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, x³ = t

Differentiating both sides:

⇒ 3x² dx = dt

⇒ x² dx = 1/3 dt

Substituting x³ with t, we have:

∴ I =

As I match with the form:

∴ I =

Putting the value of t i.e. t = x³

⇒ I =