The integrals below involve `tan ax`
1) `int tan ax dx = -1/a ln cos ax=1/a ln sec ax`
2) `int tan^2 ax dx = (tan ax)/a-x`
3) `int tan^3 ax dx = (tan^2 ax)/(2a)+1/a ln cos ax`
4) `int tan^n ax*sec^2 ax dx = (tan^(n+1) ax)/((n+1)a)`
5) `int (sec^2 ax)/(tan ax) dx = 1/aln tan ax`
6) `int 1/(tan ax) dx = 1/a ln sin ax`
7) `int x tan ax dx = 1/a^2{(ax)^3/3+(ax)^5/15+(2(ax)^7)/105+...+(2^(2n)(2^(2n)-1)B_n(ax)^(2n+1))/((2n+1)!)+...}`
8) `int (tan ax)/x dx = ax+(ax)^3/9+(2(ax)^5)/75+...+(2^(2n)(2^(2n)-1)B_n(ax)^(2n-1))/((2n-1)(2n)!)+...`
9) `int x*tan^2 ax dx = (x tan ax)/a+1/a^2 ln cos ax-x^2/2`
10) `int 1/(p+q tan ax) dx = (px)/(p^2+q^2)+q/(a(p^2+q^2)) ln (q sin ax+p cos ax)`
11) `int tan^n ax dx = (tan^(n-1) ax)/((n-1)a)-int tan^(n-2) ax dx`