How do I integrate $f (x) = \frac{x^{3} e^{2 x}}{{(x^{2} + 1)}^{2}}$ $f(x)=(x^3e^(2x))/(x^2 +1)^2$ by parts?

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How do I integrate $f (x) = \frac{x^{3} e^{2 x}}{{(x^{2} + 1)}^{2}}$ $f(x)=(x^3e^(2x))/(x^2 +1)^2$ by parts?

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Answer 1 · 2015-03-28T00:52:25

Wolfram Alpha gives an answer of
$\frac{1}{2} [(1 + i) e^{2 i} E i (2 x - 2 i) + (1 - i) e^{- 2 i} E i (2 x + 2 i) + \frac{e^{2} x}{x^{2} + 1}] + C$ $1/2[(1+i)e^(2i)Ei(2x-2i)+(1-i)e^(-2i)Ei(2x+2i)+(e^2x)/(x^2+1)]+C$

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How do I integrate $f (x) = \frac{x^{3} e^{2 x}}{{(x^{2} + 1)}^{2}}$ $f(x)=(x^3e^(2x))/(x^2 +1)^2$ by parts?

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How do I integrate f(x)=(x^3e^(2x))/(x^2 +1)^2f(x)=x3e2x(x2+1)2f(x)=(x^3e^(2x))/(x^2 +1)^2 by parts?

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How do I integrate $f (x) = \frac{x^{3} e^{2 x}}{{(x^{2} + 1)}^{2}}$ $f(x)=(x^3e^(2x))/(x^2 +1)^2$ by parts?