Evaluate the following integrals:

Given

Integral is of form

Writing numerator as

⇒ px + q = λ(2ax + b) + μ

⇒ 2x + 3 = λ (2x + 4) + μ

∴ λ = 1/2 and μ = -1

Let 2x + 3 = 2x + 4 – 1 and split,

Consider

Let

We know that

Consider

Let u = x + 2 → dx = du

We know that

Then,