Evaluate the following integrals:

Given

Integral is of form

Writing numerator as

⇒ px + q = λ(2ax + b) + μ

⇒ 2x + 1 = λ (2x + 2) + μ

∴ λ = 1 and μ = -1

Let 2x + 1 = 2x + 2 – 1 and split,

Consider

Let

We know that

Consider

Let

We know that

Then,