$\int\frac{dx}{x(x^n+1)}$ is equal to :
Answer & explanation
Correct answer: option 1
$I=\int\frac{dx}{x(x^n+1)}$
Put $x^n+1=t,nx^{n-1}dx=dt$
$I=\frac{1}{n}\int\frac{dt}{t(t-1)}=\frac{1}{n}\int(\frac{1}{t-1}-\frac{1}{t})dt=\frac{1}{n}\log(\frac{t-1}{t})+c=\frac{1}{n}\log(\frac{x^n}{x^n+1})+C$