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https://texercises.com/exercise/integral-quadratisches-erganzen/
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Exercise:
displaystyle fxfracx^-x+

Solution:
Fx tcbhighmathaufgabe fracx^-x+ ddx fracleftsqrtx -fracsqrt right^ + frac ddx fracfrac fracfracleftsqrtx -fracsqrt right^ + ddx frac fracleftsqrtfracsqrtx -sqrtfracfracsqrt right^ + ddx frac fracleftfracsqrtx -fracsqrt right^ + ddx frac fracleftfracsqrtx - right^ + ddx substitutiony:fracsqrtx- quad ddxfracsqrtddy frac fracy^ + fracsqrtddy fracsqrt tcbhighmathalready fracy^+ ddy fracsqrt arctan y + c tcbhighmathloesungfracsqrt arctanfracx-sqrt+c
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Exercise:
displaystyle fxfracx^-x+

Solution:
Fx tcbhighmathaufgabe fracx^-x+ ddx fracleftsqrtx -fracsqrt right^ + frac ddx fracfrac fracfracleftsqrtx -fracsqrt right^ + ddx frac fracleftsqrtfracsqrtx -sqrtfracfracsqrt right^ + ddx frac fracleftfracsqrtx -fracsqrt right^ + ddx frac fracleftfracsqrtx - right^ + ddx substitutiony:fracsqrtx- quad ddxfracsqrtddy frac fracy^ + fracsqrtddy fracsqrt tcbhighmathalready fracy^+ ddy fracsqrt arctan y + c tcbhighmathloesungfracsqrt arctanfracx-sqrt+c
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Topic
Tags
gebrochen, integralrechnung, mathematik, quadratisches ergänzen, rational
Difficulty
(3, default)
Points
3 (default)
Language
GER (Deutsch)
Type
Calculative / Quantity
Decoration
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