A Level

MATHEMATICS · Multi-part · A Level · Mathematics · Integration · Integration

Problem

Evaluate (i) \int \left( \frac{1-x^{-2}}{x^{1/2}-x^{-1/2}} - \frac{2}{x^{3/2}} + \frac{x^{-2}-x}{x^{1/2}-x^{-1/2}} \right) dx (ii) \int \left( \frac{x^{-6}-64}{4+2x^{-1}+x^{-2}} \cdot \frac{x^2}{4-4x^{-1}+x^{-2}} - \frac{4x^2(2x+1)}{1-2x} \right) dx

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