Assuming that you mean:
#int (cos(x)-sin^2(x))/(sin(x)cos(x)) dx#
Separate into two integrals:
#int (cos(x)-sin^2(x))/(sin(x)cos(x)) dx = int cos(x)/(sin(x)cos(x)) dx -int sin^2(x)/(sin(x)cos(x)) dx#
Cancel common factors in both integrals:
#int (cos(x)-sin^2(x))/(sin(x)cos(x)) dx = int cancel(cos(x))/(sin(x)cancel(cos(x))) dx -int sin^cancel(2)(x)/(cancel(sin(x))cos(x)) dx#
Remove the cancelled terms:
#int (cos(x)-sin^2(x))/(sin(x)cos(x)) dx = int 1/sin(x) dx -int sin(x)/cos(x) dx#
Substitute #1/sin(x) = csc(x)# and #sin(x)/cos(x) = tan(x)#:
#int (cos(x)-sin^2(x))/(sin(x)cos(x)) dx = int csc(x) dx -int tan(x) dx#
These integrals can be found in any list of integrals:
#int (cos(x)-sin^2(x))/(sin(x)cos(x)) dx = -ln(cot(x)+ csc(x)) +ln( cos(x))+ C#
