Question

用分部积分法求定积分

高数
定积分
救救孩子

Answer 1

令 √(2x-1) = u, x = (1+u^2)/2, dx = udu
I = ∫<0, 1>e^u udu = ∫<0, 1>ude^u
= [ue^u]<0, 1> - ∫<0, 1>e^udu
= e - [e^u]<0, 1> = e-e+1 = 1