8ycksiLCJtYWMiOiIzMDQyNGE3ODllNmI1NGNmYjdkYzU5Y2I3MmFhMmU1ZWU0ZTE2NWU2OWE3MjljYjhkNzMwYTNjMzE1MGMxODE1IiwidGFnIjoiIn0%3D; expires=Mon, 23-Jun-2025 01:18:27 GMT; Max-Age=7200; path=/; samesite=lax ◀XSRF-TOKEN=eyJpdiI6IlI1TUhtZXU0aGJvNVB6WXM2dHlQRUE9PSIsInZhbHVlIjoiTHJnV1l2eTZiNHN1WjJSMXNsbVhGRDRMK0o1L0ZrOTB3Z3hTd01TTzM4WXhLZUlCa3Vmd2xNdFRHT3czNEpvbklsdE1FU ▶"
    1 => "askhelpdesk_session=eyJpdiI6ImtCVUhLM0VJd3BTUzFDNCtFM3hVL1E9PSIsInZhbHVlIjoibGNjQTZ2dXhvMFNET1hMbFhNL3BsaEg5MEN3MFN1R3J3UWpBWWE1ZWdxMXd2RDQyOEd6NlFkc3FaZ3Q0Nm5QYmdycEpXbDVLRTlnNlowREQrcHUxMlRoL1FGMzlFcllYd3ROZmd4M1lhQ0RXbzc2a29XQ1dEYzJ1aXA5dXZiS1giLCJtYWMiOiIxYmRhNTNlNTBjNzIzMTg2NTdkZTYyOGQ4NTM0YTEzN2QyNzZmZTgyZDZhNTk3MDgxOWE0OGZjMDRmNTYyNDk5IiwidGFnIjoiIn0%3D; expires=Mon, 23-Jun-2025 01:18:27 GMT; Max-Age=7200; path=/; httponly; samesite=lax ◀askhelpdesk_session=eyJpdiI6ImtCVUhLM0VJd3BTUzFDNCtFM3hVL1E9PSIsInZhbHVlIjoibGNjQTZ2dXhvMFNET1hMbFhNL3BsaEg5MEN3MFN1R3J3UWpBWWE1ZWdxMXd2RDQyOEd6NlFkc3FaZ3Q0Nm5Q ▶"
  ]
  "Set-Cookie" => array:2 [▶
    0 => "XSRF-TOKEN=eyJpdiI6IlI1TUhtZXU0aGJvNVB6WXM2dHlQRUE9PSIsInZhbHVlIjoiTHJnV1l2eTZiNHN1WjJSMXNsbVhGRDRMK0o1L0ZrOTB3Z3hTd01TTzM4WXhLZUlCa3Vmd2xNdFRHT3czNEpvbklsdE1FUm8xZXpPRUlNREdnM05RZGJsbSt1dHU2VFJzNzV2Q2Y2bVFBbHBHbGU5bHFTT09jbVZUNkpaYk8ycksiLCJtYWMiOiIzMDQyNGE3ODllNmI1NGNmYjdkYzU5Y2I3MmFhMmU1ZWU0ZTE2NWU2OWE3MjljYjhkNzMwYTNjMzE1MGMxODE1IiwidGFnIjoiIn0%3D; expires=Mon, 23-Jun-2025 01:18:27 GMT; path=/ ◀XSRF-TOKEN=eyJpdiI6IlI1TUhtZXU0aGJvNVB6WXM2dHlQRUE9PSIsInZhbHVlIjoiTHJnV1l2eTZiNHN1WjJSMXNsbVhGRDRMK0o1L0ZrOTB3Z3hTd01TTzM4WXhLZUlCa3Vmd2xNdFRHT3czNEpvbklsdE1FU ▶"
    1 => "askhelpdesk_session=eyJpdiI6ImtCVUhLM0VJd3BTUzFDNCtFM3hVL1E9PSIsInZhbHVlIjoibGNjQTZ2dXhvMFNET1hMbFhNL3BsaEg5MEN3MFN1R3J3UWpBWWE1ZWdxMXd2RDQyOEd6NlFkc3FaZ3Q0Nm5QYmdycEpXbDVLRTlnNlowREQrcHUxMlRoL1FGMzlFcllYd3ROZmd4M1lhQ0RXbzc2a29XQ1dEYzJ1aXA5dXZiS1giLCJtYWMiOiIxYmRhNTNlNTBjNzIzMTg2NTdkZTYyOGQ4NTM0YTEzN2QyNzZmZTgyZDZhNTk3MDgxOWE0OGZjMDRmNTYyNDk5IiwidGFnIjoiIn0%3D; expires=Mon, 23-Jun-2025 01:18:27 GMT; path=/; httponly ◀askhelpdesk_session=eyJpdiI6ImtCVUhLM0VJd3BTUzFDNCtFM3hVL1E9PSIsInZhbHVlIjoibGNjQTZ2dXhvMFNET1hMbFhNL3BsaEg5MEN3MFN1R3J3UWpBWWE1ZWdxMXd2RDQyOEd6NlFkc3FaZ3Q0Nm5Q ▶"
  ]
]
          session_attributes
            0 of 0   
          array:4 [▼
  "_token" => "eOKGIXz1TL4cmRMTejkKL4F4r3cuNNvrE4AIq8cp"
  "_previous" => array:1 [▶
    "url" => "https://receivinghelpdesk.com/ask/cos-2x-integration"
  ]
  "_flash" => array:2 [▶
    "old" => []
    "new" => []
  ]
  "PHPDEBUGBAR_STACK_DATA" => []
]