Question

求不定积分∫xln(1+x^2)dx

Answer 1

∫xln(1+x^2)dx

=1/2∫ln(1+x^2)dx^2

=1/2∫ln(1+x^2)d(1+x^2)

=1/2(1+x^2)ln(1+x^2)-1/2∫(1+x^2)dln(1+x^2)

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

=1/2(1+x^2)ln(1+x^2)-1/2∫dx^2

=1/2(1+x^2)ln(1+x^2)-1/2x^2+C