Techniques of Integration - Integration by Substitution

Techniques of Integration - Integration by Substitution

Find \(\displaystyle \displaystyle\int{\frac{1}{{{x}^{2}}\sqrt{4-{{x}^{2}}}}}\,\mathrm{d}x\) using the substitution \(x=\frac{2}{u}\).

Solution:

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Answer:\(-\frac{\sqrt{4-x^2}}{4x}+C\), on \((-2,0)\) or \((0,2)\), with independent constants on the two intervals.

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