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Math Help - Integration by parts

  1. #1
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    Integration by parts

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

    I did this:
    u= \frac {1}{(x^2+1)^2} -> du= \frac {-4x}{(x^2+1)^3}
    dv= x^3e^{x^2} -> v= \frac {1}{2}(x^2-1)e^{x^2}

    Am I going in the right direction?? This is so frustrating...
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  2. #2
    o_O
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    Try:
    u = x^2e^{x^2} \ \Rightarrow \ du = \left(2xe^{x^2} + 2x^3e^{x^2}\right)dx = 2xe^{x^2} (1 + x^2)dx
    dv = \frac{x}{(1+x^2)^2} \ dx \ \Leftrightarrow \ v = -\frac{1}{2(x^2+1)}

    So: \int \frac{x^3e^{x^2}}{(x^2+1)^2} \ dx  = -\frac{x^2e^{x^2}}{2(x^2+1)} + \int xe^{x^2} dx
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