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Math Help - integration question

  1. #1
    Junior Member cinder's Avatar
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    integration question

    Evaluate the integral (in book, this is the "Integration by parts" section):

    \int x\cos(5x)dx

    Something like...

    x(\frac{1}{5})\sin5x - \int\frac{1}{5}\sin(5x)dx

    and then...? Or am I way off?

    Wait, I think I got it. Is the answer:

    \frac{1}{5}x\sin5x + \frac{1}{25}\cos5x + C

    ?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by cinder View Post
    Evaluate the integral (in book, this is the "Integration by parts" section):

    \int x\cos(5x)dx

    Something like...

    x(\frac{1}{5})\sin5x - \int\frac{1}{5}\sin(5x)dx

    and then...? Or am I way off?

    Wait, I think I got it. Is the answer:

    \frac{1}{5}x\sin5x + \frac{1}{25}\cos5x + C

    ?
    You can check your answer by differentiating it:

    \frac{d}{dx}\left[ \frac{1}{5}x\sin5x + \frac{1}{25}\cos5x + C \right]= \frac{1}{5}\sin5x +x\cos5x - \frac{1}{5}\sin5x =x\cos5x,

    which is the integrand, so yes you have the correct integral.

    RonL
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