Evaluate the following integrals:

Given

Integral is of form

Writing numerator as

⇒ px + q = λ(2ax + b) + μ

⇒ x = λ (2x + 6) + μ

∴ λ = 1/2 and μ = -3

Let x = 1/2(2x + 6) – 3 and split,

Consider

Let

We know that

Consider

Let u = x + 3 → dx = du

We know that

Then,