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Math Help - integration by parts

  1. #1
    Junior Member
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    integration by parts

    I am trying to do this:
    integral sign xsec^2(3x)dx
    I am stuck on how to do it help plz. How do you do these types of problems?
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  2. #2
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    Hello, davecs77!

    \int x\sec^2(3x)\,dx

    By parts: . \begin{array}{ccccccc}u & = & x & \quad & dv & = & \sec^2(3x)\,dx \\ du & = & dx & \quad & v & = & \frac{1}{3}\tan(3x)\end{array}

    Then: . \frac{1}{3}x\tan(3x) - \frac{1}{3}\int\tan(3x)\,dx \;=\;\frac{1}{3}x\tan(3x) + \frac{1}{9}\ln\left|\cos(3x)\right| + C

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