Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

$https://latex.codecogs.com/png.image?\dpi{110}\int \!\frac{1}{3x^2+1}\; dx\, =$	A. \(\boldsymbol{\frac {\sqrt 3} {3} \text{Bgtan } (x\sqrt 3)+C }\)
	B. \(\boldsymbol{\frac {1} {3} \text{Bgtan } (x)+C }\)
	C. \(\boldsymbol{\sqrt 3 \:\text{Bgtan } (x\sqrt 3)+C }\)
	D. \(\boldsymbol{\frac {1} {3} \text{Bgtan } (3x)+C }\)
	E. \(\boldsymbol{\frac {1} {3} \text{Bgtan } (3x^2+1)+C }\)

[ 6-4233 - op net sinds 9.9.2019-(E)- ]

Translation in E N G L I S H

See above

Oplossing - Solution

$\int\frac{1}{3x^2+1}dx=\frac{1}{\sqrt{3}}\int\frac{1}{(\sqrt{3}x)^2+1}d(3\sqrt{x})=\frac{\sqrt{3}}3{\,Bgtan(\sqrt{3}\,x)}+C$