Evaluate the following integrals:

Given


Integral is of form


Writing numerator as


px + q = λ(2ax + b) + μ


3x + 1 = λ (-2x – 2) + μ


λ = -3/2 and μ = -2


Let 3x + 1 = – (3/2)(–2x – 2) – 2




Consider


Let




We know that




Consider



Let




We know that



Then,





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