Найдите общий вид первообразных для функции f(x)= sin^4 х

$\int sin^4x \ dx = \int (sin^2x)(1-cos^2x) \ dx =\\\\ \int sin^2x \ dx -\int sin^2xcos^2x \ dx =\\\\ \int \frac{1-cos2x}{2} \ dx -\int \frac{1}{4}sin^22x \ dx =\\\\ \int \frac{1-cos2x}{2} \ dx -\int \frac{1}{4}\frac{1-cos4x}{2} \ dx =\\\\ \frac{x}{2} - \frac{1}{4}sin2x - \frac{x}{8} + \frac{1}{32}sin4x + C =\\\\ \frac{3x}{8} - \frac{1}{4}sin2x + \frac{1}{32}sin4x + C$