Integrali comodi

$$\int_{-\infty}^{+\infty}{x^{2n}\exp{(-\lambda x^2)}dx}=\sqrt{\frac{\pi}{\lambda^{2n+1}}}\frac{(2n-1)!!}{2^n}$$

$$\int_{-\infty}^{+\infty}{x^{2n+1}\exp{(-\lambda x^2)}dx}=\frac{n!}{2^{\lambda{n+1}}}$$

$$\int_{0}^{+\infty}{x^{n}\exp{(-\lambda x)}dx}=\frac{n!}{\lambda^{n+1}}$$