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Math Help - integration

  1. #1
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    integration

    would you possibly be able to show me step by step how to integrate this with respect to x:

    ((-x)^2)/(1+x^3)

    Thanks
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  2. #2
    Behold, the power of SARDINES!
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    Quote Originally Posted by daaavo View Post
    would you possibly be able to show me step by step how to integrate this with respect to x:

    ((-x)^2)/(1+x^3)

    Thanks
    \int \frac{(-x)^2}{1+x^3}dx=\int \frac{x^2}{1+x^3}dx

    let u=1+x^3 \mbox{ then } du=3x^2dx \iff \frac{1}{3}du=x^2dx

    so

    \int \frac{x^2}{1+x^3}dx=\frac{1}{3} \int \frac{1}{u}du =\frac{1}{3}\ln|u|+C =\frac{1}{3}\ln|1+x^3|+C
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  3. #3
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    Quote Originally Posted by daaavo View Post
    would you possibly be able to show me step by step how to integrate this with respect to x:

    ((-x)^2)/(1+x^3)

    Thanks

    \int \frac{(-x)^2}{1+x^3} \, dx

    \int \frac{x^2}{1+x^3} \, dx

    \frac13 \int \frac{3x^2}{1+x^3} \, dx

    Now make the substitution u = x^3 \Rightarrow 3x^2 \, dx = du

    \frac13 \int \frac{1}{1+u} \, du = \frac13\ln |u + 1| + C= \frac13\ln|1+x^3| +C
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