\( \int\left(\sin (101 x) \cdot \sin ^{99} x\right) d x \) is equal...

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\( \int\left(\sin (101 x) \cdot \sin ^{99} x\right) d x \) is equals:
\( \mathrm{P} \)
W
(1) \( \frac{\sin (100 x)(\sin x)^{100}}{100}+C \)
(2) \( \frac{\cos (100 x)(\sin x)^{100}}{100}+C \)
(3) \( \frac{\cos (100 x)(\cos x)^{100}}{100}+C \)
(4) \( \frac{\sin (100 x)(\sin x)^{101}}{101}+C \)
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