Study the phenomena of resonance for an oscilating system where f(x)=sinx*cos2x

To study the phenomena of resonance, we'll just have to
calculate the indefinite integral of the given
function:f(x)=sinx*cos2x

Int sinx*cos 2x
dx

To calculate the integral, we'll have to transform the
product of trigonometric functions into an algebraic
sum:

We'll use the product formula
for:

sin a*cos b =
[sin(a-b)+sin(a+b)]/2

We'll substitute a by x and b by
2x:

sinx*cos 2x =
[sin(x-2x)+sin(x+2x)]/2

sinx*cos 2x = (sin3x - sin
x)/2

We'll substitute the product by the
difference:

Int sinx*cos 2x dx = Int (sin3x - sin
x)dx/2

Int (sin3x - sin x)dx/2 = (1/2)*[Int (sin3x)dx - Int
(sin x)dx]

Int (sin3x - sin x)dx/2 = -cos 3x/6 + cos x/2 +
C