Question

Интеграл cosx dx/2sinx-5

Answer 1

$\int\limits { \frac{cos(x)}{2sin(x)-5} } \, dx=\\|\ 2sin(x)-5= t\ |\\|\ 2cos(x)\ dx=dt\ |\\|\ dx= \frac{dt}{2cos(x)}\ \ \ \ \ |\\= \int\limits { \frac{dt}{2t} }= \frac{1}{2} \int\limits {t^{-1}} \, dt= \frac{1}{2} ln|t|= \frac{1}{2}ln|2sin(x)-5|+C$