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 =