MCQ
$\int_0^\infty {\frac{{x\,dx}}{{(1 + x)(1 + {x^2})}}} = $
- ✓$\frac{\pi }{4}$
- B$\frac{\pi }{3}$
- C$\frac{\pi }{6}$
- Dએકપણ નહીં.
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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