Is Partial Integration the Correct Method for Solving This Integral?

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SUMMARY

The discussion centers on the application of partial integration to solve the integral of the function x/sqrt[x^2+1] * x^2 dx. The user suggests that integrating this function using partial integration leads to a more complex integral involving x sqrt[x^2+1], which is proportional to (x^2+1)^(3/2). The conclusion drawn is that while partial integration can be applied, it complicates the solution rather than simplifying it.

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Homework Statement



My answer should not be correct. Right?:rolleyes:
Refer to the attachment please.

Homework Equations



Refer to the attachment please.

The Attempt at a Solution



Refer to the attachment please.

Cheers
 

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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).
 

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