Find the integral?

Question

Find ∫ (sin(6x))²(cos(6x))² dx.

Answer 1

 

∫ (sin(6x))²(cos(6x))² dx

= ∫ (1/4)(sin(12x))² dx, since sin(12x) = 2sin(6x)cos(6x)

= ∫ (1/8)(1-cos(24x)) dx, since(sin(12x))^2 = (1/2)(1-cos(24x))

= (1/8)x - (1/192)sin(24x) + c

Answer 2

∫ [sin²(6x)]*[cos²(6x)]dx = 

 

(x/8) - (1/192)sin(24x)

 

Here is a link to a webpage where you can do this integration:

 

http://www.wolframalpha.com/widgets/view.jsp?id=893912ad72b01acedd76b68aa3ffc4df