Дано
$$frac{1}{4} left(frac{1}{4} left(4 x sin{left (4 x right )} + cos{left (4 x right )}right) + 2 sin{left (4 x right )}right)$$
Подстановка условия
$$frac{1}{4} left(frac{1}{4} left(4 x sin{left (4 x right )} + cos{left (4 x right )}right) + 2 sin{left (4 x right )}right)$$
(((4*(-2))*sin(4*(-2)) + cos(4*(-2)))/4 + 2*sin(4*(-2)))/4
$$frac{1}{4} left(frac{1}{4} left(4 (-2) sin{left (4 (-2) right )} + cos{left (4 (-2) right )}right) + 2 sin{left (4 (-2) right )}right)$$
(((4*(-2))*sin(4*(-2)) + cos(4*(-2)))/4 + 2*sin(4*(-2)))/4
$$frac{1}{4} left(2 sin{left (-2 cdot 4 right )} + frac{1}{4} left(cos{left (-2 cdot 4 right )} + -2 cdot 4 sin{left (-2 cdot 4 right )}right)right)$$
$$frac{1}{16} cos{left (8 right )}$$
Степени
$$frac{x}{4} sin{left (4 x right )} + frac{1}{2} sin{left (4 x right )} + frac{1}{16} cos{left (4 x right )}$$
Численный ответ
0.0625*cos(4*x) + 0.5*sin(4*x) + 0.25*x*sin(4*x)
Рациональный знаменатель
$$frac{x}{4} sin{left (4 x right )} + frac{1}{2} sin{left (4 x right )} + frac{1}{16} cos{left (4 x right )}$$
Объединение рациональных выражений
$$frac{1}{16} left(4 x sin{left (4 x right )} + 8 sin{left (4 x right )} + cos{left (4 x right )}right)$$
Общее упрощение
sin(4*x) cos(4*x) x*sin(4*x)
——– + ——– + ———-
2 16 4
$$frac{x}{4} sin{left (4 x right )} + frac{1}{2} sin{left (4 x right )} + frac{1}{16} cos{left (4 x right )}$$
Соберем выражение
$$frac{1}{16} left(4 x sin{left (4 x right )} + cos{left (4 x right )}right) + frac{1}{2} sin{left (4 x right )}$$
cos(4*x) (8 + 4*x)*sin(4*x)
——– + ——————
16 16
$$frac{1}{16} left(4 x + 8right) sin{left (4 x right )} + frac{1}{16} cos{left (4 x right )}$$
Общий знаменатель
sin(4*x) cos(4*x) x*sin(4*x)
——– + ——– + ———-
2 16 4
$$frac{x}{4} sin{left (4 x right )} + frac{1}{2} sin{left (4 x right )} + frac{1}{16} cos{left (4 x right )}$$
Тригонометрическая часть
sin(4*x) cos(4*x) x*sin(4*x)
——– + ——– + ———-
2 16 4
$$frac{x}{4} sin{left (4 x right )} + frac{1}{2} sin{left (4 x right )} + frac{1}{16} cos{left (4 x right )}$$
Комбинаторика
8*sin(4*x) + 4*x*sin(4*x) + cos(4*x)
————————————
16
$$frac{1}{16} left(4 x sin{left (4 x right )} + 8 sin{left (4 x right )} + cos{left (4 x right )}right)$$
Раскрыть выражение
4 4 2 2 / 3 3
cos (x) sin (x) 3 3 3*cos (x)*sin (x) x* – 4*sin (x)*cos(x) + 4*cos (x)*sin(x)/
——- + ——- – 2*sin (x)*cos(x) + 2*cos (x)*sin(x) – —————– + —————————————–
16 16 8 4
$$frac{x}{4} left(- 4 sin^{3}{left (x right )} cos{left (x right )} + 4 sin{left (x right )} cos^{3}{left (x right )}right) + frac{1}{16} sin^{4}{left (x right )} – 2 sin^{3}{left (x right )} cos{left (x right )} – frac{3}{8} sin^{2}{left (x right )} cos^{2}{left (x right )} + 2 sin{left (x right )} cos^{3}{left (x right )} + frac{1}{16} cos^{4}{left (x right )}$$
