Differentialrechnung
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(Difference between revisions)
(→weitere Integrale) |
(→weitere Integrale) |
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|<math>-\coth x+C</math> | |<math>-\coth x+C</math> | ||
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| - | |<math>\frac 1{\sqrt{ | + | |<math>\frac 1{\sqrt{x^2+1}}</math> |
|<math>\operatorname{arsinh} x+C = \ln\, \left|x+\sqrt{x^2+1}\right|+C</math> | |<math>\operatorname{arsinh} x+C = \ln\, \left|x+\sqrt{x^2+1}\right|+C</math> | ||
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| Line 116: | Line 116: | ||
|<math>\operatorname{arcosh} x+C = \ln\, \left|x+\sqrt{x^2-1}\right|+C</math> | |<math>\operatorname{arcosh} x+C = \ln\, \left|x+\sqrt{x^2-1}\right|+C</math> | ||
|- | |- | ||
| - | |<math></math> | + | |<math>\frac 1{\sqrt{1-x^2}}</math> |
| - | |<math></math> | + | |<math>\operatorname{artanh} x+C = \frac 1 2 \ln\frac{1+x}{1-x}+C</math> |
| + | |- | ||
| + | |<math>\frac 1{\sqrt{1-x^2}}</math> | ||
| + | |<math>\operatorname{arcoth} x+C = \frac 1 2 \ln\frac{x+1}{x-1}+C</math> | ||
|- | |- | ||
|<math></math> | |<math></math> | ||
Revision as of 07:37, 17 September 2008
| Funktion | Ableitung | Integral |
weitere Integrale
| Funktion | Integral |
