Resolver ∫ 1-sin^2(x)/cos(x) wrt x

$$\int \frac { 1 - \sin ^ { 2 } ( x ) } { \cos ( x ) } d x$$

Calcular

$$\ln(|\sin(\frac{x}{2})+\cos(\frac{x}{2})|)-\ln(|\cos(\frac{x}{2})-\sin(\frac{x}{2})|)+\frac{\ln(|\sin(x)-1|)}{2}-\frac{\ln(|-\sin(x)-1|)}{2}+\sin(x)+С$$

Diferenciar w.r.t. x

$$\frac{\cos(x)\left(\sin(x)\cos(\frac{x}{2})\right)^{2}-\cos(x)\left(\sin(x)\sin(\frac{x}{2})\right)^{2}+\left(\sin(x)\sin(\frac{x}{2})\right)^{2}+\left(\sin(x)\cos(\frac{x}{2})\right)^{2}-1}{\cos(x)\left(\left(\sin(x)\right)^{2}-1\right)}$$