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    I am trying to do:

    \int^\infty_0 x^2 e^{-x^2} dx

    So I am doing this by parts. I know that the integral of e^-x^2 is \sqrt{\frac{\pi}{2}} but if I let dv=e^{-x^2} can I integrate it to get v=-\frac{1}{2x}e^{-x^2} when using integration by parts?
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    Write the integrand as {x}*{xe^(-x^2)}: the second term can be elementarily integrated and so using integration by parts will leave you with something you know.
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    (Original post by Glutamic Acid)
    Write the integrand as {x}*{xe^(-x^2)}: the second term can be elementarily integrated and so using integration by parts will leave you with something you know.

    But would xe^-(x^2) not need integration by parts itself?
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    (Original post by Big_Sam)
    But would xe^-(x^2) not need integration by parts itself?
    No you just need substitution/recognition for this
    Use the substitution u=x^2
 
 
 
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