Wiskunde Multiple Choice Vraag

$\int \sqrt{x\sqrt{x\sqrt{x\sqrt{...}}}}\;dx=$	A. $x+C$
	B. $\frac1{\sqrt x}+C$
	C. $\sqrt x+C$
	D. $\frac12x+C$
	E. $\frac12x^2+C$

[ 6-A259 - op net sinds 21.7.2026-(E)-22.7.2026 ]

Translation in E N G L I S H

See above

Oplossing - Solution

$\inline\\Stel\;\;y=\sqrt{x\sqrt{x\sqrt{x\sqrt{...}}}}\;\;dan\;\;is\\ y=\sqrt{x\cdot y}\;\Rightarrow\;y^2=xy\;\Rightarrow\;y=x\\ \int x\:dx=\frac{x^2}{2}+C$

GWB

$\int \sqrt{x\sqrt{x\sqrt{x\sqrt{...}}}}\;dx=$	A. \(x+C\)
	B. \(\frac1{\sqrt x}+C\)
	C. \(\sqrt x+C\)
	D. \(\frac12x+C\)
	E. \(\frac12x^2+C\)