Evaluate the following integrals:
Given
Rationalizing the denominator,
Integral is of form
Writing numerator as
⇒ px + q = λ(2ax + b) + μ
⇒ -x + 1 = λ (-2x) + μ
∴ λ = 1/2 and μ = 1
Let -x + 1 = 1/2(-2x) + 1 and split,
Consider
Let
We know that
Consider
We know that
Then,