Question

Integrate dx/x(1+x^m) with m Real and m differente from 0.
The exercise tells to add and subtract x^m on the numerator.
I'd love some help. Thank you =)

Answer 1

\[\frac{1}{x(1+x^m)}=\frac{1+x^m-x^m}{x(1+x^m)}=\frac{1}{x}-\frac{x^{m-1}}{1+x^m}\]
Now setting \(u=1+x^m\) gives \(du=mx^{m-1}\,dx\) (for the second term).

Answer 2

Thank you very much! =)