Question

интеграл от sinx/(cos^2x-2cosx+5)

Answer 1

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