Дано
$$frac{1}{sqrt{21}} log{left (frac{- sqrt{21} + frac{2 sin{left (x right )}}{cos{left (x right )} + 1} – 5}{-5 + sqrt{21} + frac{2 sin{left (x right )}}{cos{left (x right )} + 1}} right )}$$
Подстановка условия
$$frac{1}{sqrt{21}} log{left (frac{- sqrt{21} + frac{2 sin{left (x right )}}{cos{left (x right )} + 1} – 5}{-5 + sqrt{21} + frac{2 sin{left (x right )}}{cos{left (x right )} + 1}} right )}$$
log(((2*sin((-1/3)))/(1 + cos((-1/3))) – sqrt(21) – 5)/(-5 + sqrt(21) + (2*sin((-1/3)))/(1 + cos((-1/3)))))/sqrt(21)
$$frac{1}{sqrt{21}} log{left (frac{- sqrt{21} + frac{2 sin{left ((-1/3) right )}}{cos{left ((-1/3) right )} + 1} – 5}{-5 + sqrt{21} + frac{2 sin{left ((-1/3) right )}}{cos{left ((-1/3) right )} + 1}} right )}$$
log(((2*sin(-1/3))/(1 + cos(-1/3)) – sqrt(21) – 5)/(-5 + sqrt(21) + (2*sin(-1/3))/(1 + cos(-1/3))))/sqrt(21)
$$frac{1}{sqrt{21}} log{left (frac{-5 + – sqrt{21} + frac{2 sin{left (- frac{1}{3} right )}}{cos{left (- frac{1}{3} right )} + 1}}{-5 + sqrt{21} + frac{2 sin{left (- frac{1}{3} right )}}{cos{left (- frac{1}{3} right )} + 1}} right )}$$
sqrt(21)*log((-5 – sqrt(21) – 2*sin(1/3)/(1 + cos(1/3)))/(-5 + sqrt(21) – 2*sin(1/3)/(1 + cos(1/3))))/21
$$frac{sqrt{21}}{21} log{left (frac{-5 – sqrt{21} – frac{2 sin{left (frac{1}{3} right )}}{cos{left (frac{1}{3} right )} + 1}}{-5 – frac{2 sin{left (frac{1}{3} right )}}{cos{left (frac{1}{3} right )} + 1} + sqrt{21}} right )}$$
Степени
$$frac{sqrt{21}}{21} log{left (frac{-5 – sqrt{21} + frac{2 sin{left (x right )}}{cos{left (x right )} + 1}}{-5 + sqrt{21} + frac{2 sin{left (x right )}}{cos{left (x right )} + 1}} right )}$$
Численный ответ
0.218217890235992*log(((2*sin(x))/(1 + cos(x)) – sqrt(21) – 5)/(-5 + sqrt(21) + (2*sin(x))/(1 + cos(x))))
Рациональный знаменатель
$$frac{sqrt{21}}{21} log{left (- frac{2 left(- sqrt{21} + 5 – frac{2 sin{left (x right )}}{cos{left (x right )} + 1}right) sin{left (x right )} + sqrt{21} left(- 5 cos{left (x right )} + sqrt{21} cos{left (x right )} – 5 + sqrt{21} + frac{2 sin{left (x right )} cos{left (x right )}}{cos{left (x right )} + 1} + frac{2 sin{left (x right )}}{cos{left (x right )} + 1}right) – 25 cos{left (x right )} + 5 sqrt{21} cos{left (x right )} – 25 + 5 sqrt{21} + frac{10 sin{left (x right )} cos{left (x right )}}{cos{left (x right )} + 1} + frac{10 sin{left (x right )}}{cos{left (x right )} + 1}}{left(-5 + sqrt{21} + frac{2 sin{left (x right )}}{cos{left (x right )} + 1}right) left(- 5 cos{left (x right )} + sqrt{21} cos{left (x right )} – 5 + sqrt{21} + frac{2 sin{left (x right )} cos{left (x right )}}{cos{left (x right )} + 1} + frac{2 sin{left (x right )}}{cos{left (x right )} + 1}right)} right )}$$
Объединение рациональных выражений
$$frac{sqrt{21}}{21} log{left (frac{- sqrt{21} left(cos{left (x right )} + 1right) + 2 sin{left (x right )} – 5 cos{left (x right )} – 5}{left(-5 + sqrt{21}right) left(cos{left (x right )} + 1right) + 2 sin{left (x right )}} right )}$$
Общее упрощение
/ / ____
____ | 2*sin(x) – (1 + cos(x))*5 + / 21 /|
/ 21 *log|————————————-|
| / ____|
2*sin(x) + (1 + cos(x))* -5 + / 21 //
————————————————-
21
$$frac{sqrt{21}}{21} log{left (frac{- left(sqrt{21} + 5right) left(cos{left (x right )} + 1right) + 2 sin{left (x right )}}{left(-5 + sqrt{21}right) left(cos{left (x right )} + 1right) + 2 sin{left (x right )}} right )}$$
Соберем выражение
$$frac{sqrt{21}}{21} log{left (frac{- sqrt{21} + frac{2 sin{left (x right )}}{cos{left (x right )} + 1} – 5}{-5 + sqrt{21} + frac{2 sin{left (x right )}}{cos{left (x right )} + 1}} right )}$$
/ ____ / ____
____ |-5 – / 21 + 2*sin(x) + -5 – / 21 /*cos(x)|
/ 21 *log|———————————————|
| ____ / ____ |
-5 + / 21 + 2*sin(x) + -5 + / 21 /*cos(x)/
———————————————————
21
$$frac{sqrt{21}}{21} log{left (frac{2 sin{left (x right )} + left(-5 – sqrt{21}right) cos{left (x right )} – 5 – sqrt{21}}{2 sin{left (x right )} + left(-5 + sqrt{21}right) cos{left (x right )} – 5 + sqrt{21}} right )}$$
Общий знаменатель
/ ____
____ | 5 / 21 2*sin(x) |
/ 21 *log|- ———————— – ———————— + ———————————————————————|
| ____ 2*sin(x) ____ 2*sin(x) ____ ____ 2*sin(x) 2*cos(x)*sin(x)|
| -5 + / 21 + ———- -5 + / 21 + ———- -5 + / 21 – 5*cos(x) + / 21 *cos(x) + ———- + —————|
1 + cos(x) 1 + cos(x) 1 + cos(x) 1 + cos(x) /
—————————————————————————————————————————————–
21
$$frac{sqrt{21}}{21} log{left (frac{2 sin{left (x right )}}{- 5 cos{left (x right )} + sqrt{21} cos{left (x right )} – 5 + sqrt{21} + frac{2 sin{left (x right )} cos{left (x right )}}{cos{left (x right )} + 1} + frac{2 sin{left (x right )}}{cos{left (x right )} + 1}} – frac{5}{-5 + sqrt{21} + frac{2 sin{left (x right )}}{cos{left (x right )} + 1}} – frac{sqrt{21}}{-5 + sqrt{21} + frac{2 sin{left (x right )}}{cos{left (x right )} + 1}} right )}$$
Тригонометрическая часть
/ ____ 2*sin(x)
|-5 – / 21 + ———-|
____ | 1 + cos(x)|
/ 21 *log|————————|
| ____ 2*sin(x) |
|-5 + / 21 + ———-|
1 + cos(x)/
————————————
21
$$frac{sqrt{21}}{21} log{left (frac{-5 – sqrt{21} + frac{2 sin{left (x right )}}{cos{left (x right )} + 1}}{-5 + sqrt{21} + frac{2 sin{left (x right )}}{cos{left (x right )} + 1}} right )}$$
Комбинаторика
/ ____
____ | 5 / 21 2*sin(x) |
/ 21 *log|- ———————— – ———————— + ———————————————————————|
| ____ 2*sin(x) ____ 2*sin(x) ____ ____ 2*sin(x) 2*cos(x)*sin(x)|
| -5 + / 21 + ———- -5 + / 21 + ———- -5 + / 21 – 5*cos(x) + / 21 *cos(x) + ———- + —————|
1 + cos(x) 1 + cos(x) 1 + cos(x) 1 + cos(x) /
—————————————————————————————————————————————–
21
$$frac{sqrt{21}}{21} log{left (frac{2 sin{left (x right )}}{- 5 cos{left (x right )} + sqrt{21} cos{left (x right )} – 5 + sqrt{21} + frac{2 sin{left (x right )} cos{left (x right )}}{cos{left (x right )} + 1} + frac{2 sin{left (x right )}}{cos{left (x right )} + 1}} – frac{5}{-5 + sqrt{21} + frac{2 sin{left (x right )}}{cos{left (x right )} + 1}} – frac{sqrt{21}}{-5 + sqrt{21} + frac{2 sin{left (x right )}}{cos{left (x right )} + 1}} right )}$$
Раскрыть выражение
/ ____ 2*sin(x)
|-5 – / 21 + ———-|
____ | 1 + cos(x)|
/ 21 *log|————————|
| ____ 2*sin(x) |
|-5 + / 21 + ———-|
1 + cos(x)/
————————————
21
$$frac{sqrt{21}}{21} log{left (frac{-5 – sqrt{21} + frac{2 sin{left (x right )}}{cos{left (x right )} + 1}}{-5 + sqrt{21} + frac{2 sin{left (x right )}}{cos{left (x right )} + 1}} right )}$$
____ / / ____ 2*sin(x) / ____ 2*sin(x)
/ 21 *|- log|-5 + / 21 + ———-| + log|-5 – / 21 + ———-||
1 + cos(x)/ 1 + cos(x)//
————————————————————————
21
$$frac{sqrt{21}}{21} left(log{left (-5 – sqrt{21} + frac{2 sin{left (x right )}}{cos{left (x right )} + 1} right )} – log{left (-5 + sqrt{21} + frac{2 sin{left (x right )}}{cos{left (x right )} + 1} right )}right)$$
