Differentialrechnung

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(weitere Integrale)
Line 154: Line 154:
|-
|-
|<math>\frac 1{a^2+x^2}</math>
|<math>\frac 1{a^2+x^2}</math>
-
|<math>\frac 1 a \arctan\frac x a+C</math>
+
|<math>\frac 1 a \cdot \arctan\frac x a+C</math>
|-
|-
|<math>\frac 1{a^2-x^2}</math>
|<math>\frac 1{a^2-x^2}</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>\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>\frac 1{x^2-a^2}</math>
|<math>\frac 1{x^2-a^2}</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>\begin{cases}-\frac 1 a \operatorname{arcoth}\frac x a + C,& |x|>a\\\frac 1{2a}\ln\frac {x-a}{x+a} + C\end{cases}</math>
|-
|-
|<math>\frac 1{sqrt{a^2-x^2}}</math>
|<math>\frac 1{sqrt{a^2-x^2}}</math>
Line 170: Line 170:
|<math>\frac 1{sqrt{x^2-a^2}}</math>
|<math>\frac 1{sqrt{x^2-a^2}}</math>
|<math>\begin{cases}\operatorname{arcosh}\frac x a + C,& |x|>a\\\ln \left(x+\sqrt{x^2-a^2} \right)+C\end{cases}</math>
|<math>\begin{cases}\operatorname{arcosh}\frac x a + C,& |x|>a\\\ln \left(x+\sqrt{x^2-a^2} \right)+C\end{cases}</math>
 +
|-
 +
|<math>\sin^2 x</math>
 +
|<math>\frac 1 2 (x-\sin x \cos x)</math>
 +
|-
 +
|<math>\cos^2 x</math>
 +
|<math>\frac 1 2 (x+\sin x \cos x)</math>
 +
|-
 +
|<math></math>
 +
|<math></math>
 +
|-
 +
|<math></math>
 +
|<math></math>
 +
|-
 +
|<math></math>
 +
|<math></math>
 +
|-
 +
|<math></math>
 +
|<math></math>
|}
|}

Revision as of 10:08, 17 September 2008

Funktion MathImage Ableitung MathImage Integral MathImage
MathImage MathImage MathImage
MathImage MathImage MathImage
MathImage MathImage MathImage
MathImage MathImage MathImage
MathImage MathImage MathImage
MathImage MathImage MathImage
MathImage MathImage MathImage
MathImage MathImage
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MathImage MathImage MathImage
MathImage MathImage MathImage
MathImage MathImage MathImage
MathImage MathImage
MathImage MathImage
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MathImage MathImage
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MathImage MathImage MathImage
MathImage MathImage MathImage
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MathImage MathImage
MathImage MathImage
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Integrationsregeln

MathImage

MathImage

MathImage

MathImage

MathImage

MathImage

MathImage

MathImage unbestimmtes Integral

Integration durch Substitution:

MathImage oder

MathImage

partielle Integration:

MathImage oder MathImage oder

MathImage

weitere Integrale

Funktion MathImage Integral MathImage
MathImage MathImage
MathImage MathImage
MathImage MathImage
MathImage MathImage
MathImage MathImage
MathImage MathImage
MathImage MathImage
MathImage MathImage
MathImage MathImage
MathImage MathImage
MathImage MathImage
MathImage MathImage
MathImage MathImage
MathImage MathImage
MathImage MathImage
MathImage MathImage
MathImage MathImage
MathImage MathImage
MathImage MathImage
MathImage MathImage
MathImage MathImage

Integralfunktionen

Integralsinus MathImage Eulersche Konstante MathImage
Integralcosinus MathImage
Exponentialintegral MathImage
Integrallogarithmus MathImage
Gaußsches Fehlerintegral MathImage
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