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The value of the Dirichlet integral $\int_{0}^{\infty} \frac{\sin x}{x} dx$ is $\frac{\pi}{2}$. The video also states that the squared form $\int_{0}^{\infty} \left(\frac{\sin x}{x}\right)^2 dx$ yields the same result, $\frac{\pi}{2}$.

Conditions: The integral is an improper Riemann integral (or Lebesgue integral).; The lower limit is 0 and the upper limit is $\infty$.; The integrand is $\frac{\sin x}{x}$.

The value of the Dirichlet integral $\int_{0}^{\infty} \frac{\sin x}{x} dx$ is $\frac{\pi}{2}$. The video also states that the squared form $\int_{0}^{\infty} \left(\frac{\sin x}{x}\right)^2 dx$ yields the same result, $\frac{\pi}{2}$.

Conditions: The integral is an improper Riemann integral (or Lebesgue integral).; The lower limit is 0 and the upper limit is $\infty$.; The integrand is $\frac{\sin x}{x}$.