What is the integral of #cos^2(x)#?

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What is the integral of #cos^2(x)#?

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Answer 1 · 2016-05-16T10:50:16

#int cos(x)^2 dx = x/2 + 1/4 Sin(2 x)+C#

Explanation:

#cos(alpha+beta)=cos(alpha)cos(beta)-sin(alpha)sin(beta)#
Making #alpha=beta->cos(2alpha) = cos(alpha)^2-sin(alpha)^2#
but #cos(alpha)^2+sin(alpha)^2=1# then
#cos(alpha)^2=( 1+cos(2 alpha))/2#
so #int cos(x)^2dx = int( 1+cos(2 x))/2dx = 1/2int dx + 1/2intcos(2x)dx#
Finally #int cos(x)^2 dx = x/2 + 1/4 Sin(2 x)+C#

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What is the integral of #cos^2(x)#?

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