Evaluate the following integrals:

Given


Integral is of form


Writing numerator as


px + q = λ(2ax + b) + μ


x = λ (-2x + 1) + μ


λ = -1/2 and μ = -1/2


Let x = -1/2(-2x + 1) – 1/2 and split,




Consider


Let




We know that




Consider



Let




We know that




Then,





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