定积分∫1(上标)-2(下标)1/(11+5x)^3dx的详细计算过程
问题描述:
定积分∫1(上标)-2(下标)1/(11+5x)^3dx的详细计算过程
答
∫[-2,1] 1/(11+5x)^3dx
=1/5∫[-2,1] (11+5x)^(-3)d(11+5x)
=1/5*(11+5x)^(-3+1)/(-3+1)[-2,1]
=-1/[10(11+5x)^2][-2,1]
=-[1/2560-1/10]
=51/5121/5*(11+5x)^(-3+1)/(-3+1)[-2,1]这一步如何求得公式:积分x^adx=x^(a+1)/(a+1)+C