Evaluate the integral:

Key points to solve the problem:

• Such problems require the use of the method of substitution along with a method of integration by parts. By the 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, sin x = t

Differentiating both sides:

⇒ cos x dx = dt

Substituting sin x with t, we have:

∴ I =

As I match with the form:

∴ I =

Putting the value of t i.e. t = sin x

⇒ I =