Indefinite Integrals with cot(x)

cotangent
$\int \cot a x d x = \frac {1}{a} \ln {\sin a x } +C$
$\int \cot ^2 a x d x = -\frac { \cot ax}{a} - x +C$
$\int \cot ^3 a x d x = - \frac {\cot^2 ax}{2a} - \frac{1}{a} \ln {\sin a x}+C$
$\int \frac {\cot^n ax }{\sin^2 a x}dx = -\frac {\cot^{n+1} a x}{(n+1)a} +C$
$\int \frac {dx}{\sin^2 a x \cot ax }= - \frac {1}{a} \ln {\cot a x} +C$
$\int \frac {dx}{ \cot ax } = -\frac {1}{a} \ln {\cos a x} +C$
$\int x \cot ax dx = \frac {1}{a^2} \left \{ ax - \frac{(a x)^3}{9} - \cdot \cdot \cdot - \frac {2^{2n}Bn(ax)^{2n+1}}{(2n+1)!} + \cdot \cdot \cdot \right \} +C$
$\int \frac {\cot ax } {x} dx = -\frac {1}{ax} - \frac{a x}{3} - \frac{(ax)^3}{135} - \cdot \cdot \cdot - \frac {2^{2n}Bn(ax)^{2n-1}}{(2n-1)(2n)!} - \cdot \cdot \cdot +C$
$\int x \cot^2 ax dx = - \frac {x \cot ax}{a} + \frac {1}{a^2} \ln {\sin a x} - \frac {x^2}{2} +C$
$\int \frac {dx}{p+q \cot ax} = \frac {px}{p^2+q^2} - \frac {q}{a(p^2+q^2)} \ln {\left( p\sin a x + q \cos ax \right)} +C$
$\int \cot^n ax dx = -\frac {\cot^{n-1}ax}{(n+1)a} -\int \cot^{n-2} a x dx$

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