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Math Help - Very tough integral problem.

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    Very tough integral problem.

    integrate: x^2dx/x^2+2x+1


    I have no idea how to do this one, please help!!
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    Quote Originally Posted by navynukejones View Post
    integrate: x^2dx/x^2+2x+1


    I have no idea how to do this one, please help!!
    \int \frac{x^2}{x^2+2x+1}dx=\int \frac{x^2}{(x+1)^2}dx

    let u=x+1 and du=dx x=u-1

    so we get

    \int \frac{x^2}{(x+1)^2}dx=\int \frac{(u-1)^2}{u^2}du=

    \int \frac{u^2-2u+1}{u^2}du=\int \left( 1-\frac{2}{u}+\frac{1}{u^2}\right)du

    =u-2\ln|u|-\frac{1}{u}+c=(x+1)-2\ln|x+1|-\frac{1}{x+1}+c
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