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Home  >>  JEEMAIN and NEET  >>  Mathematics  >>  Class12  >>  Integral Calculus

Integrate : $\int \limits_0^{\infty} \large\frac{\log x}{1+x^2}$$dx$

\[\begin {array} {1 1} (a)\;0 \\ (b)\;-1 \\ (c)\;1 \\ (d)\;2 \end {array}\]

1 Answer

Put $ x= \cot \theta$
$dx= -cosec ^2 \theta.d\theta$
$x=0, \theta=\large\frac{\pi}{2}$
$x=\infty, \theta=0$
$\int \limits^0_\frac{\pi}{2} \large\frac{\log \cot \theta}{1+\cot^2 \theta} $$(- cosec^2 \theta)d \theta$
By using property
$\int \limits^0_\frac{\pi}{2} \log \cot \theta.d \theta$
$\qquad=0$
Hence a is the answer.
answered Dec 13, 2013 by meena.p
 
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