$\int\limits_{-\pi / 4}^{\pi / 4} \frac{e^x(x \sin x)}{e^{2 x}-1} d x$ is equal to
Answer & explanation
Correct answer: option 1
$I=\int\limits_{-\pi / 4}^{\pi / 4} \frac{e^x(x \sin x)}{e^{2 x}-1} d x$
∵ property $\int\limits_{-a}^a f(x) d x=0$ (f (–x) = –f (x), odd function)
Hence I = 0
Hence (1) is the correct answer.