Question

интеграл от sinx/(cos^2x-2cosx+5)

Answer 1

$\int\limit { \frac{sin(x)}{cos^2(x)-2cos(x)+5} } \, dx= \int\limits { \frac{sinx}{(cos(x)-1)^2+4} } \, dx =\\|\ cos(x)-1=t\ |\\|\ -sin(x)\ dx=dt\ |\\|\ dx= -\frac{dt}{sin(x)}\ \ \ \ \ \ \ |\\= \int\limits { \frac{sin(x)}{-sin(x)(t^2+4)} } \, dt= -\int\limits { \frac{dt}{t^2+4} }= -\frac{1}{2}*arctg( \frac{t}{2})=\\-\frac{1}{2}*arctg( \frac{cos(x)-1}{2})+C$