∫cottan−1x4cosec2tan−1xdx1+x2tan−1x=

T=∫cottan−1x4cosec2tan−1xdx1+x2tan−1x Put tan−1⁡x=yT=∫coty4cosec2ydx Put cot⁡y=zcos⁡ec2ydy=−dzT=∫z4(−dz)=−z55+C=−15(cot⁡y)5+C=−15cot5⁡tanh−1x+C