$\displaystyle \int {\csc^5{x}}dx$

Solutions:

$\displaystyle \int {\csc^3{x}}(1+\cot^2{x})dx$

$\displaystyle \int {\csc^3{x}}dx + \int {\cot^2{x}}{\csc^3{x}}dx$

solving for int of $\displaystyle \int {\csc^3{x}}dx$

$\displaystyle \frac{1}{2}(-\cot{x}\csc{x} + \ln |\csc{x} - \cot{x}|)$

this is where i got stuck for solving for $\displaystyle \int {\cot^2{x}}{\csc^3{x}}dx$ :

$\displaystyle \int {\cot^2{x}}{\csc^3{x}}dx$

$\displaystyle \int {\csc^5{x} - \csc^3{x} }dx$

which is repeating the csc^5{x}

help with hints

thanks