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Thread: Integration by Parts Help

  1. #1
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    Integration by Parts Help

    Hey everybody,

    My class is learning integration by substitution and integration by parts right now, and I'm having a lot of trouble with them.

    Right now, I need to find the antiderivative of [(x^2)/(x^2 + 1)]dx.

    I've tried letting u = x^2 and dv = [1/(x^2 + 1)]dx, but I don't know if that's correct, because now I'm stuck at a weird place where I have to find the antiderivative of [x arctan(x)]dx, and I don't think we're supposed to have to do that much at this level.

    Could anyone please help me out or point me in the right direction? Thank you!
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  2. #2
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     <br />
\int\frac{x^2}{x^2+1}~dx = \int 1-\frac{1}{x^2+1}~dx<br />
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  3. #3
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    Or, in order to use integation by parts, write the integral as
    \int x\left(\frac{x}{x^2+ 1}\right)dx
    and let u= x, dv= \frac{x}{x^2+1}dx.
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