Question

∫x^2*ln(1+x^2)dx的积分怎么做

Answer 1

先分部积分把ln去掉

原式=1/3*x^3*ln(1+x^2)-∫1/3*x^3*(2x/(1+x^2))dx

=1/3*x^3*ln(1+x^2)-2/3*∫(x^2-x^2/(1+x^2))dx

=1/3*x^3*ln(1+x^2)-2/3*(1/3*x^3-x+arctanx)

=1/3*x^3*ln(1+x^2)-2/9*x^3+2/3*x-2/3*arctanx