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Let \( \mathrm{n} \geq 2 \) be a natural number and \( 0<\theta<\pi / 2 \). Then\( \int \frac{\left(\sin ^{n} \theta-\sin \theta\right)^{\frac{1}{n}} \cos \theta}{\sin ^{n+1} \theta} d \theta \) is equal to:(where \( \mathrm{C} \) is a constant of integration)
[JEE Main - 2019 (January)]
(1) \( \frac{n}{n^{2}-1}\left(1-\frac{1}{\sin ^{n-1} \theta}\right)^{n+1}+C \)
(2) \( \frac{n}{n^{2}+1}\left(1-\frac{1}{\sin ^{n-1} \theta}\right)^{\frac{n+1}{n}}+C \)
(3) \( \frac{n}{n^{2}-1}\left(1+\frac{1}{\sin ^{n-1} \theta}\right)^{\frac{n+1}{n}}+C \)
(4) \( \frac{n}{n^{2}-1}\left(1-\frac{1}{\sin ^{n+1} \theta}\right)^{\frac{n+1}{n}}+C \)
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