Question

求∫ x^5e^(-x^2)

Answer 1

设t=-x²

则原式=-1/2∫t²e^tdt

=-1/2(t²e^t-2∫te^tdt)

=-1/2(t²e^t-2te^t+e^t)

=-1/2(t-1)²e^t+C

回代即可得-1/2(x²+1)²e^(-x²)+c