Дано
$$frac{2 left(sqrt{x} log{left (13 right )} – 1right)}{log^{2}{left (13 right )}} e^{sqrt{x} log{left (13 right )}}$$
Подстановка условия
$$frac{2 left(sqrt{x} log{left (13 right )} – 1right)}{log^{2}{left (13 right )}} e^{sqrt{x} log{left (13 right )}}$$
((2*(log(13)*sqrt((1/3)) – 1))*E^(log(13)*sqrt((1/3))))/log(13)^2
$$frac{2 left(sqrt{(1/3)} log{left (13 right )} – 1right)}{log^{2}{left (13 right )}} e^{sqrt{(1/3)} log{left (13 right )}}$$
((2*(log(13)*sqrt(1/3) – 1))*E^(log(13)*sqrt(1/3)))/log(13)^2
$$frac{2 left(-1 + frac{1}{sqrt{3}} log{left (13 right )}right)}{log^{2}{left (13 right )}} e^{frac{1}{sqrt{3}} log{left (13 right )}}$$
13^(sqrt(3)/3)*(-2 + 2*sqrt(3)*log(13)/3)/log(13)^2
$$frac{13^{frac{sqrt{3}}{3}}}{log^{2}{left (13 right )}} left(-2 + frac{2 sqrt{3}}{3} log{left (13 right )}right)$$
Степени
$$frac{e^{sqrt{x} log{left (13 right )}}}{log^{2}{left (13 right )}} left(2 sqrt{x} log{left (13 right )} – 2right)$$
Численный ответ
0.303999175747568*2.71828182845905^(2.56494935746154*x^0.5)*(-1.0 + 2.56494935746154*x^0.5)
Рациональный знаменатель
$$frac{1}{log^{2}{left (13 right )}} left(2 sqrt{x} e^{sqrt{x} log{left (13 right )}} log{left (13 right )} – 2 e^{sqrt{x} log{left (13 right )}}right)$$
Объединение рациональных выражений
$$frac{e^{sqrt{x} log{left (13 right )}}}{log^{2}{left (13 right )}} left(2 sqrt{x} log{left (13 right )} – 2right)$$
Общее упрощение
___
/ ___ / x *log(13)
2* -1 + / x *log(13)/*e
————————————-
2
log (13)
$$frac{2 e^{sqrt{x} log{left (13 right )}}}{log^{2}{left (13 right )}} left(sqrt{x} log{left (13 right )} – 1right)$$
Соберем выражение
$$frac{e^{sqrt{x} log{left (13 right )}}}{log^{2}{left (13 right )}} left(2 sqrt{x} log{left (13 right )} – 2right)$$
___ ___
/ x *log(13) ___ / x *log(13)
– 2*e + / x *e *log(169)
————————————————–
2
log (13)
$$frac{1}{log^{2}{left (13 right )}} left(sqrt{x} e^{sqrt{x} log{left (13 right )}} log{left (169 right )} – 2 e^{sqrt{x} log{left (13 right )}}right)$$
___
/ ___ log(13)*/ x
-2 + 2*/ x *log(13)/*e
————————————-
2
log (13)
$$frac{e^{sqrt{x} log{left (13 right )}}}{log^{2}{left (13 right )}} left(2 sqrt{x} log{left (13 right )} – 2right)$$
Общий знаменатель
___ ___
/ x *log(13) ___ / x *log(13)
– 2*e + 2*/ x *e *log(13)
—————————————————
2
log (13)
$$frac{1}{log^{2}{left (13 right )}} left(2 sqrt{x} e^{sqrt{x} log{left (13 right )}} log{left (13 right )} – 2 e^{sqrt{x} log{left (13 right )}}right)$$
Комбинаторика
___
/ ___ / x *log(13)
2* -1 + / x *log(13)/*e
————————————-
2
log (13)
$$frac{2 e^{sqrt{x} log{left (13 right )}}}{log^{2}{left (13 right )}} left(sqrt{x} log{left (13 right )} – 1right)$$
Раскрыть выражение
___
/ ___ / x *log(13)
2* -1 + / x *log(13)/*e
————————————-
2
log (13)
$$frac{2 e^{sqrt{x} log{left (13 right )}}}{log^{2}{left (13 right )}} left(sqrt{x} log{left (13 right )} – 1right)$$
