Let n ≥ 2 be a natural number and 0<θ<π / 2. Then ∫ (( sin^n θ- sin θ)^(1/n) cos θ)/(sin^n +1 θ) d θ is equal to: (where C is a constant of…

Let $\displaystyle n \geqslant 2$ be a natural number and $\displaystyle 0<\theta<\pi / 2$.Then $\displaystyle \int \frac{\left(\sin ^{\mathrm{n}} \theta-\sin \theta\right)^{\frac{1}{\mathrm{n}}} \cos \theta}{\sin ^{\mathrm{n}+1} \theta} \mathrm{~d} \theta$ is equal to : (where $\displaystyle C$ is a constant of integration )