If $I=\int \left(\frac{{\left(\sin x\right)}^n-{\sin x}^{\frac{1}{n}}}{{\left(\sin x\right)}^{n+1}\cos x}\right)dx$ is eqaul to (a) $\left(\frac{n}{n^2-1}\right){\left(1-\frac{1}{{\sin x}^{n-1}}\right)}^{\frac{1}{n}+1}+c$ (b) $\left(\frac{n}{n^2+1}\right){\left(1-\frac{1}{{\sin x}^{n-1}}\right)}^{\frac{1}{n}+1}+c$ (c) $\left(\frac{n}{n^2+1}\right){\left(1-\frac{1}{{\sin x}^{n-1}}\right)}^{\frac{1}{n}}+c$ (d) $\left(\frac{n}{n^2-1}\right){\left(1-\frac{1}{\sin x}\right)}^{\frac{1}{n}+1}+c$

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