求x+x^(n+1)分之dx的不定积分

Question

如题所述

Answer 1

∫dx/[x+x^(n+1)]
=∫dx/[x(1+x^n)]
=∫[(1+x^n)-x^n]dx/[x(1+x^n)]
=∫dx/x -∫x^(n-1)dx/(1+x^n)
=lnx-x^n/n!+C