Differentialrechnung
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|Integralcosinus | |Integralcosinus | ||
| - | |<math>Ci(x) = \int_x^\infty\frac{\cos\,t}t dt = C+\ln|x|+\frac{x}{1\cdot 1!}+\frac{x^2}{2\cdot 2!}-\frac{x^3}{3\cdot 3!} + | + | |<math>Ci(x) = \int_x^\infty\frac{\cos\,t}t dt = C+\ln|x|+\frac{x}{1\cdot 1!}+\frac{x^2}{2\cdot 2!}-\frac{x^3}{3\cdot 3!} + \cdots,\ |x|<0</math> |
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| - | | | + | |Exponentialintegral |
| - | |<math>Ei(x) = \int_{-\infty}^x\frac{e^t}t dt = </math> | + | |<math>Ei(x) = \int_{-\infty}^x\frac{e^t}t dt = C+\ln|x|+frac x{1\cdot 1!}+\frac{x^2}{2\cdot 2!}-\frac{x^3}{3\cdot 3!} + \cdots,\ x<0</math> |
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|Integrallogarithmus | |Integrallogarithmus | ||
| - | |<math>Li(x) = \int_0^x\frac{dt}{\ln t}t = </math> | + | |<math>Li(x) = \int_0^x\frac{dt}{\ln\,t}t = \int_{-\infty}^x\frac{e^t}t dt = C+\ln\left|\ln x\right|+\frac{\ln x}{1\cdot 1!}+\frac{(\ln\,x)^2}{2\cdot 2!}-\frac{(\ln\,x)^3}{3\cdot 3!} + \cdots,\ 0<x<\infty</math> |
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|Gaußsches Fehlerintegral | |Gaußsches Fehlerintegral | ||
Revision as of 09:34, 17 September 2008
| Funktion | Ableitung | Integral |
Integrationsregeln
unbestimmtes Integral
Integration durch Substitution,
oder
partielle Integration
weitere Integrale
| Funktion | Integral |
Integralfunktionen
| Integralsinus | Eulersche Konstante | |
| Integralcosinus | ||
| Exponentialintegral | ||
| Integrallogarithmus | ||
| Gaußsches Fehlerintegral |
