Vtgyjfy

Could I please have some starting points on solving the following indefinite integral:

$$int frac{1 - sin(x)}{1+sin(x)} space dx\$$

Is there a known method(s) for tackling this sort of integral?

Note that $$begin{gather}
int frac{1 - sin(x)}{1+sin(x)} spacemathrm{d}x\
= int frac{(1 - sin(x))^2}{1-sin(x)^2} spacemathrm{d}x\
= int frac{(1 - sin(x))^2}{cos^2(x)} spacemathrm{d}x\
= int frac{(1 - 2cdotsin(x)) + sin^2(x)}{cos^2(x)} spacemathrm{d}x\
= int left(sec^2(x) - 2 cdotfrac{sin(x)}{cos^2(x)}+tan^2(x)right) spacemathrm{d}x\
= int left(sec^2(x) - 2 cdotsec(x)tan(x) + tan^2(x) right)spacemathrm{d}x\
= tan(x) - 2 cdotsec(x) + int tan^2(x) spacemathrm{d}x space(+C)\
= 2cdottan(x) - 2 cdotsec(x) - x space (+C)
end{gather}$$