Question

∫ln（1+x^2）*xdx

Answer 1

原式=1/2∫ln(1+x²)d(1+x²)

=1/2(1+x²)ln(1+x²)-1/2∫(1+x²)dln(1+x²)

=1/2(1+x²)ln(1+x²)-1/2∫(1+x²)*1/(1+x²)*2xdx

=1/2(1+x²)ln(1+x²)-1/2∫2xdx

=1/2(1+x²)ln(1+x²)-x²/2+C