Дано
$$frac{5}{x} left(- sin{left (x right )} – frac{720}{x^{5}} cos{left (x right )} – frac{360}{x^{4}} sin{left (x right )} – frac{6}{x} cos{left (x right )} + frac{30}{x^{2}} sin{left (x right )} + frac{120}{x^{3}} cos{left (x right )} + frac{720}{x^{6}} sin{left (x right )}right)$$
Подстановка условия
$$frac{5}{x} left(- sin{left (x right )} – frac{720}{x^{5}} cos{left (x right )} – frac{360}{x^{4}} sin{left (x right )} – frac{6}{x} cos{left (x right )} + frac{30}{x^{2}} sin{left (x right )} + frac{120}{x^{3}} cos{left (x right )} + frac{720}{x^{6}} sin{left (x right )}right)$$
(5*(-sin((1)) – 720*cos((1))/(1)^5 – 360*sin((1))/(1)^4 – 6*cos((1))/(1) + (30*sin((1)))/(1)^2 + (120*cos((1)))/(1)^3 + (720*sin((1)))/(1)^6))/(1)
$$frac{5}{(1)} left(- sin{left ((1) right )} – frac{720}{(1)^{5}} cos{left ((1) right )} – frac{360}{(1)^{4}} sin{left ((1) right )} – frac{6}{(1)} cos{left ((1) right )} + frac{30}{(1)^{2}} sin{left ((1) right )} + frac{120}{(1)^{3}} cos{left ((1) right )} + frac{720}{(1)^{6}} sin{left ((1) right )}right)$$
(5*(-sin(1) – 720*cos(1)/1^5 – 360*sin(1)/1^4 – 6*cos(1)/1 + (30*sin(1))/1^2 + (120*cos(1))/1^3 + (720*sin(1))/1^6))/1
/ 720*cos(1) 360*sin(1) 6*cos(1) 30*sin(1) 120*cos(1) 720*sin(1)
5*|-sin(1) – ———- – ———- – ——– + ——— + ———- + ———-|
| 5 4 1 2 3 6 |
1 1 1 1 1 /
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1
-3030*cos(1) + 1945*sin(1)
$$- 3030 cos{left (1 right )} + 1945 sin{left (1 right )}$$
Степени
$$frac{1}{x} left(- 5 sin{left (x right )} – frac{30}{x} cos{left (x right )} + frac{150}{x^{2}} sin{left (x right )} + frac{600}{x^{3}} cos{left (x right )} – frac{1800}{x^{4}} sin{left (x right )} – frac{3600}{x^{5}} cos{left (x right )} + frac{3600}{x^{6}} sin{left (x right )}right)$$
Численный ответ
5.0*(-sin(x) + 30.0*sin(x)/x^2 + 120.0*cos(x)/x^3 + 720.0*sin(x)/x^6 – 6.0*cos(x)/x – 360.0*sin(x)/x^4 – 720.0*cos(x)/x^5)/x
Рациональный знаменатель
$$frac{1}{x^{22}} left(3600 x^{15} sin{left (x right )} + 5 x^{6} left(120 x^{12} cos{left (x right )} + x^{3} left(30 x^{10} sin{left (x right )} + x^{2} left(- 6 x^{9} cos{left (x right )} + x left(- 360 x^{5} sin{left (x right )} + x^{4} left(- x^{5} sin{left (x right )} – 720 cos{left (x right )}right)right)right)right)right)right)$$
Объединение рациональных выражений
$$frac{1}{x^{7}} left(5 x left(- x^{5} sin{left (x right )} – 6 x^{4} cos{left (x right )} + 30 x^{3} sin{left (x right )} + 120 x^{2} cos{left (x right )} – 360 x sin{left (x right )} – 720 cos{left (x right )}right) + 3600 sin{left (x right )}right)$$
Общее упрощение
/ 6 2 5 4 3
5*720*sin(x) – x *sin(x) – 720*x*cos(x) – 360*x *sin(x) – 6*x *cos(x) + 30*x *sin(x) + 120*x *cos(x)/
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7
x
$$frac{1}{x^{7}} left(- 5 x^{6} sin{left (x right )} – 30 x^{5} cos{left (x right )} + 150 x^{4} sin{left (x right )} + 600 x^{3} cos{left (x right )} – 1800 x^{2} sin{left (x right )} – 3600 x cos{left (x right )} + 3600 sin{left (x right )}right)$$
Соберем выражение
$$frac{1}{x} left(- 5 sin{left (x right )} + frac{3600}{x^{6}} sin{left (x right )} – frac{3600}{x^{5}} cos{left (x right )} – frac{1800}{x^{4}} sin{left (x right )} + frac{600}{x^{3}} cos{left (x right )} + frac{150}{x^{2}} sin{left (x right )} – frac{30}{x} cos{left (x right )}right)$$
3600*cos(x) 1800*sin(x) 30*cos(x) 5*sin(x) 150*sin(x) 600*cos(x) 3600*sin(x)
– ———– – ———– – ——— – ——– + ———- + ———- + ———–
6 5 2 x 3 4 7
x x x x x x
$$- frac{5}{x} sin{left (x right )} – frac{30}{x^{2}} cos{left (x right )} + frac{150}{x^{3}} sin{left (x right )} + frac{600}{x^{4}} cos{left (x right )} – frac{1800}{x^{5}} sin{left (x right )} – frac{3600}{x^{6}} cos{left (x right )} + frac{3600}{x^{7}} sin{left (x right )}$$
Общий знаменатель
/ 3 4 6 5 2
– -3600*sin(x) – 600*x *cos(x) – 150*x *sin(x) + 5*x *sin(x) + 30*x *cos(x) + 1800*x *sin(x) + 3600*x*cos(x)/
————————————————————————————————————–
7
x
$$- frac{1}{x^{7}} left(5 x^{6} sin{left (x right )} + 30 x^{5} cos{left (x right )} – 150 x^{4} sin{left (x right )} – 600 x^{3} cos{left (x right )} + 1800 x^{2} sin{left (x right )} + 3600 x cos{left (x right )} – 3600 sin{left (x right )}right)$$
Комбинаторика
/ 6 3 4 5 2
-5* -720*sin(x) + x *sin(x) – 120*x *cos(x) – 30*x *sin(x) + 6*x *cos(x) + 360*x *sin(x) + 720*x*cos(x)/
——————————————————————————————————–
7
x
$$- frac{1}{x^{7}} left(5 x^{6} sin{left (x right )} + 30 x^{5} cos{left (x right )} – 150 x^{4} sin{left (x right )} – 600 x^{3} cos{left (x right )} + 1800 x^{2} sin{left (x right )} + 3600 x cos{left (x right )} – 3600 sin{left (x right )}right)$$
Тригонометрическая часть
3600*cos(x) 1800*sin(x) 30*cos(x) 150*sin(x) 600*cos(x) 3600*sin(x)
-5*sin(x) – ———– – ———– – ——— + ———- + ———- + ———–
5 4 x 2 3 6
x x x x x
—————————————————————————————–
x
$$frac{1}{x} left(- 5 sin{left (x right )} – frac{30}{x} cos{left (x right )} + frac{150}{x^{2}} sin{left (x right )} + frac{600}{x^{3}} cos{left (x right )} – frac{1800}{x^{4}} sin{left (x right )} – frac{3600}{x^{5}} cos{left (x right )} + frac{3600}{x^{6}} sin{left (x right )}right)$$
Раскрыть выражение
3600*cos(x) 1800*sin(x) 30*cos(x) 150*sin(x) 600*cos(x) 3600*sin(x)
-5*sin(x) – ———– – ———– – ——— + ———- + ———- + ———–
5 4 x 2 3 6
x x x x x
—————————————————————————————–
x
$$frac{1}{x} left(- 5 sin{left (x right )} – frac{30}{x} cos{left (x right )} + frac{150}{x^{2}} sin{left (x right )} + frac{600}{x^{3}} cos{left (x right )} – frac{1800}{x^{4}} sin{left (x right )} – frac{3600}{x^{5}} cos{left (x right )} + frac{3600}{x^{6}} sin{left (x right )}right)$$
