Evaluate the integral:

Key points to solve the problem:

• Such problems require the use of method of substitution along with method of integration by parts. By method of integration by parts if we have

• To solve the integrals of the form: after applying substitution and integration by parts we have direct formulae as described below:

Let, I =

Let, log x = t

Differentiating both sides:

⇒

Substituting (log x) with t, we have:

We have:

I =

As I match with the form:

∴ I =

Putting the value of t back:

⇒ I =