\displaystyle \frac{1}{\sqrt{2\pi}}\int_{-\infty}^{+\infty} (t\sigma+\mu)^3e^{\frac{-t^2}{2}}dt=\frac{1}{\sqrt{2\pi}}\int_{-\infty}^{+\infty}( (t\sigma)^3+3t\sigma\mu^2+3(t\sigma)^2\mu + \mu^3)e^{\frac{-t^2}{2}}dt=\frac{\sigma^3}{\sqrt{2\pi}}\int_{-\infty}^{+\infty}t^3e^{\frac{-t^2}{2}}dt +\frac{3\sigma\mu^2}{\sqrt{2\pi}}\int_{-\infty}^{+\infty}te^{\frac{-t^2}{2}}dt+\frac{3\sigma^2\mu}{\sqrt{2\pi}}\int_{-\infty}^{+\infty}t^2e^{\frac{-t^2}{2}}dt+\frac{\mu^3}{\sqrt{2\pi}}\int_{-\infty}^{+\infty} e^{\frac{-t^2}{2}}dt