Differentialrechnung

From SkyWiki

(Difference between revisions)
Jump to: navigation, search
(Integralfunktionen)
(Integralfunktionen)
Line 168: Line 168:
|-
|-
|Integralcosinus
|Integralcosinus
-
|<math>Ci(x) = \int_x^\infty\frac{\cos\,t}t dt = C+\ln|x|+\frac{x}{1\cdot 1!}+\frac{x^2}{2\cdot 2!}-\frac{x^3}{3\cdot 3!} + \cdots,\ |x|<0</math>
+
|<math>Ci(x) = \int_x^\infty\frac{\cos\,t}t dt = C+\ln|x|+\frac{x}{1\cdot 1!}+\frac{x^2}{2\cdot 2!}+\frac{x^3}{3\cdot 3!} + \cdots,\ |x|<\infty</math>
|-
|-
|Exponentialintegral
|Exponentialintegral
-
|<math>Ei(x) = \int_{-\infty}^x\frac{e^t}t dt = C+\ln|x|+frac x{1\cdot 1!}+\frac{x^2}{2\cdot 2!}-\frac{x^3}{3\cdot 3!} + \cdots,\ x<0</math>
+
|<math>Ei(x) = \int_{-\infty}^x\frac{e^t}t dt = C+\ln|x|+\frac x{1\cdot 1!}+\frac{x^2}{2\cdot 2!}+\frac{x^3}{3\cdot 3!} + \cdots,\ x<0</math>
|-
|-
|Integrallogarithmus
|Integrallogarithmus
Line 177: Line 177:
|-
|-
|Gaußsches Fehlerintegral
|Gaußsches Fehlerintegral
-
|<math>F(x) = \frac 1{\sqrt{2\pi}}\int_{-\infty}^xe^{-\frac{t^2} 2} dt = </math>
+
|<math>F(x) = \frac 1{\sqrt{2\pi}} \int_{-\infty}^xe^{-\frac{t^2} 2} dt = \frac 1 2 + \frac 1{\sqrt{2\pi}} \left(\frac x 1-\frac{x^3}{2\cdot3\cdot1!}+\frac{x^5}{2^2\cdot5\cdot2!}-\frac{x^7}{2^3\cdot7\cdot3!}+-\cdots\right),\ |x|<\infty</math>
|}
|}
[[category:Mathematik]]
[[category:Mathematik]]

Revision as of 09:41, 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 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

Integrationsregeln

MathImage

MathImage

MathImage

MathImage

MathImage

MathImage

MathImage

MathImage unbestimmtes Integral

MathImage Integration durch Substitution, MathImage

MathImage oder MathImagepartielle Integration

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

Integralfunktionen

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