Lösung 2.2:4d - Versionsgeschichte

Moni um 10:09, 22. Aug. 2009

2009-08-22T10:09:50Z

← Nächstältere Version		Version vom 10:09, 22. Aug. 2009
Zeile 1:		Zeile 1:
-	Der Integrand kann durch Polynomdivision vereinfacht werden. Wir addieren und subtrahieren 1 vom Zähler, und erhalten so	+	Der Integrand kann durch Polynomdivision vereinfacht werden. Wir addieren und subtrahieren 1 vom Zähler und erhalten so

	{{Abgesetzte Formel\|\|<math>\frac{x^2}{x^{2}+1} = \frac{x^2+1-1}{x^2+1} = \frac{x^2+1}{x^2+1} - \frac{1}{x^2+1} = 1-\frac{1}{x^2+1}\,\textrm{.}</math>}}		{{Abgesetzte Formel\|\|<math>\frac{x^2}{x^{2}+1} = \frac{x^2+1-1}{x^2+1} = \frac{x^2+1}{x^2+1} - \frac{1}{x^2+1} = 1-\frac{1}{x^2+1}\,\textrm{.}</math>}}

2009-05-05T13:50:59Z

← Nächstältere Version		Version vom 13:50, 5. Mai 2009
Zeile 1:		Zeile 1:
-	~~The integral can be simplified by a so-called polynomial division~~. ~~We add and take away~~ 1 ~~in the numerator and can thus eliminate the <math>x^2</math>-term from the numerator~~	+	Der Integrand kann durch Polynomdivision vereinfacht werden. Wir addieren und subtrahieren 1 vom Zähler, und erhalten so

	{{Abgesetzte Formel\|\|<math>\frac{x^2}{x^{2}+1} = \frac{x^2+1-1}{x^2+1} = \frac{x^2+1}{x^2+1} - \frac{1}{x^2+1} = 1-\frac{1}{x^2+1}\,\textrm{.}</math>}}		{{Abgesetzte Formel\|\|<math>\frac{x^2}{x^{2}+1} = \frac{x^2+1-1}{x^2+1} = \frac{x^2+1}{x^2+1} - \frac{1}{x^2+1} = 1-\frac{1}{x^2+1}\,\textrm{.}</math>}}

-	~~Thus, we have~~	+	Daher ist

	{{Abgesetzte Formel\|\|<math>\int\frac{x^2}{x^2+1}\,dx = \int\Bigl(1-\frac{1}{x^2+1} \Bigr)\,dx = x-\arctan x+C\,\textrm{.}</math>}}		{{Abgesetzte Formel\|\|<math>\int\frac{x^2}{x^2+1}\,dx = \int\Bigl(1-\frac{1}{x^2+1} \Bigr)\,dx = x-\arctan x+C\,\textrm{.}</math>}}

2009-03-11T10:25:35Z

← Nächstältere Version

Version vom 10:25, 11. Mär. 2009

2009-03-10T13:03:14Z

Robot: Automated text replacement (-{{Displayed math +{{Abgesetzte Formel)

← Nächstältere Version		Version vom 13:03, 10. Mär. 2009
Zeile 1:		Zeile 1:
	The integral can be simplified by a so-called polynomial division. We add and take away 1 in the numerator and can thus eliminate the <math>x^2</math>-term from the numerator		The integral can be simplified by a so-called polynomial division. We add and take away 1 in the numerator and can thus eliminate the <math>x^2</math>-term from the numerator

-	{{~~Displayed math~~\|\|<math>\frac{x^2}{x^{2}+1} = \frac{x^2+1-1}{x^2+1} = \frac{x^2+1}{x^2+1} - \frac{1}{x^2+1} = 1-\frac{1}{x^2+1}\,\textrm{.}</math>}}	+	{{Abgesetzte Formel\|\|<math>\frac{x^2}{x^{2}+1} = \frac{x^2+1-1}{x^2+1} = \frac{x^2+1}{x^2+1} - \frac{1}{x^2+1} = 1-\frac{1}{x^2+1}\,\textrm{.}</math>}}

	Thus, we have		Thus, we have

-	{{~~Displayed math~~\|\|<math>\int\frac{x^2}{x^2+1}\,dx = \int\Bigl(1-\frac{1}{x^2+1} \Bigr)\,dx = x-\arctan x+C\,\textrm{.}</math>}}	+	{{Abgesetzte Formel\|\|<math>\int\frac{x^2}{x^2+1}\,dx = \int\Bigl(1-\frac{1}{x^2+1} \Bigr)\,dx = x-\arctan x+C\,\textrm{.}</math>}}

2008-10-28T15:36:14Z

← Nächstältere Version		Version vom 15:36, 28. Okt. 2008
Zeile 1:		Zeile 1:
-	The integral can be simplified by a so-called polynomial division. We add and take away	+	The integral can be simplified by a so-called polynomial division. We add and take away 1 in the numerator and can thus eliminate the <math>x^2</math>-term from the numerator
-	~~<math>\text{~~1~~}</math>~~	+
-	in the numerator and can thus eliminate the	+
-	<math>x^{2}</math>	+
-	-term from the numerator	+
-		+
-		+
-	~~<math>\frac{x^{2}}{x^{2}+1}=\frac{x^{2}+1-1}{x^{2}+1}=\frac{x^{2}+1}{x^{2}+1}-\frac{1}{x^{2}+1}=1-\frac{1}{x^{2}+1}</math>~~	+

		+	{{Displayed math\|\|<math>\frac{x^2}{x^{2}+1} = \frac{x^2+1-1}{x^2+1} = \frac{x^2+1}{x^2+1} - \frac{1}{x^2+1} = 1-\frac{1}{x^2+1}\,\textrm{.}</math>}}

	Thus, we have		Thus, we have

-		+	{{Displayed math\|\|<math>\int\frac{x^2}{x^2+1}\,dx = \int\Bigl(1-\frac{1}{x^2+1} \Bigr)\,dx = x-\arctan x+C\,\textrm{.}</math>}}
-	<math>\int{\frac{x^{2}}{x^{2}+1}\,dx=\int{\~~left~~( 1-\frac{1}{x^{2}+1} \~~right~~)}}\,dx=x-\arctan x+C</math>	+

2008-10-21T12:57:27Z

← Nächstältere Version		Version vom 12:57, 21. Okt. 2008
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-	{{~~NAVCONTENT_START}~~}	+	The integral can be simplified by a so-called polynomial division. We add and take away
-	<~~center~~> ~~[[Image:2_2_4d.gif]]~~ </~~center~~>	+	<math>\text{1}</math>
-	{{~~NAVCONTENT_STOP~~}}	+	in the numerator and can thus eliminate the
		+	<math>x^{2}</math>
		+	-term from the numerator
		+
		+
		+	<math>\frac{x^{2}}{x^{2}+1}=\frac{x^{2}+1-1}{x^{2}+1}=\frac{x^{2}+1}{x^{2}+1}-\frac{1}{x^{2}+1}=1-\frac{1}{x^{2}+1}</math>
		+
		+
		+	Thus, we have
		+
		+
		+	<math>\int{\frac{x^{2}}{x^{2}+1}\,dx=\int{\left( 1-\frac{1}{x^{2}+1} \right)}}\,dx=x-\arctan x+C</math>

2008-09-16T14:46:01Z

← Nächstältere Version

Version vom 14:46, 16. Sep. 2008

2008-08-21T08:02:44Z

Robot: Automated text replacement (-[[Bild: +[[Image:)

2008-04-07T09:27:48Z

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