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Suppose I have the integral

\(\displaystyle 2 \int 4 \sin^2x \, dx\)

So I understand that \(\displaystyle \sin^2x = \frac{1 - \cos2x}{2}\)

**we have a**

*BUT***in front of it, so shouldn't we pull the \(\displaystyle 4\) out in front of the integral to get:**

*4*\(\displaystyle 8 \int \frac{1 - \cos 2x}{2} \, dx\)

then pull out the \(\displaystyle \frac{1}{2}\) to get: \(\displaystyle 4 \int 1 - \cos 2x \, dx\)

then:

\(\displaystyle 8 [ x + \frac{1}{2} \sin2x ] + C\)?