Differentialrechnung

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(weitere Integrale)
(weitere Integrale)
Line 129: Line 129:
|'''Funktion <math>f(x)</math>'''
|'''Funktion <math>f(x)</math>'''
|'''Integral <math>F(x)=\int f(x) d x</math>'''
|'''Integral <math>F(x)=\int f(x) d x</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>\frac 1{\cos^2 x}</math>
|<math>\frac 1{\cos^2 x}</math>
Line 177: Line 183:
|<math>\frac 1{sqrt{x^2 \pm a^2}}</math>
|<math>\frac 1{sqrt{x^2 \pm a^2}}</math>
|<math>ln \left|x+\sqrt{x^2 \pm a^2} \right|+C</math>
|<math>ln \left|x+\sqrt{x^2 \pm a^2} \right|+C</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>\sqrt{a^2-x^2}</math>
|<math>\sqrt{a^2-x^2}</math>
Line 190: Line 190:
|<math>\frac x 2 \sqrt{a^2+x^2} + \frac{a^2}2 \ln(x+\sqrt{a^2+x^2})+C</math>
|<math>\frac x 2 \sqrt{a^2+x^2} + \frac{a^2}2 \ln(x+\sqrt{a^2+x^2})+C</math>
|-
|-
-
|<math></math>
+
|<math>(a x + b)^n</math>
-
|<math></math>
+
|<math>\frac{(a x + b)^{n+1}}{a(n+1)},\ n\ne-1</math>
|-
|-
-
|<math></math>
+
|<math>\frac 1{ax+b}</math>
-
|<math></math>
+
|<math>\frac 1 a \ln|ax+b|</math>
|}
|}

Revision as of 10:56, 17 September 2008

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