∫etan−1x(1+x+x2).d(tan−1x)=

∫etan−1x.(1+x+x2).11+x2dx=∫etan−1x(1+x2+x1+x2)dx =∫etan−1x(1+x1+x2)dx=∫etan−1xdx+∫x.etan−1x1+x2dx=∫etan−1x+x∫etan−1x1+x2dx−∫1.∫etan−1x1+x2dxdx=∫etan−1xdx+x.etan−1x−∫etan−1x.dx =x.etan−1x+c