Table of Integrals - Forms Involving `csc ax`

The integrals below involve `csc ax`.

1) `int  csc ax  dx = 1/a ln(csc ax-cot ax)=1/a ln tan ((ax)/2)`

2) `int  csc^2 ax  dx = -(cot ax)/a`

3) `int  csc^3 ax  dx = -(csc ax*cot ax)/(2a)+1/(2a)ln tan((ax)/2)`

4) `int  csc^n ax*cot ax  dx = -(csc^n ax)/(na)`

5) `int  1/(csc ax)  dx = -(cos ax)/a`

6) `int  x*csc ax  dx = 1/a^2{ax+(ax)^3/18+(7(ax)^5)/1800+...+(2(2^(2n-1)-1)B_n(ax)^(2n+1))/((2n+1)!)+...}`

7) `int  (csc ax)/x  dx = -1/(ax)+(ax)/6+(7(ax)^3)/1080+...+(2(2^(2n-1)-1)B_n(ax)^(2n-1))/((2n-1)(2n)!)+...`

8) `int  x*csc^2 ax  dx = -(x cot ax)/a+1/a^2 ln sin ax`

9) `int  1/(q+p csc ax)  dx = x/q-p/qint  1/(p+q sin ax)  dx`

                    **[See integral #22 in the table involving `sin ax`]

10) `int  csc^n ax  dx = -(csc^(n-2)ax*cot ax)/(a(n-1))+(n-2)/(n-1) int  csc^(n-2) ax  dx`