integral 6 sin 4x cos 5x dx

=> Integral (6 sin 4x * cos 5x) dx
=> 6*Integral (sin 4x * cos 5x) dx
=> 6*Integral (sin (4x+5x) + sin (4x-5x))/2 dx
=> 6*1/2*Integral (sin (4x+5x) + sin (4x-5x))dx
=> 6*1/2*(Integral (sin (4x+5x)dx) + integral (sin (4x-5x)dx)
=> 6*1/2*((-1/9) cos (9x)) + (cos (x))
=> 3*((-1/9) cos (9x)) + (cos (x))
=> ((-1/3) cos (9x)) + 3(cos (x)) + c