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https://texercises.com/exercise/integrale-mit-arcus-und-areafunktionen-und-substitution/
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Exercise:
nprvmulticols prvmulticols abclist abc displaystyle fracx^ + ddx abc displaystyle frac-x^ - ddx abc displaystyle frac - x^ ddx abc displaystyle fracx^ - ddx abclist multicols

Solution:
abcliste %a abc Fx fracx^ + ddx substitutiony:sqrtx quad ddysqrtddx fracy^+ fracsqrtddy fracsqrt arctan y + c fracsqrt arctansqrtx + c %b abc Fx frac-x^ - ddx - fracx^ + ddx - frac fracfracx^ + ddx substitutiony:sqrtfracx quad ddysqrtfracddx -frac fracy^+ fracsqrtfracddy -frac sqrtfrac arctan y + c -fracsqrt arctansqrtfracx + c %c abc Fx frac - x^ ddx frac frac-fracx^ddx substitutiony:sqrtfracx quad ddysqrtfracddx frac frac-y^ fracsqrtfracddy frac sqrtfrac operatornameartanhy + c fracsqrt operatornameartanhsqrtfracx + c %d abc Fx fracx^ - ddx - frac-x^ ddx - frac frac-fracx^ddx substitutiony:sqrtfracx quad ddysqrtfracddx -frac frac-y^ fracsqrtfracddy -frac sqrtfrac operatornameartanhy + c -fracsqrt operatornameartanhleftsqrtfracxright + c abcliste
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Exercise:
nprvmulticols prvmulticols abclist abc displaystyle fracx^ + ddx abc displaystyle frac-x^ - ddx abc displaystyle frac - x^ ddx abc displaystyle fracx^ - ddx abclist multicols

Solution:
abcliste %a abc Fx fracx^ + ddx substitutiony:sqrtx quad ddysqrtddx fracy^+ fracsqrtddy fracsqrt arctan y + c fracsqrt arctansqrtx + c %b abc Fx frac-x^ - ddx - fracx^ + ddx - frac fracfracx^ + ddx substitutiony:sqrtfracx quad ddysqrtfracddx -frac fracy^+ fracsqrtfracddy -frac sqrtfrac arctan y + c -fracsqrt arctansqrtfracx + c %c abc Fx frac - x^ ddx frac frac-fracx^ddx substitutiony:sqrtfracx quad ddysqrtfracddx frac frac-y^ fracsqrtfracddy frac sqrtfrac operatornameartanhy + c fracsqrt operatornameartanhsqrtfracx + c %d abc Fx fracx^ - ddx - frac-x^ ddx - frac frac-fracx^ddx substitutiony:sqrtfracx quad ddysqrtfracddx -frac frac-y^ fracsqrtfracddy -frac sqrtfrac operatornameartanhy + c -fracsqrt operatornameartanhleftsqrtfracxright + c abcliste
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Attributes & Decorations
Tags
integral, integralrechnung, mathematik
Content image
Difficulty
(3, default)
Points
4 (default)
Language
GER (Deutsch)
Type
Calculative / Quantity
Creator uz
Decoration