求反常积分 ∫(1-->e)dx/x *根号下面是{1-(lnx)^2}
问题描述:
求反常积分 ∫(1-->e)dx/x *根号下面是{1-(lnx)^2}
答
用换元法:令u = lnx,x = e^u ==> dx = e^u du当x = 1,u = 0:当x = e,u = 1==> ∫(0~1) e^u/[e^u * √(1 - u²)] du= ∫(0~1) du/√(1 - u²)令u = sinz ==> du = cosz dz当u = 0,z = 0:当u = 1,z = π/2=...