I know that the antiderivative is cos^2(x) is (x+cos(x)sin(x))/2, but how the heck can you derive it?

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- Apr 3rd 2008, 05:37 PMjaggedIntigrating this seemingly simple expression
I know that the antiderivative is cos^2(x) is (x+cos(x)sin(x))/2, but how the heck can you derive it?

- Apr 3rd 2008, 05:45 PMmr fantastic
Make the appropriate substitution suggested by the double angle formula:

$\displaystyle \cos (2x) = 2 \cos^2 (x) - 1 \Rightarrow \cos^2 (x) = \frac{1}{2} \, (\cos(2x) + 1)$.

Then, after integrating, make the substitution $\displaystyle \sin (2x) = 2 \sin x \cos x$ in your answer. - Apr 3rd 2008, 05:53 PMjagged
thanks... ive forgotten basic methods of integration since spring break :D