# Evaluate the following integrals:

Given

Integral is of form

Writing numerator as

px + q = λ(2ax + b) + μ

2x + 1 = λ (2x + 4) + μ

λ = 1 and μ = -3

Let 2x + 1 = 2x + 4 – 3 and split,

Consider

Let

We know that

Consider

Let u = x + 2 dx = du

We know that

Then,

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