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Math Help - u substitution

  1. #1
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    u substitution

    I would like to evaluate this integral using u substitution, I tried

    let u = sin x

    but that did not seem to do anything, should I be changing the sec^2x - 1 to something else?

    u substitution-capture.png

    Any help is appreciated!
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  2. #2
    MHF Contributor harish21's Avatar
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    Do you know that: sec^{2}x-tan^{2}x=1 ??
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  3. #3
    MHF Contributor chisigma's Avatar
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    Quote Originally Posted by DarK View Post
    I would like to evaluate this integral using u substitution, I tried

    let u = sin x

    but that did not seem to do anything, should I be changing the sec^2x - 1 to something else?

    Click image for larger version. 

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    Any help is appreciated!
    In integrals like this the following substitution works 'almost always'...

    \displaystyle t= \tan \frac{x}{2} \implies dx= 2\ \frac{dt}{1+t^{2}}, \sin x = \frac{2t}{1+t^{2}}, \cos x = \frac{1-t^{2}}{1+t^{2}}

    Kind regards

    \chi \sigma
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  4. #4
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    sec(x)= 1/cos(x) so sec^2(x)= 1/cos^2(x). I presume you know how to "change" cos(x) into sin(x).
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  5. #5
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    Let \displaystyle u = \sec(x). That substitution kills the integral on one-go.
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