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 =