Is Partial Integration the Correct Method for Solving This Integral?

[ARYT]

Homework Statement

My answer should not be correct. Right?
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Homework Equations

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The Attempt at a Solution

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Cheers

 

[Count Iblis]

Why not do a partial integration?

x/sqrt[x^2+1] * x^2 dx

You can integrate x/sqrt[x^2+1] this is proportional to
sqrt[x^2+1]

So, if you do a partial integration, you'll have to deal with the integral:

x sqrt[x^2+1]

where the x comes from the derivative of x^2. But this is then proportional to (x^2+1)^(3/2).