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Question Number 34561 by math khazana by abdo last updated on 08/May/18

$$findthevalueof{\int }_0^{+\mathrm{\infty }}\frac{arctan\left(x\right)}{{(1+x^2)}^2}dx$$

Commented by math khazana by abdo last updated on 09/May/18

$${\int }_0^{\mathrm{\infty }}\frac{arctanx}{{(1+x^2)}^2}dx={[\frac{1}{4}{\left(arctanx\right)}^2+\frac{1}{4}sin\left(2arctanx\right)]}_0^{+\mathrm{\infty }}$$$$=\frac{1}{4}{\left(\frac{\pi }{2}\right)}^2+0=\frac{{\pi }^2}{16}.$$

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