Evaluate the following integrals:

Question

Philoid · Accepted Answer

Given

Integral is of form

Writing numerator as

⇒ px + q = λ(2ax + b) + μ

⇒ x + 2 = λ (2x + 2) + μ

∴ λ = 1/2 and μ = 1

Let x + 2 = 1/2(2x + 2) + 1 and split,

Consider

Let

We know that

Consider

Let

We know that

Then,