100Integrals

∫cos⁡xsin⁡3x=∫cot⁡xcsc⁡2xdx=−∫cot⁡xd(cot⁡x)=−12cot⁡2x\int \frac{\cos x}{\sin^3x}=\int \cot x\csc^2xdx=-\int \cot xd(\cot x)=-\frac{1}{2}\cot^2x