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Math Help - Trig Substitution

  1. #1
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    Trig Substitution

    Evaluate the integral


    so I did x=atanΘ. which is x=3tanΘ and dx is 3sec^2\Theta. Then it is

    \sqrt[]{9tan^2\Theta+9}* 3sec^2\Theta which evaluates after factoring to \sqrt[]{9sec^2\Theta}* 3sec^2\Theta which is then 3sec\Theta*3sec^2\Theta If i take the 9 out of the integral, that leaves sec^3\Theta. And i'm stuck
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  2. #2
    Ted
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    Quote Originally Posted by bfpri View Post
    Evaluate the integral


    so I did x=atanΘ. which is x=3tanΘ and dx is 3sec^2\Theta. Then it is

    \sqrt[]{9tan^2\Theta+9}* 3sec^2\Theta which evaluates after factoring to \sqrt[]{9sec^2\Theta}* 3sec^2\Theta which is then 3sec\Theta*3sec^2\Theta If i take the 9 out of the integral, that leaves sec^3\Theta. And i'm stuck
    1- dx=3sec^2(\theta){\color{red}d\theta}.
    2- \int sec^3(\theta) d\theta=\int sec(\theta) sec^2(\theta) d\theta , use integration by parts with: u=sec(\theta) and dv=sec^2(\theta)d\theta.
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  3. #3
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    Ah, Thanks.
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