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, x² = t

Differentiating both sides:

⇒ 2x dx = dt ⇒ x dx = 1/2 dt

Substituting x² with t, we have:

We have:

I =

As I match with the form:

∴ I =

⇒ I =

Putting the value of t back:

⇒ I =

⇒ I =