Question

请教一条高数题目，不定积分，如图

请点击图片

Answer 1

两边同时积分最后化成F(X)的平方=多少,具体不求了,应该会作的

Answer 2

f(x)F(x)=xe^x/[2(1-x)^2]
F(0)=1
f(0)=0
F(x)=∫f(x)dx
∫f(x)F(x)dx=∫F(x)dF(x)=[F(x)]^2/2
∫xe^x/[2(1-x)^2]dx=(1/2)∫[1-(1-x)]e^xdx/(1-x)^2
=(1/2)∫e^xdx/(1-x)^2-(1/2)∫e^xdx/(1-x)
=(1/2)e^x/(x-1)+(1/2)∫e^xdx/(1-x)^2 -(1/2)∫e^xdx/(1-x)^2
=(1/2)e^x/(x-1)
e^x/(1-x)=F(x)^2
F(x)=e^(x/2)/√(x-1)
f(x)=F'(x)=(1/2)e^(x/2)/√(x-1) - (1/2)e^(x/2)/√(x-1)^3