Formelsammlung Mathematik: Bestimmte Integrale: Form R(x,arccot)
2.1Bearbeiten
- {\displaystyle \int _{0}^{\infty }{\text{arccot}}(ax)\cdot {\text{arccot}}(bx)\ dx={\frac {\pi }{2}}\left[{\frac {1}{a}}\log \left({\frac {a+b}{b}}\right)-{\frac {1}{b}}\log \left({\frac {a+b}{a}}\right)\right]\qquad a,b>0}
![{\displaystyle \int _{0}^{\infty }{\text{arccot}}(ax)\cdot {\text{arccot}}(bx)\ dx={\frac {\pi }{2}}\left[{\frac {1}{a}}\log \left({\frac {a+b}{b}}\right)-{\frac {1}{b}}\log \left({\frac {a+b}{a}}\right)\right]\qquad a,b>0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2302222d8efbb74f027dcb5ff3395b905508b4de)
