[求助] 如下积分结果怎样化成第二类椭圆积分呢？

3楼: Originally posted by hank612 at 2014-11-09 11:36:42
作变量替换z=e^{-\gamma t}, 那么
\int_{0}^{T}\sqrt{\eta^2e^{-2\gamma t}+\frac{1}{e^{2\gamma t}-1}}dt=\frac{\sqrt{1+\eta^2}}{\gamma}\int_{e^{-\gamma T}}^1\frac{\sqrt{1-\frac{\eta^2}{1+\eta^2}z^2}}{\sq ...