Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

$https://latex.codecogs.com/png.image?\dpi{110}\int \frac{\sin x}{\sin x - \cos x}\;dx=$	A. ln \| sin x − cos x \| + C
B. ln \| sin x − cos x \| + x + C
C. ln \| sin x − cos x \| + C
D. ln \| sin x − cos x \| + x + C
E. ( ln \| sin x − cos x \| + x ) + C

${\color{Yellow} .}\newline I=\int \frac{\sin x}{\sin x-\cos x}\; dx=\int \frac{-\sin x+\cos x+\sin x+\sin x-\cos x}{\sin x-\cos x}\; dx \newline =-\, I+\int \frac{\cos x+\sin x}{\sin x-\cos x}\; dx +\int \frac{\sin x-\cos x}{\sin x-\cos x}\; dx\newline \Rightarrow 2I=ln\left | \sin x-\cos x \right |+\int dx\newline \Rightarrow I=\frac{1}{2}(ln\left | \sin x-\cos x \right |+x)+C$

$https://latex.codecogs.com/png.image?\dpi{110}\int \frac{\sin x}{\sin x - \cos x}\;dx=$	A. ln \| sin x − cos x \| + C
	B. ln \| sin x − cos x \| + x + C
	C. ln \| sin x − cos x \| + C
	D. ln \| sin x − cos x \| + x + C
	E. ( ln \| sin x − cos x \| + x ) + C