Дано
$$frac{1}{4} left(frac{3}{4} left(left(4 x + 3right) sin{left (4 x + 3 right )} + cos{left (4 x + 3 right )}right) – frac{1}{4} sin{left (4 x + 3 right )}right)$$
Подстановка условия
$$frac{1}{4} left(frac{3}{4} left(left(4 x + 3right) sin{left (4 x + 3 right )} + cos{left (4 x + 3 right )}right) – frac{1}{4} sin{left (4 x + 3 right )}right)$$
((3*((4*(-1/3) + 3)*sin(4*(-1/3) + 3) + cos(4*(-1/3) + 3)))/4 – sin(4*(-1/3) + 3)/4)/4
$$frac{1}{4} left(frac{3}{4} left(left(4 (-1/3) + 3right) sin{left (4 (-1/3) + 3 right )} + cos{left (4 (-1/3) + 3 right )}right) – frac{1}{4} sin{left (4 (-1/3) + 3 right )}right)$$
((3*((4*(-1)/3 + 3)*sin(4*(-1)/3 + 3) + cos(4*(-1)/3 + 3)))/4 – sin(4*(-1)/3 + 3)/4)/4
$$frac{1}{4} left(- frac{1}{4} sin{left (frac{-4}{3} + 3 right )} + frac{3}{4} left(cos{left (frac{-4}{3} + 3 right )} + left(frac{-4}{3} + 3right) sin{left (frac{-4}{3} + 3 right )}right)right)$$
sin(5/3)/4 + 3*cos(5/3)/16
$$frac{3}{16} cos{left (frac{5}{3} right )} + frac{1}{4} sin{left (frac{5}{3} right )}$$
Степени
$$frac{3}{16} left(4 x + 3right) sin{left (4 x + 3 right )} – frac{1}{16} sin{left (4 x + 3 right )} + frac{3}{16} cos{left (4 x + 3 right )}$$
Численный ответ
0.1875*cos(4*x + 3) – 0.0625*sin(4*x + 3) + 0.1875*(3.0 + 4.0*x)*sin(4*x + 3)
Рациональный знаменатель
$$frac{1}{16} left(12 x sin{left (4 x + 3 right )} + 8 sin{left (4 x + 3 right )} + 3 cos{left (4 x + 3 right )}right)$$
Объединение рациональных выражений
$$frac{1}{16} left(3 left(4 x + 3right) sin{left (4 x + 3 right )} – sin{left (4 x + 3 right )} + 3 cos{left (4 x + 3 right )}right)$$
Общее упрощение
sin(3 + 4*x) 3*cos(3 + 4*x) 3*x*sin(3 + 4*x)
———— + ————– + —————-
2 16 4
$$frac{3 x}{4} sin{left (4 x + 3 right )} + frac{1}{2} sin{left (4 x + 3 right )} + frac{3}{16} cos{left (4 x + 3 right )}$$
Соберем выражение
$$frac{1}{16} left(12 x + 8right) sin{left (4 x + 3 right )} + frac{3}{16} cos{left (4 x + 3 right )}$$
sin(4*x + 3) 3*((4*x + 3)*sin(4*x + 3) + cos(4*x + 3))
– ———— + —————————————–
4*4 4*4
$$frac{3}{16} left(left(4 x + 3right) sin{left (4 x + 3 right )} + cos{left (4 x + 3 right )}right) – frac{1}{16} sin{left (4 x + 3 right )}$$
Общий знаменатель
sin(3 + 4*x) 3*cos(3 + 4*x) 3*x*sin(3 + 4*x)
———— + ————– + —————-
2 16 4
$$frac{3 x}{4} sin{left (4 x + 3 right )} + frac{1}{2} sin{left (4 x + 3 right )} + frac{3}{16} cos{left (4 x + 3 right )}$$
Тригонометрическая часть
sin(3 + 4*x) 3*cos(3 + 4*x) 3*x*sin(3 + 4*x)
———— + ————– + —————-
2 16 4
$$frac{3 x}{4} sin{left (4 x + 3 right )} + frac{1}{2} sin{left (4 x + 3 right )} + frac{3}{16} cos{left (4 x + 3 right )}$$
Комбинаторика
3*cos(3 + 4*x) + 8*sin(3 + 4*x) + 12*x*sin(3 + 4*x)
—————————————————
16
$$frac{1}{16} left(12 x sin{left (4 x + 3 right )} + 8 sin{left (4 x + 3 right )} + 3 cos{left (4 x + 3 right )}right)$$
Раскрыть выражение
3*sin(3)*sin(4*x) cos(3)*sin(4*x) cos(4*x)*sin(3) 3*(3 + 4*x)*(cos(3)*sin(4*x) + cos(4*x)*sin(3)) 3*cos(3)*cos(4*x)
– —————– – ————— – ————— + ———————————————– + —————–
16 16 16 16 16
$$frac{3}{16} left(4 x + 3right) left(sin{left (4 x right )} cos{left (3 right )} + sin{left (3 right )} cos{left (4 x right )}right) – frac{3}{16} sin{left (3 right )} sin{left (4 x right )} – frac{1}{16} sin{left (4 x right )} cos{left (3 right )} + frac{3}{16} cos{left (3 right )} cos{left (4 x right )} – frac{1}{16} sin{left (3 right )} cos{left (4 x right )}$$
