Find the value of the integral I=∫0∞xe−x2cos(x)dxI = \int_{0}^{\infty} x e^{-x^2} \cos(x) dxI=∫0∞xe−x2cos(x)dx.
12−π4e−1/4\frac{1}{2} - \frac{\sqrt{\pi}}{4} e^{-1/4}21−4πe−1/4
12−π4erf(1/2)\frac{1}{2} - \frac{\sqrt{\pi}}{4} \text{erf}(1/2)21−4πerf(1/2)
12(1−π2e−1/4)\frac{1}{2} (1 - \frac{\sqrt{\pi}}{2} e^{-1/4})21(1−2πe−1/4)
π4e−1/4\frac{\sqrt{\pi}}{4} e^{-1/4}4πe−1/4