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,
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Consider ![]()
Let ![]()
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We know that ![]()
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Consider ![]()

Let ![]()

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We know that ![]()
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Then,
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