定积分∫(-ln2,0)√(1-e^(2x))dx

∫(-ln2->0)√(1-e^(2x))dxlete^x = sinye^x dx = cosy dydx = (cosy/siny) dyx=0 ,y= π/2x=-ln2,y =π/6∫(-ln2->0)√(1-e^(2x))dx=∫(π/6->π/2) [(cosy)^2/siny] dy=∫(π/6->π/2) [(1-(siny)^2)/siny] dy =∫(π/6->π/2) (cscy -siny) dy=[ln|cscy-coty| +cosy](π/6->π/2)= - ln(2-√3) - √3/2