MHB LP_Rocks' question at Yahoo Answers regarding an indefinite integral

[MarkFL]

Here is the question:

Integration question!?

Whats the integration of cos^2 2x . sin 2x?
The answer is -1/12 cos^3 2x + c
But I don't see how..

Here is a link to the question:

Integration question!? - Yahoo! Answers

I have posted a link there to this topic so the OP can find my response.

 

[MarkFL]

Hello LP_Rocks,

We are given to evaluate:

$$\int\cos^2(2x)\sin(2x)\,dx$$

Using the substitution:

$$u=\cos(2x)\,\therefore\,du=-2\sin(2x)\,dx$$

we have:

$$-\frac{1}{2}\int u^2\,du=-\frac{1}{6}u^3+C=-\frac{1}{6}\cos^3(2x)+C$$

As you can see the given result is incorrect.