What is the problem of difference between instruction's answer and my answer? Here is the question and its answer from instructor.

But I noticed that my solution is slightly different,
$$\int \sin^{4}x\,dx = \int (\frac{1-\cos{2x}}{2})^{2}\,dx = \frac{1}{4}\int{1-2\cos{2x} + \cos^{2}{2x}}\,dx = $$
$$ \frac{1}{4}\int{1-2\cos2x + \frac{1+\cos4x}{2}} = \frac{1}{4}(x - \sin{2x} + \frac{1}{2}x + \frac{1}{8}\sin{4x}) + C
$$
The difference of answers is the sign of  $+$ or $-$ $(1/8) x$ after calculation is finished. But I cannot see why.
What is the main reason of this difference?

You have $\dfrac{1}{4}\cdot \left(x+\dfrac{1}{2}x\right) = \dfrac{1}{4}\cdot \dfrac{3}{2}x = \dfrac{3}{8}x$.
The answer on the board has
$$\dfrac{1}{2}x- \dfrac{1}{8}x = \dfrac{3}{8}x$$
