Evaluate $\int\frac {\csc^2{x}-2005}{\cos^{2005}{x}} dx $
HINT:
Integrate by parts $$\int(\sec^{2005}x\cdot\csc^2x)dx$$
$$=\sec^{2005}x\int\csc^2x\ dx-\int\left(\frac{d(\sec^{2005}x)}{dx}\int\csc^2x\ dx\right)dx$$
$$\int \frac{\csc^2 x-2005}{\cos^{2005}x}dx = \int \frac{\cos^{2005}x\csc^2 x-2005\cos^{2005}x}{(\cos^{2005}x)^2}dx$$
$$\int \frac{d}{dx}\bigg(\frac{-\cot x}{\cos^{2005}x}\bigg)dx = -\frac{\cot x}{\cos^{2005}x}+C$$