Дано
$$frac{8}{81} left(- 9 x cos{left (9 x right )} + sin{left (9 x right )}right)$$
Подстановка условия
$$frac{8}{81} left(- 9 x cos{left (9 x right )} + sin{left (9 x right )}right)$$
(8*(sin(9*(1)) – 9*(1)*cos(9*(1))))/81
$$frac{8}{81} left(- 9 (1) cos{left (9 (1) right )} + sin{left (9 (1) right )}right)$$
(8*(sin(9) – 9*cos(9)))/81
$$frac{8}{81} left(sin{left (9 right )} – 9 cos{left (9 right )}right)$$
-8*cos(9)/9 + 8*sin(9)/81
$$frac{8}{81} sin{left (9 right )} – frac{8}{9} cos{left (9 right )}$$
Степени
$$- frac{8 x}{9} cos{left (9 x right )} + frac{8}{81} sin{left (9 x right )}$$
Численный ответ
0.0987654320987654*sin(9*x) – 0.888888888888889*x*cos(9*x)
Рациональный знаменатель
$$- frac{8 x}{9} cos{left (9 x right )} + frac{8}{81} sin{left (9 x right )}$$
Объединение рациональных выражений
$$- frac{8 x}{9} cos{left (9 x right )} + frac{8}{81} sin{left (9 x right )}$$
Общее упрощение
8*sin(9*x) 8*x*cos(9*x)
———- – ————
81 9
$$- frac{8 x}{9} cos{left (9 x right )} + frac{8}{81} sin{left (9 x right )}$$
Соберем выражение
$$- frac{8 x}{9} cos{left (9 x right )} + frac{8}{81} sin{left (9 x right )}$$
8*sin(9*x) 8*x*cos(9*x)
———- – ————
81 9
$$- frac{8 x}{9} cos{left (9 x right )} + frac{8}{81} sin{left (9 x right )}$$
Общий знаменатель
8*sin(9*x) 8*x*cos(9*x)
———- – ————
81 9
$$- frac{8 x}{9} cos{left (9 x right )} + frac{8}{81} sin{left (9 x right )}$$
Тригонометрическая часть
8*sin(9*x) 8*x*cos(9*x)
———- – ————
81 9
$$- frac{8 x}{9} cos{left (9 x right )} + frac{8}{81} sin{left (9 x right )}$$
Комбинаторика
-8*(-sin(9*x) + 9*x*cos(9*x))
—————————–
81
$$- frac{1}{81} left(72 x cos{left (9 x right )} – 8 sin{left (9 x right )}right)$$
Раскрыть выражение
9 6 3 2 7 / 9 3 6 7 2 8 5 4 8 4 5
8*sin (x) 224*cos (x)*sin (x) 32*cos (x)*sin (x) 8*x*cos (x) – 84*cos (x)*sin (x) – 36*cos (x)*sin (x) + 9*sin (x)*cos(x) + 126*cos (x)*sin (x)/ 8*cos (x)*sin(x) 112*cos (x)*sin (x)
——— – ——————- – —————— – ———————————————————————————————— + —————- + ——————-
81 27 9 9 9 9
$$- frac{8 x}{9} left(9 sin^{8}{left (x right )} cos{left (x right )} – 84 sin^{6}{left (x right )} cos^{3}{left (x right )} + 126 sin^{4}{left (x right )} cos^{5}{left (x right )} – 36 sin^{2}{left (x right )} cos^{7}{left (x right )} + cos^{9}{left (x right )}right) + frac{8}{81} sin^{9}{left (x right )} – frac{32}{9} sin^{7}{left (x right )} cos^{2}{left (x right )} + frac{112}{9} sin^{5}{left (x right )} cos^{4}{left (x right )} – frac{224}{27} sin^{3}{left (x right )} cos^{6}{left (x right )} + frac{8}{9} sin{left (x right )} cos^{8}{left (x right )}$$
