What is the integral of (x^2)/(x^2+1)
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What is the integral of (x^2)/(x^2+1)

[From: ] [author: ] [Date: 12-04-10] [Hit: ]
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Please show me the steps. I know it with end up with a inverse trig function. I also believe that it can be done with integration by parts but if it is do-able with out integration by part please show me. Thank you in advance.

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x^2/(x^2 + 1) = 1 - 1/(x^2 + 1)
∫ x^2/(x^2 + 1) dx =
∫ 1 - 1/(x^2 + 1) dx =
x - arctanx + c

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∫(x²)/(x² + 1) dx

∫(x² + 1 - 1)/(x² + 1) dx

∫(1 - 1/(x² + 1)) dx = x - arctan(x) + C

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x = tan(u)
1
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