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Math Help - integrate sex^3xtanx

  1. #1
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    integrate sex^3xtanx

    hi, please help me with a question:

    integrate  sec^3x tanx

    i simplified the expression to this:  tanx sec^2x secx

    i don't know how to integrate the above expression though

    thank you in advance
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  2. #2
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by differentiate View Post
    hi, please help me with a question:

    integrate  sec^3x tanx

    i get something  tanx sec^2x secx

    i don't know how to proceed from here.

    thank you in advance
    \int(\sec^2{x}\sec{x}\tan{x})dx

    Now let u=\sec{x} so that du=\sec{x}\tan{x}dx

    And you have

    \int{u}^2du
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  3. #3
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    Quote Originally Posted by differentiate View Post
    hi, please help me with a question:

    integrate  sec^3x tanx

    i get something  tanx sec^2x secx

    i don't know how to proceed from here.

    thank you in advance
    Rewrite as

    \int{\sec^2{x}\sec{x}\tan{x}\,dx}.


    Let u = \sec{x} so that \frac{du}{dx} = \sec{x}\tan{x}.


    So the integral becomes

    \int{u^2\,\frac{du}{dx}\,dx}

     = \int{u^2\,du}

     = \frac{1}{3}u^3 + C

     = \frac{1}{3}\sec^3{x} + C.
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  4. #4
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    Quote Originally Posted by VonNemo19 View Post
    \int(\sec^3{x}\sec{x}\tan{x})dx

    Now let u=\sec{x} so that du=\sec{x}\tan{x}dx

    And you have

    \int{u}^3du
    Actually it's \int{u^2\,du} because you need to rewrite it as \int{\sec^2{x}\sec{x}\tan{x}\,dx}.
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  5. #5
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by Prove It View Post
    Actually it's \int{u^2\,du} because you need to rewrite it as \int{\sec^2{x}\sec{x}\tan{x}\,dx}.
    Arggghhhhhhhhhhhh!!!!!!!!


    I wrote that too, but then double checked.


    It's time to go to bed.
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  6. #6
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    Quote Originally Posted by VonNemo19 View Post
    Arggghhhhhhhhhhhh!!!!!!!!


    I wrote that too, but then double checked.


    It's time to go to bed.
    Goodnight mate
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