Дано
$$frac{1}{1 + 64 log^{2}{left (e right )}} left(-1 left(e^{72} cdot 8 sin{left (x + 9 right )} log{left (e right )} + e^{72} cos{left (x + 9 right )}right) e^{- 8 left(x + 9right) log{left (e right )}}right)$$
Подстановка условия
$$frac{1}{1 + 64 log^{2}{left (e right )}} left(-1 left(e^{72} cdot 8 sin{left (x + 9 right )} log{left (e right )} + e^{72} cos{left (x + 9 right )}right) e^{- 8 left(x + 9right) log{left (e right )}}right)$$
((-E^((-8*((3) + 9))*log(E)))*(((8*sin((3) + 9))*E^72)*log(E) + cos((3) + 9)*E^72))/(1 + 64*log(E)^2)
$$frac{1}{1 + 64 log^{2}{left (e right )}} left(-1 left(e^{72} cdot 8 sin{left ((3) + 9 right )} log{left (e right )} + e^{72} cos{left ((3) + 9 right )}right) e^{- 8 left((3) + 9right) log{left (e right )}}right)$$
((-E^((-8*(3 + 9))*log(E)))*(((8*sin(3 + 9))*E^72)*log(E) + cos(3 + 9)*E^72))/(1 + 64*log(E)^2)
$$frac{1}{1 + 64 log^{2}{left (e right )}} left(-1 left(e^{72} cdot 8 sin{left (3 + 9 right )} log{left (e right )} + e^{72} cos{left (3 + 9 right )}right) e^{- 8 left(3 + 9right)}right)$$
-(cos(12)*exp(72) + 8*exp(72)*sin(12))*exp(-96)/65
$$- frac{1}{65 e^{96}} left(8 e^{72} sin{left (12 right )} + e^{72} cos{left (12 right )}right)$$
Степени
$$left(- frac{8 e^{72}}{65} sin{left (x + 9 right )} – frac{e^{72}}{65} cos{left (x + 9 right )}right) e^{- 8 x – 72}$$
/ 72 72 -72 – 8*x
-cos(9 + x)*e + 8*e *sin(9 + x)/*e
————————————————
65
$$- frac{1}{65} left(8 e^{72} sin{left (x + 9 right )} + e^{72} cos{left (x + 9 right )}right) e^{- 8 x – 72}$$
Численный ответ
-0.0153846153846154*2.71828182845905^(-72.0 – 8.0*x)*(1.85867174528412e+31*cos(x + 9) + 1.4869373962273e+32*sin(x + 9))
Рациональный знаменатель
$$- frac{e^{72}}{65} left(8 sin{left (x + 9 right )} + cos{left (x + 9 right )}right) e^{- 8 x – 72}$$
Объединение рациональных выражений
$$- frac{e^{72}}{65} left(8 sin{left (x + 9 right )} + cos{left (x + 9 right )}right) e^{- 8 x – 72}$$
Общее упрощение
-8*x
-(8*sin(9 + x) + cos(9 + x))*e
———————————–
65
$$- frac{1}{65} left(8 sin{left (x + 9 right )} + cos{left (x + 9 right )}right) e^{- 8 x}$$
Соберем выражение
$$- frac{e^{- 8 left(x + 9right) log{left (e right )}}}{1 + 64 log^{2}{left (e right )}} left(e^{72} cdot 8 sin{left (x + 9 right )} log{left (e right )} + e^{72} cos{left (x + 9 right )}right)$$
/ 72 72 -8*(x + 9)*log(E)
-8*sin(x + 9)*E *log(E) + cos(x + 9)*E /*e
—————————————————————
2
1 + 64*log (E)
$$- frac{e^{- 8 left(x + 9right) log{left (e right )}}}{1 + 64 log^{2}{left (e right )}} left(e^{72} cdot 8 sin{left (x + 9 right )} log{left (e right )} + e^{72} cos{left (x + 9 right )}right)$$
/ 72 72 -72 – 8*x
-cos(9 + x)*e + 8*e *sin(9 + x)/*e
————————————————
65
$$- frac{1}{65} left(8 e^{72} sin{left (x + 9 right )} + e^{72} cos{left (x + 9 right )}right) e^{- 8 x – 72}$$
72 -72 – 8*x 72 -72 – 8*x
8*e *e *sin(9 + x) cos(9 + x)*e *e
– ————————— – ————————-
65 65
$$- frac{8 e^{72}}{65} e^{- 8 x – 72} sin{left (x + 9 right )} – frac{e^{72}}{65} e^{- 8 x – 72} cos{left (x + 9 right )}$$
Общий знаменатель
-8*x
-(8*sin(9 + x) + cos(9 + x))*e
———————————–
65
$$- frac{1}{65} left(8 sin{left (x + 9 right )} + cos{left (x + 9 right )}right) e^{- 8 x}$$
Тригонометрическая часть
72 -8*(x + 9)*log(E)
-(8*sin(9 + x) + cos(9 + x))*e *e
—————————————————-
2
1 + 64*log (E)
$$- frac{e^{72} e^{- 8 left(x + 9right) log{left (e right )}}}{1 + 64 log^{2}{left (e right )}} left(8 sin{left (x + 9 right )} + cos{left (x + 9 right )}right)$$
Комбинаторика
-8*x
-(8*sin(9 + x) + cos(9 + x))*e
———————————–
65
$$- frac{1}{65} left(8 sin{left (x + 9 right )} + cos{left (x + 9 right )}right) e^{- 8 x}$$
Раскрыть выражение
/ 72 72 -72 – 8*x
– cos(9 + x)*e – 8*e *sin(9 + x)/*e
————————————————
65
$$frac{1}{65} left(- 8 e^{72} sin{left (x + 9 right )} – e^{72} cos{left (x + 9 right )}right) e^{- 8 x – 72}$$
/ 72 72 -72 – 8*x
– (cos(9)*cos(x) – sin(9)*sin(x))*e – 8*(cos(9)*sin(x) + cos(x)*sin(9))*e /*e
——————————————————————————————
65
$$frac{1}{65} left(- left(- sin{left (9 right )} sin{left (x right )} + cos{left (9 right )} cos{left (x right )}right) e^{72} – 8 left(sin{left (x right )} cos{left (9 right )} + sin{left (9 right )} cos{left (x right )}right) e^{72}right) e^{- 8 x – 72}$$
