Differentialrechnung

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(weitere Integrale)
(weitere Integrale)
Line 110: Line 110:
|<math>-\coth x+C</math>
|<math>-\coth x+C</math>
|-
|-
-
|<math>\frac 1{\sqrt{1+x^2}}</math>
+
|<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>
|-
|-
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

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weitere Integrale

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