Найти первообразную функция y=sin^4 (x/2)

[latex]f(x)=sin ^{4} \frac{x}{2}=(sin ^{2} \frac{x}{2}) ^{2} = (\frac{1-cosx}{2}) ^{2}= \frac{1-2cosx+cos ^{2}x }{4}= \\ = \frac{1}{4}- \frac{1}{2}cosx+ \frac{1}{4}\cdot \frac{1+cos2x}{2}= \frac{1}{4}- \frac{cosx}{2}+ \frac{1}{8}+ \frac{cos2x}{8}= \frac{3}{8}- \frac{cosx}{2}+ \frac{cos2x}{8}, \\ F(x) = \frac{3}{8}x- \frac{1}{2}sinx+ \frac{1}{16}sin2x +C [/latex]