find-the-value-of-0-arctan-x-1-x-2-2-dx-

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

f i n d t h e v a l u e o f \int_{0}^{+ \infty} \frac{a r c t a n (x)}{{(1 + x^{2})}^{2}} d x

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

\int_{0}^{\infty} \frac{a r c t a n x}{{(1 + x^{2})}^{2}} d x = {[\frac{1}{4} {(a r c t a n x)}^{2} + \frac{1}{4} s i n (2 a r c t a n x)]}_{0}^{+ \infty}

= \frac{1}{4} {(\frac{π}{2})}^{2} + 0 = \frac{π^{2}}{16} .