Question

Integration 1/x(xⁿ + 1)

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

Answer 1

\(\int\frac{dx}{x(x^n+1)}\) 

Let t = xⁿ + 1 ⇒ dt = nx^n-1dx = \(\frac{nx^ndx}x\) = \(\frac{n(t-1)dx}x\)