Question

对（e的负s乘以x次方）乘以x的n次方在0到正无穷上求定积分.急,明天考~

Answer 1

∫[0,+∞)x^n*e^(-sx)*dx

=1/s^(n+1)∫[0,+∞)t^[(n+1)-1]*e^(-t)dt(设t=sx)

=1/s^(n+1)*Γ(n+1)

=n!/s^(n+1)