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Exercise:
Berechne displaystyle ds_^ dfractexte^x+texte^x mboxdx mit der Substitution xt ln t.

Solution:
x ln t ddx fractddt Grenzen: damit x von nach läuft muss t von nach texte laufen. _^ dfractexte^x+texte^x ddx _^texte dfractexte^ln t+texte^ln t dfract ddt _^texte dfract+t dfract ddt _^texte dfrac+t ddt bigln|+t|big_^texte ln+texte - ln ln dfrac+texte
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Exercise:
Berechne displaystyle ds_^ dfractexte^x+texte^x mboxdx mit der Substitution xt ln t.

Solution:
x ln t ddx fractddt Grenzen: damit x von nach läuft muss t von nach texte laufen. _^ dfractexte^x+texte^x ddx _^texte dfractexte^ln t+texte^ln t dfract ddt _^texte dfract+t dfract ddt _^texte dfrac+t ddt bigln|+t|big_^texte ln+texte - ln ln dfrac+texte
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Attributes & Decorations
Tags
integralrechnung, mathematik, substitution
Difficulty
(3, default)
Points
4 (default)
Language
GER (Deutsch)
Type
Calculative / Quantity
Decoration
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