_0^ x (1 , , + , ,x) , ,(1 , , + , , x^2 ) d x : - Vidyadip

MCQ

$\int\limits_0^\infty $ $\frac{x}{{(1\,\, + \,\,x)\,\,(1\,\, + \,\,{x^2})}}$ $d x$ :

A
$\frac{\pi }{4}$
B
$\frac{\pi }{2}$
C
is same as $\int\limits_0^\infty $ $\frac{x}{{(1\,\, + \,\,x)\,\,(1\,\, + \,\,{x^2})}}$
✓
both $(A)$ and $(C)$

✓

Answer

Correct option: D.

both $(A)$ and $(C)$

d
Put $x = 1/t$ and add the two integrals

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