∫x(arctanx)dx
=(1/2)∫ (arctanx)d(x^2)
= (1/2)x^2(arctanx) -(1/2)∫ x^2 (1/(1+x^2) dx
= (1/2)x^2(arctanx) - (1/2)∫ dx+ (1/2)∫ 1/(1+x^2) dx
= (1/2)x^2(arctanx) - (1/2)x + (1/2) arctanx + C