\[ \int_{0}^{2000 \pi} \frac{d x}{1+e^{\sin x}} \] (a) \( 1000 \pi \) (b) \( 200 \pi \) (c) \( 9...

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\[
\int_{0}^{2000 \pi} \frac{d x}{1+e^{\sin x}}
\]
(a) \( 1000 \pi \)
(b) \( 200 \pi \)
(c) \( 900 \pi \)
(d) \( 800 \pi \)
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