Find $\displaystyle\int{\frac{1}{{{x}^{2}}\sqrt{4-{{x}^{2}}}}}\mathrm{ d}x$ using the substitution $

Question

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

Accepted Answer

$-\displaystyle\frac{1}{4}\sqrt{\frac{4}{x^2}-1} + C$

Practice 4 Q21