Question

.Помогите решить интеграл...

Answer 1

$int , sin^4x, cos^4x, dx=int , (sinxcdot cosx)^4, dx=int (frac{1}{2}sin2x)^4dx= \\=frac{1}{16}int (sin^22x)^2, dx= frac{1}{16}int (frac{1-cos4x}{2})^2, dx=frac{1}{64}int (1-2cos4x+cos^24x), dx=\\=frac{1}{64}int (1-2cos4x+frac{1+cos8x}{2}), dx=frac{1}{64}int (frac{3}{2}-2cos4x+frac{1}{2}cos8x), dx=\\=frac{1}{64}, (frac{3}{2}x-frac{2}{4}sin4x+frac{1}{16}sin8x)+C=frac{1}{64}, (frac{3}{2}x-frac{1}{2} sin4x+frac{1}{16}sin8x)+C$