A) \[\frac{\pi }{4}\]
B) \[\frac{\pi }{3}\]
C) \[\frac{\pi }{6}\]
D) None of these
Correct Answer: A
Solution :
\[I=\int_{0}^{\infty }{\frac{xdx}{(1+x)(1+{{x}^{2}})}}\] Put \[x=\tan \theta \], we get \[I=\int_{0}^{\pi /2}{\frac{\tan \theta }{1+\tan \theta }d\theta =\int_{0}^{\pi /2}{\frac{\sin \theta }{\cos \theta +\sin \theta }d\theta =\frac{\pi }{4}}}\].
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