Question

Интеграл. $intlimits frac{56 cos*2x}{ cos^{2} *xsin^2*x} dx^_ {} ,$

Answer 1

$int frac{56cdot cos2x}{cos^2xsin^2x} dx=[cosxsinx=frac{1}{2}sin2x]=int frac{56cdot cos2x}{frac{1}{4}sin^22x}dx=\\=[sin2x=t,; dt=2cos2x, dx]=56cdot 2cdot int frac{dt}{t^2}=\\=112cdot frac{-1}{t}+C=-frac{112}{sin2x}+C$