Дано
$$frac{5 sqrt{frac{5184}{25} e^{frac{24 x}{5}} + 1}}{12 log{left (e right )}} + frac{5}{24 log{left (e right )}} log{left (sqrt{frac{5184}{25} e^{frac{24 x}{5}} + 1} – 1 right )} + frac{1}{24 log{left (e right )}} left(-1 cdot 5 log{left (sqrt{frac{5184}{25} e^{frac{24 x}{5}} + 1} + 1 right )}right)$$
Подстановка условия
$$frac{5 sqrt{frac{5184}{25} e^{frac{24 x}{5}} + 1}}{12 log{left (e right )}} + frac{5}{24 log{left (e right )}} log{left (sqrt{frac{5184}{25} e^{frac{24 x}{5}} + 1} – 1 right )} + frac{1}{24 log{left (e right )}} left(-1 cdot 5 log{left (sqrt{frac{5184}{25} e^{frac{24 x}{5}} + 1} + 1 right )}right)$$
(-5*log(sqrt((5184*E^((24*(3))/5))/25 + 1) + 1))/(24*log(E)) + (5*log(sqrt((5184*E^((24*(3))/5))/25 + 1) – 1))/(24*log(E)) + (5*sqrt((5184*E^((24*(3))/5))/25 + 1))/(12*log(E))
$$frac{5 sqrt{frac{5184}{25} e^{frac{24 (3)}{5}} + 1}}{12 log{left (e right )}} + frac{5}{24 log{left (e right )}} log{left (sqrt{frac{5184}{25} e^{frac{24 (3)}{5}} + 1} – 1 right )} + frac{1}{24 log{left (e right )}} left(-1 cdot 5 log{left (sqrt{frac{5184}{25} e^{frac{24 (3)}{5}} + 1} + 1 right )}right)$$
(-5*log(sqrt((5184*E^((24*3)/5))/25 + 1) + 1))/(24*log(E)) + (5*log(sqrt((5184*E^((24*3)/5))/25 + 1) – 1))/(24*log(E)) + (5*sqrt((5184*E^((24*3)/5))/25 + 1))/(12*log(E))
$$frac{1}{24 log{left (e right )}} left(-1 cdot 5 log{left (1 + sqrt{1 + frac{5184}{25} e^{frac{72}{5} 1}} right )}right) + frac{5}{24 log{left (e right )}} log{left (-1 + sqrt{1 + frac{5184}{25} e^{frac{72}{5} 1}} right )} + frac{5 sqrt{1 + frac{5184}{25} e^{frac{72}{5} 1}}}{12 log{left (e right )}}$$
-5*log(1 + sqrt(1 + 5184*exp(72/5)/25))/24 + 5*sqrt(1 + 5184*exp(72/5)/25)/12 + 5*log(-1 + sqrt(1 + 5184*exp(72/5)/25))/24
$$- frac{5}{24} log{left (1 + sqrt{1 + frac{5184 e^{frac{72}{5}}}{25}} right )} + frac{5}{24} log{left (-1 + sqrt{1 + frac{5184 e^{frac{72}{5}}}{25}} right )} + frac{5}{12} sqrt{1 + frac{5184 e^{frac{72}{5}}}{25}}$$
Степени
$$frac{5}{12} sqrt{frac{5184}{25} e^{frac{24 x}{5}} + 1} + frac{5}{24} log{left (sqrt{frac{5184}{25} e^{frac{24 x}{5}} + 1} – 1 right )} – frac{5}{24} log{left (sqrt{frac{5184}{25} e^{frac{24 x}{5}} + 1} + 1 right )}$$
Численный ответ
0.208333333333333*log(sqrt((5184*E^((24*x)/5))/25 + 1) – 1) + 0.416666666666667*(1.0 + 207.36*2.71828182845905^(4.8*x))^0.5 – 0.208333333333333*log(sqrt((5184*E^((24*x)/5))/25 + 1) + 1)
Рациональный знаменатель
$$frac{1}{24} left(2 sqrt{5184 e^{frac{24 x}{5}} + 25} + 5 log{left (sqrt{frac{5184}{25} e^{frac{24 x}{5}} + 1} – 1 right )} – 5 log{left (sqrt{frac{5184}{25} e^{frac{24 x}{5}} + 1} + 1 right )}right)$$
Объединение рациональных выражений
$$frac{1}{24} left(2 sqrt{5184 e^{frac{24 x}{5}} + 25} + 5 log{left (frac{1}{5} left(sqrt{5184 e^{frac{24 x}{5}} + 25} – 5right) right )} – 5 log{left (frac{1}{5} left(sqrt{5184 e^{frac{24 x}{5}} + 25} + 5right) right )}right)$$
Общее упрощение
/ _________________ / _________________
| / 24*x | | / 24*x |
| / —- | _________________ | / —- |
| / 5 | / 24*x | / 5 |
| / 25 + 5184*e | / —- | / 25 + 5184*e |
5*log|1 + ———————-| / 5 5*log|-1 + ———————-|
5 / / 25 + 5184*e 5 /
– ——————————— + ———————- + ———————————-
24 12 24
$$frac{1}{12} sqrt{5184 e^{frac{24 x}{5}} + 25} + frac{5}{24} log{left (frac{1}{5} sqrt{5184 e^{frac{24 x}{5}} + 25} – 1 right )} – frac{5}{24} log{left (frac{1}{5} sqrt{5184 e^{frac{24 x}{5}} + 25} + 1 right )}$$
Собрать выражение
/ 5
|/ _________________ |
|| / 24*x | |
|| / —- | |
|| / 5 | |
| -5 + / 25 + 5184*e / |
log|——————————| ________________
| 5 | / 24*x
|/ _________________ | / —-
|| / 24*x | | / 5
|| / —- | | / 5184*e
|| / 5 | | 5* / 1 + ———-
5 + / 25 + 5184*e / / / 25
———————————– + ————————-
24 12
$$frac{5}{12} sqrt{frac{5184}{25} e^{frac{24 x}{5}} + 1} + frac{1}{24} log{left (frac{left(sqrt{5184 e^{frac{24 x}{5}} + 25} – 5right)^{5}}{left(sqrt{5184 e^{frac{24 x}{5}} + 25} + 5right)^{5}} right )}$$
Общий знаменатель
/ ________________ / ________________
| / 24*x | | / 24*x |
| / —- | _________________ | / —- |
| / 5 | / 24*x | / 5 |
| / 5184*e | / —- | / 5184*e |
5*log|1 + / 1 + ———- | / 5 5*log|-1 + / 1 + ———- |
/ 25 / / 25 + 5184*e / 25 /
– ———————————- + ———————- + ———————————–
24 12 24
$$frac{1}{12} sqrt{5184 e^{frac{24 x}{5}} + 25} + frac{5}{24} log{left (sqrt{frac{5184}{25} e^{frac{24 x}{5}} + 1} – 1 right )} – frac{5}{24} log{left (sqrt{frac{5184}{25} e^{frac{24 x}{5}} + 1} + 1 right )}$$
Комбинаторика
/ / ________________ / ________________
| | / 24*x | _________________ | / 24*x ||
| | / —- | / 24*x | / —- ||
| | / 5 | / —- | / 5 ||
| | / 5184*e | / 5 | / 5184*e ||
-|- 5*log|-1 + / 1 + ———- | – 2*/ 25 + 5184*e + 5*log|1 + / 1 + ———- ||
/ 25 / / 25 //
———————————————————————————————————
24
$$- frac{1}{24} left(- 2 sqrt{5184 e^{frac{24 x}{5}} + 25} – 5 log{left (sqrt{frac{5184}{25} e^{frac{24 x}{5}} + 1} – 1 right )} + 5 log{left (sqrt{frac{5184}{25} e^{frac{24 x}{5}} + 1} + 1 right )}right)$$
Раскрыть выражение
/ ________________ ________________ / ________________
| / 24*x | / 24*x | / 24*x |
| / —- | / —- | / —- |
| / 5 | / 5 | / 5 |
| / 5184*E | / 5184*E | / 5184*E |
5*log| / ———- + 1 + 1| 5* / ———- + 1 5*log| / ———- + 1 – 1|
/ 25 / / 25 / 25 /
– ———————————- + ————————- + ———————————-
24*log(E) 12*log(E) 24*log(E)
$$frac{5 sqrt{frac{5184}{25} e^{frac{24 x}{5}} + 1}}{12 log{left (e right )}} + frac{5}{24 log{left (e right )}} log{left (sqrt{frac{5184}{25} e^{frac{24 x}{5}} + 1} – 1 right )} – frac{5}{24 log{left (e right )}} log{left (sqrt{frac{5184}{25} e^{frac{24 x}{5}} + 1} + 1 right )}$$
/ ________________ ________________ / ________________
| / 24*x | / 24*x | / 24*x |
| / —- | / —- | / —- |
| / 5 | / 5 | / 5 |
| / 5184*e | / 5184*e | / 5184*e |
5*log|1 + / 1 + ———- | 5* / 1 + ———- 5*log|-1 + / 1 + ———- |
/ 25 / / 25 / 25 /
– ———————————- + ————————- + ———————————–
24 12 24
$$frac{5}{12} sqrt{frac{5184}{25} e^{frac{24 x}{5}} + 1} + frac{5}{24} log{left (sqrt{frac{5184}{25} e^{frac{24 x}{5}} + 1} – 1 right )} – frac{5}{24} log{left (sqrt{frac{5184}{25} e^{frac{24 x}{5}} + 1} + 1 right )}$$
