Differentialrechnung

(Difference between revisions)

Revision as of 08:38, 17 September 2008

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 |<math>\begin{cases}\operatorname{artanh}x+C=\frac 1 2 \ln\frac{1+x}{1-x}+C,& |x|<1\\\operatorname{arcoth}x+C=\frac 1 2 \ln\frac{x+1}{x-1}+C,& |x|>1\end{cases}</math>
 |-
-|<math></math>
+|<math>\frac 1{a^2+x^2}</math>
-|<math></math>
+|<math>\frac 1 a \arctan\frac x a+C</math>
 |-
-|<math></math>
+|<math>\frac 1{a^2-x^2}</math>
-|<math></math>
+|<math>\begin{cases}\frac 1 a \operatorname{artanh}\frac x a + C,& |x|<a\\\frac 1{2a}\ln\frac {a-x}{a+x} + C,& |x|>a\end{cases}</math>
 |-
-|<math></math>
+|<math>\frac 1{x^2-a^2}</math>
-|<math></math>
+|<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>