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, ex = t
Differentiating both sides:
⇒ ex dx = dt
Substituting ex with t, we have:
We have:
I =
As I match with the form:
∴ I =
⇒ I =
Putting the value of t back:
⇒ I =