Question

求x(arctanx)的不定积分

Answer 1

∫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