Differentialrechnung

(Difference between revisions)

Revision as of 10:08, 17 September 2008

$MathImage$

$MathImage$ unbestimmtes Integral

Integration durch Substitution:

$MathImage$ oder

$MathImage$

partielle Integration:

$MathImage$ oder $MathImage$ oder

$MathImage$

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

@@ Line 154: / Line 154: @@
 |-
 |<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>\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>\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>
@@ Line 170: / Line 170: @@
 |<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>\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>
 |}