积分 dx/[e^x+e^(2-x)]

来源：学生作业帮编辑：百度作业网作业帮分类：数学作业时间：2024/04/27 17:55:01

积分 dx/[e^x+e^(2-x)]
请看清楚题目作答

令t=e^x,则dt=e^x*dx=tdx
dx/[e^x+e^(2-x)]=dx/[t+(e^2/t)]=tdx/(t^2+e^2)
=dt/(t^2+e^2)
令t/e=u,t=eu,则dt=edu,
dt/(t^2+e^2)=edu/[e^2(1+u^2)]=du/e(1+u^2)
∫dx/[e^x+e^(2-x)]
=∫du/e(1+u^2)=(1/e)∫du/(1+u^2)
=arctan(u)/e+C1
=arctan(t/e)/e+C2
=arctan(e^x/e)/e+C3=arctan[e^(x-1)]/e+C

积分 dx/[e^x+e^(2-x)] 积分 ∫(e^x)/(x+2)dx 积分∫dx /(e^x+e^-x) 积分dx/[e^x+e^-x] dx/(1+e^x)^2的积分求∫e^(-x^2) dx积分求积分∫e^(X^2)dx 积分dx/1-e^x 求 (e^x)/(1+e^2x)dx的积分求积分 (1-e^2x)/(1-e^x)dx 积分 e^x sin x dx = ? 反常积分∫x e^(-x)dx