∫tan−1(x31+x2)+tan−1(1+x2x3)dx
=∫tan−1⎡⎢⎣x31+x2+1+x2x31−(x31+x2)(1+x2x3)⎤⎥⎦dx
=∫tan−1⎛⎜ ⎜ ⎜ ⎜⎝x6+(1+x2)2(1+x2)(x3)0⎞⎟ ⎟ ⎟ ⎟⎠dx
=∫π2dx
=π2x+c