Primitive of Square of Cosine Function/Corollary

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Corollary to Primitive of Square of Cosine Function

$\displaystyle \int \cos^2 x \rd x = \frac {x + \sin x \cos x} 2 + C$

where $C$ is an arbitrary constant.


Proof

\(\displaystyle \int \sin^2 x \rd x\) \(=\) \(\displaystyle \frac x 2 + \frac {\sin 2 x} 4 + C\) Primitive of Square of Cosine Function
\(\displaystyle \) \(=\) \(\displaystyle \frac x 2 + \frac {2 \sin x \cos x} 4 + C\) Double Angle Formula for Sine
\(\displaystyle \) \(=\) \(\displaystyle \frac {x + \sin x \cos x} 2 + C\)

$\blacksquare$


Sources