积分下限为2,上限为根号2的定积分∫[(1)/(x√(x^(2)-1))]dx
问题描述：
积分下限为2,上限为根号2的定积分∫[(1)/(x√(x^(2)-1))]dx
答
令x=sec t就行了最后就剩下dt
答
设t=√（x^2-1),则dt=xdx/√（x^2-1),
原式=∫dt/(1+t^2)=arctant|=arctan3-π/4.
答
设x=1/cost t=arc cos(1/x)dx=(sint/cos²t)dtx*√(x²-1)=(1/cost)*sint/cost=sint/cos²t所以∫[(1)/(x√(x^(2)-1))]dx =∫(sint/cos²t)*/(sint/cos²t)*dt=∫dt=t=arc cos(1/x) I(2,√2)=ar...