Evaluate the integral∫10tan−1x dx
∫10tan−1x.dx
∫tan−1x⋅dx=x.tan−1x−∫11+x2⋅x.dx
=xtan−1x−12∫2xdx1+x2
=xtan−1x−12[log(1+x2)]
=xtan−1x−log(1+x2)2
∫10tan−1x.dx=x.tan−1x−log(1+x2)2|10
=[1.tan−11−(2)2]−[0−log(1)]
=tan−11−12log2=π4−12log2
Find the real part of the complex number (1−i)(1+i)