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Math Help - Integration by Parts (with Substitution)

  1. #1
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    Integration by Parts (with Substitution)

    I'm trying to do a problem that is integration by parts.

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

    I'm pretty sure I need to do a substitution, like make g={x}^{2} but I'm not sure.

    If that is the case, I'm not sure where to go next. What should be my u and what should be my dv?

    Thanks,

    MJ
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  2. #2
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    As you said, substitute t=x^2 to get:

    \frac{1}{2} \, \int \frac{t e^t}{(t+1)^2} \, dt

    Use integraton by parts with u=t e^t and dv=\frac{dt}{(t+1)^2}

    Can you do that ?
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  3. #3
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    I have no idea how you went through the steps to get that. How did you get rid of the x^3?

    Also, thank you for the reply...
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  4. #4
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    x^3 = x^2 \cdot x ..
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