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Question Number 104789 by 175mohamed last updated on 23/Jul/20
if y^((n))  is the derivative of the function y  of the order n, then  ∫y^((n)) dx =........
$${if}\:{y}^{\left({n}\right)} \:{is}\:{the}\:{derivative}\:{of}\:{the}\:{function}\:{y} \\ $$$${of}\:{the}\:{order}\:{n},\:{then} \\ $$$$\int{y}^{\left({n}\right)} {dx}\:=…….. \\ $$
Commented by mr W last updated on 23/Jul/20
y^((n)) =((d(y^((n−1)) ))/dx)  ⇒∫y^((n)) dx=y^((n−1)) +C
$${y}^{\left({n}\right)} =\frac{{d}\left({y}^{\left({n}−\mathrm{1}\right)} \right)}{{dx}} \\ $$$$\Rightarrow\int{y}^{\left({n}\right)} {dx}={y}^{\left({n}−\mathrm{1}\right)} +{C} \\ $$

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