Question

Integrate: $\int \frac{1}{x(x^n+1)}dx$

Answer 1

According to question

$\int \frac{1}{x^{n+1}(1+x^{-n})}dx$

put, $(1+x^{-n})=t$

=> $\frac{-n}{x^{n+1}}dx=dt$

Now, $\frac{-1}{n}\int \frac{dt}{t}$

=> $\frac{-lnt}{n}+C$

=> $\frac{-ln(1+x^{-n})}{n}+C$