Question

求不定积分∫㏑(X²＋1﹚dx

Answer 1

∫ln(1+x^2)dx=xln(1+x^2)-2∫x^2/(1+x^2)dx=xln(1+x^2)-2x+2∫1/(1+x^2)dx=xln(1+x^2)-2x+2arctanx+c
用的分部积分公式

Answer 2

=xln(x²+1)-∫2x²/(x²+1)dx
=xln(x²+1)-2x+2∫1/(x²+1)dx
=xln(x²+1)-2x+2tanx