Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

$https://latex.codecogs.com/png.image?\dpi{110}\int_{0}^{2}\frac{e^x-e^{-x}}{e^x+e^{-x}}\; dx=$	A. 1
	B. 2
	C. e
	D. ln 2
	E. ${\color{DarkBlue}\mathbf{ \ln \; \frac{e^2+e^{-2}}{2}}}$

${\color{DarkGreen} I=\int_{0}^{2}\frac{e^x-e^{-x}}{e^x+e^{-x}}\: dx} \newline {\color{DarkGreen} Stel \quad \; e^x+e^{-x}=y} \newline {\color{DarkGreen} dan\; is \;\; (e^x-e^{-x})\, dx=dy} \newline {\color{DarkGreen} en \quad x = 0 \leftrightarrow y=1\! +\! 1=2} \newline {\color{DarkGreen} {\color{Yellow} .}\qquad x = 2\leftrightarrow y=e^2+e^{-2}} \newline {\color{DarkGreen} I=\int_{2}^{e^2+e^{-2}}\frac{1}{y}\: dy=\left [ \ln y \right ]_{2}^{e^2+e^{-2}}} \newline {\color{DarkGreen} =\ln (e^2+e^{-2})-\ln 2} \newline {\color{DarkGreen} =\ln\frac{e^2+e^{-2}}{2}\approx 1,325}$