Question

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

Answer 1

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