Question

What is the integral of `int (1-sinx)/(cosx) dx`?

Answer 1

`(1-sinx)/cosx = ((1-sinx))/cosx * ((1+sinx))/((1+sinx))`

`= (1-sin^2x)/(cosx(1+sinx))`

`= cos^2x/(cosx(1+sinx))`

`= cosx/(1+sinx)`

`int (1-sinx)/cosx dx = int cosx/(1+sinx) dx`

`= ln(1+sinx)+C`

(by substitution with `u=1+sinx`)