Multiply numerator and denominator by x^{n – 1}, we get

Let xⁿ = t ⇒ nx^{n – 1}dx = dt

So the above equation becomes,

The denominator is factorized, so let separate the fraction through partial fraction, hence let

⇒ 1 = A(t + 1) + Bt……(ii)

Put t = 0 in above equations we get

1 = A(0 + 1) + B(0)

⇒ A = 1

Now put t = – 1 in equation (ii) we get

1 = A( – 1 + 1) + B( – 1)

⇒ B = – 1

We put the values of A and B values back into our partial fractions in equation (i) and replace this as the integrand. We get

Split up the integral,

Let substitute

u = t + 1 ⇒ du = dt, so the above equation becomes,

On integrating we get

Substituting back the values of u, we get

Substituting back the values of t, we get

Applying the logarithm rules, we get

Note: the absolute value signs account for the domain of the natural log function (x>0).

Hence,