# LP_Rocks' question at Yahoo! Answers regarding an indefinite integral

#### MarkFL

##### Administrator
Staff member
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

##### Administrator
Staff member
Hello LP_Rocks,

We are given to evaluate:

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

Using the substitution:

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

we have:

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

As you can see the given result is incorrect.