Differentialrechnung

(Difference between revisions)

Revision as of 08:44, 17 September 2008

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 |<math>\begin{cases}-\frac 1 a \operatorname{arcoth}\frac x a + C,& |x|>a\\\frac 1{2a}\ln\frac {x-a}{x+a} + C,& |x|<a\end{cases}</math>
 |-
-|<math></math>
+|<math>\frac 1{sqrt{a^2-x^2}}</math>
-|<math></math>
+|<math>arcsin{\frac x a} + C,\ |x|<a</math>
 |-
-|<math></math>
+|<math>\frac 1{sqrt{a^2+x^2}}</math>
-|<math></math>
+|<math>\begin{cases}\operatorname{arsinh}\frac x a + C\\\ln \left(x+\sqrt{a^2+x^2} \right)+C\end{cases}</math>
 |-
-|<math></math>
+|<math>\frac 1{sqrt{x^2-a^2}}</math>
-|<math></math>
+|<math>\begin{cases}\operatorname{arcosh}\frac x a + C\\\ln \left(x+\sqrt{x^2-a^2} \right)+C\end{cases}</math>
 |-
 |<math></math>