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Math Help - Integration

  1. #1
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    Integration

    Solve the Integral

    I = xsec2x2 dx
    tanx2

    PLEASE HELP THANKS!!
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  2. #2
    Senior Member x3bnm's Avatar
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    Re: Integration

    Did you mean:

    I = \frac{x \sec^2{(x^2)}}{\tan{(x^2)}} ?
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  3. #3
    Senior Member x3bnm's Avatar
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    Re: Integration

    If you meant to integrate:

    I = \frac{x \sec^2{(x^2)}}{\tan{(x^2)}}

    Then let u = \tan{(x^2)} \therefore\,\, du = 2 x \sec^2{(x^2)}\,\,dx

    Now:
    \begin{align*}\int \frac{x \sec^2{(x^2)}}{\tan{(x^2)}}\,\,dx =& \int \frac{2x \sec^2{(x^2)}}{2 \tan{(x^2)}}\,\,dx\\ =& \int \frac{1}{2u}\,\,du....\text{[by substituting values of } u \text{ and } du\text{]}\\ =& \frac{1}{2}\ln{(u)} + C\\=& \frac{1}{2}\ln{(\tan{(x^2)})} + C....\text{[by substituting } u\text{]}\end{align*}
    Thanks from jdesak
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