User:NCC79601/sandbox

this is 1
something

this is 2
otherthings

$$\int _{0}^{\pi}\sqrt{ 1-e^{2}\sin ^{2}\alpha }\cdot \sin \alpha \, \text{d}\alpha=1+\frac{(1-e)(1+e)\cdot\ln \left( \frac{e+e^{2}}{e-e^{2}} \right) }{2\cdot e}=:f(e)$$