Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

De onbepaalde integraal $\int \frac{20}{(5x+8)^3}\:\: dx$ is gelijk aan	A. $\boldsymbol{-\, \frac{2}{(5x\,+\,8)^2}+C}$
	B. $\boldsymbol{-\, \frac{8}{(5x\,+\,8)^2}+C}$
	C. $\scriptsize\boldsymbol{4.\ln\, \|(5x\,+\,8)^3\|+C }$
	D. $\boldsymbol{-\, \frac{4}{3(5x\,+\,8)^2}+C}$
	E. $\boldsymbol{-\, \frac{10}{(5x\,+\,8)^2}+C }$

[ 6-1921 - op net sinds 8.4.13-(E)-21.11.2024 ]

Translation in E N G L I S H

$\int \frac{20}{(5x+8)^3}\:\: dx=$	A. $\boldsymbol{-\, \frac{2}{(5x\,+\,8)^2}+C}$
	B. $\boldsymbol{-\, \frac{8}{(5x\,+\,8)^2}+C}$
	C. $\scriptsize\boldsymbol{4.\ln\, \|(5x\,+\,8)^3\|+C }$
	D. $\boldsymbol{-\, \frac{4}{3(5x\,+\,8)^2}+C}$
	E. $\boldsymbol{-\, \frac{10}{(5x\,+\,8)^2}+C }$

Oplossing - Solution

$https://latex.codecogs.com/png.image?\dpi{110}\\ \int \frac{20}{(5x+8)^3}\: dx= 20\int {(5x+8)^{-3}}\: dx=\frac 15.20 \int {(5x+8)^{-3}}\: d(5x+8)\\= 4.\frac{(5x+8)^{-3+1}}{-3+1}+C=\frac{4}{-2}(5x+8)^{-2}+C=-\frac{2}{(5x+8)^2}+C$

De onbepaalde integraal $\int \frac{20}{(5x+8)^3}\:\: dx$ is gelijk aan	A. \(\boldsymbol{-\, \frac{2}{(5x\,+\,8)^2}+C}\)
	B. \(\boldsymbol{-\, \frac{8}{(5x\,+\,8)^2}+C}\)
	C. \(\scriptsize\boldsymbol{4.\ln\, \|(5x\,+\,8)^3\|+C }\)
	D. \(\boldsymbol{-\, \frac{4}{3(5x\,+\,8)^2}+C}\)
	E. \(\boldsymbol{-\, \frac{10}{(5x\,+\,8)^2}+C }\)

$\int \frac{20}{(5x+8)^3}\:\: dx=$	A. \(\boldsymbol{-\, \frac{2}{(5x\,+\,8)^2}+C}\)
	B. \(\boldsymbol{-\, \frac{8}{(5x\,+\,8)^2}+C}\)
	C. \(\scriptsize\boldsymbol{4.\ln\, \|(5x\,+\,8)^3\|+C }\)
	D. \(\boldsymbol{-\, \frac{4}{3(5x\,+\,8)^2}+C}\)
	E. \(\boldsymbol{-\, \frac{10}{(5x\,+\,8)^2}+C }\)