Дано
$$frac{1}{3600} left(- 2250 x cos{left (x right )} + 375 x cos{left (3 x right )} + – 45 x cos{left (5 x right )} + 9 sin{left (5 x right )} – 125 sin{left (3 x right )} + 2250 sin{left (x right )}right)$$
Подстановка условия
$$frac{1}{3600} left(- 2250 x cos{left (x right )} + 375 x cos{left (3 x right )} + – 45 x cos{left (5 x right )} + 9 sin{left (5 x right )} – 125 sin{left (3 x right )} + 2250 sin{left (x right )}right)$$
(9*sin(5*(3)) – 45*(3)*cos(5*(3)) – 125*sin(3*(3)) + (375*(3))*cos(3*(3)) + 2250*sin((3)) – 2250*(3)*cos((3)))/3600
$$frac{1}{3600} left(- 2250 (3) cos{left ((3) right )} + 375 (3) cos{left (3 (3) right )} + – 45 (3) cos{left (5 (3) right )} + 9 sin{left (5 (3) right )} – 125 sin{left (3 (3) right )} + 2250 sin{left ((3) right )}right)$$
(9*sin(5*3) – 45*3*cos(5*3) – 125*sin(3*3) + (375*3)*cos(3*3) + 2250*sin(3) – 2250*3*cos(3))/3600
$$frac{1}{3600} left(3 cdot 375 cos{left (3 cdot 3 right )} + – 125 sin{left (3 cdot 3 right )} + 9 sin{left (3 cdot 5 right )} – 135 cos{left (3 cdot 5 right )} + 2250 sin{left (3 right )} – 6750 cos{left (3 right )}right)$$
-15*cos(3)/8 – 5*sin(9)/144 – 3*cos(15)/80 + sin(15)/400 + 5*sin(3)/8 + 5*cos(9)/16
$$frac{5}{16} cos{left (9 right )} – frac{5}{144} sin{left (9 right )} + frac{1}{400} sin{left (15 right )} – frac{3}{80} cos{left (15 right )} + frac{5}{8} sin{left (3 right )} – frac{15}{8} cos{left (3 right )}$$
Степени
$$- frac{5 x}{8} cos{left (x right )} + frac{5 x}{48} cos{left (3 x right )} – frac{x}{80} cos{left (5 x right )} + frac{5}{8} sin{left (x right )} – frac{5}{144} sin{left (3 x right )} + frac{1}{400} sin{left (5 x right )}$$
Численный ответ
0.625*sin(x) + 0.0025*sin(5*x) – 0.0347222222222222*sin(3*x) + 0.104166666666667*x*cos(3*x) – 0.625*x*cos(x) – 0.0125*x*cos(5*x)
Рациональный знаменатель
$$- frac{5 x}{8} cos{left (x right )} + frac{5 x}{48} cos{left (3 x right )} – frac{x}{80} cos{left (5 x right )} + frac{5}{8} sin{left (x right )} – frac{5}{144} sin{left (3 x right )} + frac{1}{400} sin{left (5 x right )}$$
Объединение рациональных выражений
$$- frac{5 x}{8} cos{left (x right )} + frac{5 x}{48} cos{left (3 x right )} – frac{x}{80} cos{left (5 x right )} + frac{5}{8} sin{left (x right )} – frac{5}{144} sin{left (3 x right )} + frac{1}{400} sin{left (5 x right )}$$
Общее упрощение
5*sin(3*x) sin(5*x) 5*sin(x) 5*x*cos(x) x*cos(5*x) 5*x*cos(3*x)
– ———- + ——– + ——– – ———- – ———- + ————
144 400 8 8 80 48
$$- frac{5 x}{8} cos{left (x right )} + frac{5 x}{48} cos{left (3 x right )} – frac{x}{80} cos{left (5 x right )} + frac{5}{8} sin{left (x right )} – frac{5}{144} sin{left (3 x right )} + frac{1}{400} sin{left (5 x right )}$$
Соберем выражение
$$- frac{x}{80} cos{left (5 x right )} + frac{375 x}{3600} cos{left (3 x right )} – frac{5 x}{8} cos{left (x right )} + frac{5}{8} sin{left (x right )} – frac{5}{144} sin{left (3 x right )} + frac{1}{400} sin{left (5 x right )}$$
5*sin(3*x) sin(5*x) 5*sin(x) 5*x*cos(x) x*cos(5*x) 5*x*cos(3*x)
– ———- + ——– + ——– – ———- – ———- + ————
144 400 8 8 80 48
$$- frac{5 x}{8} cos{left (x right )} + frac{5 x}{48} cos{left (3 x right )} – frac{x}{80} cos{left (5 x right )} + frac{5}{8} sin{left (x right )} – frac{5}{144} sin{left (3 x right )} + frac{1}{400} sin{left (5 x right )}$$
Общий знаменатель
5*sin(3*x) sin(5*x) 5*sin(x) 5*x*cos(x) x*cos(5*x) 5*x*cos(3*x)
– ———- + ——– + ——– – ———- – ———- + ————
144 400 8 8 80 48
$$- frac{5 x}{8} cos{left (x right )} + frac{5 x}{48} cos{left (3 x right )} – frac{x}{80} cos{left (5 x right )} + frac{5}{8} sin{left (x right )} – frac{5}{144} sin{left (3 x right )} + frac{1}{400} sin{left (5 x right )}$$
Тригонометрическая часть
5*sin(3*x) sin(5*x) 5*sin(x) 5*x*cos(x) x*cos(5*x) 5*x*cos(3*x)
– ———- + ——– + ——– – ———- – ———- + ————
144 400 8 8 80 48
$$- frac{5 x}{8} cos{left (x right )} + frac{5 x}{48} cos{left (3 x right )} – frac{x}{80} cos{left (5 x right )} + frac{5}{8} sin{left (x right )} – frac{5}{144} sin{left (3 x right )} + frac{1}{400} sin{left (5 x right )}$$
Комбинаторика
-125*sin(3*x) + 9*sin(5*x) + 2250*sin(x) – 2250*x*cos(x) – 45*x*cos(5*x) + 375*x*cos(3*x)
—————————————————————————————–
3600
$$frac{1}{3600} left(- 2250 x cos{left (x right )} + 375 x cos{left (3 x right )} – 45 x cos{left (5 x right )} + 2250 sin{left (x right )} – 125 sin{left (3 x right )} + 9 sin{left (5 x right )}right)$$
Раскрыть выражение
5 3 2 2 3 / 5 3 2 4 4 / 3 2
sin (x) 5*sin(x) 5*sin (x) 5*x*cos(x) 5*cos (x)*sin(x) cos (x)*sin (x) x*cos (x) – 10*cos (x)*sin (x) + 5*sin (x)*cos(x)/ cos (x)*sin(x) 5*x*cos (x) – 3*sin (x)*cos(x)/
——- + ——– + ——— – ———- – —————- – ————— – ————————————————— + ————– + ——————————–
400 8 144 8 48 40 80 80 48
$$frac{5 x}{48} left(- 3 sin^{2}{left (x right )} cos{left (x right )} + cos^{3}{left (x right )}right) – frac{x}{80} left(5 sin^{4}{left (x right )} cos{left (x right )} – 10 sin^{2}{left (x right )} cos^{3}{left (x right )} + cos^{5}{left (x right )}right) – frac{5 x}{8} cos{left (x right )} + frac{1}{400} sin^{5}{left (x right )} – frac{1}{40} sin^{3}{left (x right )} cos^{2}{left (x right )} + frac{5}{144} sin^{3}{left (x right )} + frac{1}{80} sin{left (x right )} cos^{4}{left (x right )} – frac{5}{48} sin{left (x right )} cos^{2}{left (x right )} + frac{5}{8} sin{left (x right )}$$
