Is Partial Integration the Correct Method for Solving This Integral?

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The discussion centers on the use of partial integration to solve a specific integral involving x/sqrt[x^2+1]. The user suggests that integrating this expression leads to a new integral, x sqrt[x^2+1], which is proportional to (x^2+1)^(3/2). There is uncertainty about the correctness of the initial answer, prompting a reevaluation of the integration method. The conversation emphasizes the complexity introduced by the partial integration approach. Ultimately, the effectiveness of partial integration in this context remains a key point of debate.
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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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