Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

De onbepaalde integraal $https://latex.codecogs.com/png.image?\dpi{110}\int \frac{\sqrt x}{x^2}\: dx$ is gelijk aan	A. \(\large\boldsymbol{-\,\frac {2} {x\sqrt x} +C}\)
	B. \(\boldsymbol{2{\sqrt x} +C}\)
	C. \(\large\boldsymbol{\frac {2} {\sqrt x} +C}\)
	D. \(\large\boldsymbol{-\,\frac {2} {\sqrt x} +C}\)
	E. \(\large\boldsymbol{\text{geen van de vorige}}\)

[ 6-6465 - op net sinds 23.2.2020-()-4.11.2023 ]

Translation in E N G L I S H

IN CONSTRUCTION	A.
	B.
	C.
	D.
	E.

Oplossing - Solution

$\\\int\frac{\sqrt x}{x^2}\:dx=\int\frac{x^\frac12}{x^2}\:dx=\int x^{\frac12-2}\:dx=\int x^{-\frac32}\:dx\\=\frac{x^{-\frac32+1}}{-\frac32+1}+C=\frac{x^{-\frac12}}{-\frac12}+C=\frac{-2}{\sqrt2}+C$