计算 $\dps{\int_0^\infty\frac{\sin^2x}{x^2}dx=\frac{\pi}{2}}$

计算 $\dps{\int_0^\infty\frac{\sin^2x}{x^2}dx=\frac{\pi}{2}}$. 由分部积分, $$\bee\label{1}\bea \int_0^\infty\frac{\sin^2x}{x^2}dx &=-\int_0^\infty \sin^2xd\frac{1}{x}\\ &=-\left.\frac{\sin^2x}{x}\right|^\inf

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