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#### Petrus

##### Well-known member

- Feb 21, 2013

- 739

\(\displaystyle \int_0^1\int_0^1 \frac{xy}{\sqrt{x^2+y^2+1}} dxdy\)

I start with subsitate \(\displaystyle u=x <=> du=dx\) and \(\displaystyle du= \frac{y}{\sqrt{x^2+y^2+1}} <=>u=y\ln\sqrt{x^2+y^2+1}\) so we got integrate by part that

\(\displaystyle xy\ln\sqrt{x^2+y^2+1}]_0^1-\int_0^1\frac{y}{\sqrt{x^2+y^2+1}}dx\)

and we got

\(\displaystyle [xy\ln\sqrt{x^2+y^2+1}]_0^1-[y\ln{\sqrt{x^2+y^2+1}}]_0^1\)

Remember that we solve dx. Is this correct?

Regards,