Ejercicio con una integral indefinida, aperentemente complicada: $\displaystyle \int\,\dfrac{\cos(x)}{\sin(x)+3}\,dx$

$$\displaystyle \int\,\dfrac{\cos(x)}{\sin(x)+3}\,dx=\int\,\dfrac{\cos(x)\,dx}{\sin(x)+3}\overset{(1)}{=}\int\,\dfrac{d(\sin(x)+3)}{\sin(x)+3}=\ln\,(\sin(x)+3)+C$$ (1) $d(\sin(x)+3)=(sin(x)+3)'\,dx=\cos(x)\,dx$
$\diamond$