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double integral with arctan

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Post Sun Jul 16, 2017 3:56 pm

Posts: 1
Hello,

i want to calculate the integral:

$$\displaystyle \int_{0}^{\infty} \frac{1}{x^2}\int_{0}^{x}\frac{\arctan\left(\frac{x}{\sqrt{t^2+2}}\right)}{(t^2+1)\sqrt{t^2+2}}\, dt \, dx $$

I think the value is $$\displaystyle \frac{\pi}{2}\ln(2)$$, but i can´t prove it.

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