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LP_Rocks' question at Yahoo! Answers regarding an indefinite integral

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MarkFL

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Staff member
Feb 24, 2012
13,775
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.. o_O
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.
 
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MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
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.