JEE Main 20265 Apr, Morning shiftMathematicsEasyIntegral Calculus369× since 2002The value of the integral ∫0∞loge(x)x2+4 dx\displaystyle\int_0^\infty \frac{\log_e(x)}{x^2+4}\,dx∫0∞x2+4loge(x)dx is:AOption A. πloge(2)2\frac{\pi\log_e(2)}{2}2πloge(2)BOption B. πloge(2)4\frac{\pi\log_e(2)}{4}4πloge(2)COption C. 1+πloge(2)1+\pi\log_e(2)1+πloge(2)DOption D. 2+πloge(2)2+\pi\log_e(2)2+πloge(2)CheckSkip · show solution
