Дано
$$frac{1}{9} left(frac{2}{9} left(- 9 x cos{left (9 x right )} + sin{left (9 x right )}right) + 5 cos{left (9 x right )}right)$$
Подстановка условия
$$frac{1}{9} left(frac{2}{9} left(- 9 x cos{left (9 x right )} + sin{left (9 x right )}right) + 5 cos{left (9 x right )}right)$$
((2*(sin(9*(1/2)) – 9*(1/2)*cos(9*(1/2))))/9 + 5*cos(9*(1/2)))/9
$$frac{1}{9} left(frac{2}{9} left(- 9 (1/2) cos{left (9 (1/2) right )} + sin{left (9 (1/2) right )}right) + 5 cos{left (9 (1/2) right )}right)$$
((2*(sin(9/2) – 9/2*cos(9/2)))/9 + 5*cos(9/2))/9
$$frac{1}{9} left(5 cos{left (frac{9}{2} right )} + frac{2}{9} left(sin{left (frac{9}{2} right )} – frac{9}{2} cos{left (frac{9}{2} right )}right)right)$$
2*sin(9/2)/81 + 4*cos(9/2)/9
$$frac{4}{9} cos{left (frac{9}{2} right )} + frac{2}{81} sin{left (frac{9}{2} right )}$$
Степени
$$- frac{2 x}{9} cos{left (9 x right )} + frac{2}{81} sin{left (9 x right )} + frac{5}{9} cos{left (9 x right )}$$
Численный ответ
0.0246913580246914*sin(9*x) + 0.555555555555556*cos(9*x) – 0.222222222222222*x*cos(9*x)
Рациональный знаменатель
$$- frac{2 x}{9} cos{left (9 x right )} + frac{2}{81} sin{left (9 x right )} + frac{5}{9} cos{left (9 x right )}$$
Объединение рациональных выражений
$$frac{1}{81} left(- 18 x cos{left (9 x right )} + 2 sin{left (9 x right )} + 45 cos{left (9 x right )}right)$$
Общее упрощение
2*sin(9*x) 5*cos(9*x) 2*x*cos(9*x)
———- + ———- – ————
81 9 9
$$- frac{2 x}{9} cos{left (9 x right )} + frac{2}{81} sin{left (9 x right )} + frac{5}{9} cos{left (9 x right )}$$
Соберем выражение
$$frac{1}{81} left(- 18 x + 45right) cos{left (9 x right )} + frac{2}{81} sin{left (9 x right )}$$
5*cos(9*x) 2*(sin(9*x) – 9*x*cos(9*x))
———- + —————————
9 9*9
$$frac{2}{81} left(- 9 x cos{left (9 x right )} + sin{left (9 x right )}right) + frac{5}{9} cos{left (9 x right )}$$
Общий знаменатель
2*sin(9*x) 5*cos(9*x) 2*x*cos(9*x)
———- + ———- – ————
81 9 9
$$- frac{2 x}{9} cos{left (9 x right )} + frac{2}{81} sin{left (9 x right )} + frac{5}{9} cos{left (9 x right )}$$
Комбинаторика
-(-45*cos(9*x) – 2*sin(9*x) + 18*x*cos(9*x))
———————————————
81
$$- frac{1}{81} left(18 x cos{left (9 x right )} – 2 sin{left (9 x right )} – 45 cos{left (9 x right )}right)$$
Тригонометрическая часть
2*sin(9*x) 5*cos(9*x) 2*x*cos(9*x)
———- + ———- – ————
81 9 9
$$- frac{2 x}{9} cos{left (9 x right )} + frac{2}{81} sin{left (9 x right )} + frac{5}{9} cos{left (9 x right )}$$
Раскрыть выражение
9 9 3 6 6 3 2 7 / 9 3 6 7 2 8 5 4 8 4 5
2*sin (x) 5*cos (x) 7 2 8 5 4 140*cos (x)*sin (x) 56*cos (x)*sin (x) 8*cos (x)*sin (x) 2*x*cos (x) – 84*cos (x)*sin (x) – 36*cos (x)*sin (x) + 9*sin (x)*cos(x) + 126*cos (x)*sin (x)/ 2*cos (x)*sin(x) 28*cos (x)*sin (x)
——— + ——— – 20*cos (x)*sin (x) + 5*sin (x)*cos(x) + 70*cos (x)*sin (x) – ——————- – —————— – —————– – ———————————————————————————————— + —————- + ——————
81 9 3 27 9 9 9 9
$$- frac{2 x}{9} left(9 sin^{8}{left (x right )} cos{left (x right )} – 84 sin^{6}{left (x right )} cos^{3}{left (x right )} + 126 sin^{4}{left (x right )} cos^{5}{left (x right )} – 36 sin^{2}{left (x right )} cos^{7}{left (x right )} + cos^{9}{left (x right )}right) + frac{2}{81} sin^{9}{left (x right )} + 5 sin^{8}{left (x right )} cos{left (x right )} – frac{8}{9} sin^{7}{left (x right )} cos^{2}{left (x right )} – frac{140}{3} sin^{6}{left (x right )} cos^{3}{left (x right )} + frac{28}{9} sin^{5}{left (x right )} cos^{4}{left (x right )} + 70 sin^{4}{left (x right )} cos^{5}{left (x right )} – frac{56}{27} sin^{3}{left (x right )} cos^{6}{left (x right )} – 20 sin^{2}{left (x right )} cos^{7}{left (x right )} + frac{2}{9} sin{left (x right )} cos^{8}{left (x right )} + frac{5}{9} cos^{9}{left (x right )}$$
