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Thread: [SOLVED] Integration

  1. #1
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    [SOLVED] Integration

    $\displaystyle \int{\left(\frac{x}{x^2 + 1}\right)\,dx}$

    how to integrate?
    i know $\displaystyle \int{\left(\frac{1}{x^2 + 1}\right)\,dx}$
    is tan^-1 x + C

    how am i going to start answering this question
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  2. #2
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    Simple. Notice this with simple U-Substitution.

    $\displaystyle u+x^2+1$

    $\displaystyle du=2x dx$

    $\displaystyle \frac{1}{2}du=x dx$
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  3. #3
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by nameck View Post
    $\displaystyle \int{\left(\frac{x}{x^2 + 1}\right)\,dx}$

    how to integrate?
    i know $\displaystyle \int{\left(\frac{1}{x^2 + 1}\right)\,dx}$
    is tan^-1 x + C

    how am i going to start answering this question
    Let $\displaystyle u=x^2+1$, then $\displaystyle du=2x\Rightarrow\frac{1}{2}du=dx$.

    Now substituting

    $\displaystyle \int\frac{\frac{1}{2}}{u}du=\frac{1}{2}\int\frac{1 }{u}du=\frac{1}{2}\ln|u|+C$.

    Now back substitute.
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  4. #4
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    got it!! thanks guys!! =)
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