Дано
$$frac{216 x^{frac{7}{6}}}{343} left(- frac{7}{3} log{left (x right )} + frac{49}{36} log^{2}{left (x right )} + 2right)$$
Подстановка условия
$$frac{216 x^{frac{7}{6}}}{343} left(- frac{7}{3} log{left (x right )} + frac{49}{36} log^{2}{left (x right )} + 2right)$$
((216*(4)^(7/6))*((49*log((4))^2)/36 – 7*log((4))/3 + 2))/343
$$frac{216 (4)^{frac{7}{6}}}{343} left(- frac{7}{3} log{left ((4) right )} + frac{49}{36} log^{2}{left ((4) right )} + 2right)$$
((216*4^(7/6))*((49*log(4)^2)/36 – 7*log(4)/3 + 2))/343
$$frac{1}{343} 864 sqrt[3]{2} left(- frac{7}{3} log{left (4 right )} + frac{49}{36} log^{2}{left (4 right )} + 2right)$$
864*2^(1/3)*(2 – 7*log(4)/3 + 49*log(4)^2/36)/343
$$frac{864 sqrt[3]{2}}{343} left(- frac{7}{3} log{left (4 right )} + 2 + frac{49}{36} log^{2}{left (4 right )}right)$$
Степени
$$x^{frac{7}{6}} left(frac{6}{7} log^{2}{left (x right )} – frac{72}{49} log{left (x right )} + frac{432}{343}right)$$
/ 2
7/6 | 7*log(x) 49*log (x)|
216*x *|2 – ——– + ———-|
3 36 /
————————————
343
$$frac{216 x^{frac{7}{6}}}{343} left(frac{49}{36} log^{2}{left (x right )} – frac{7}{3} log{left (x right )} + 2right)$$
Численный ответ
0.629737609329446*x^1.16666666666667*(2.0 + 1.36111111111111*log(x)^2 – 2.33333333333333*log(x))
Рациональный знаменатель
$$frac{2 x^{frac{7}{6}}}{343} left(147 log^{2}{left (x right )} – 252 log{left (x right )} + 216right)$$
Объединение рациональных выражений
$$frac{6 x^{frac{7}{6}}}{343} left(7 left(7 log{left (x right )} – 12right) log{left (x right )} + 72right)$$
Общее упрощение
7/6 / 2
6*x *72 – 84*log(x) + 49*log (x)/
————————————
343
$$frac{6 x^{frac{7}{6}}}{343} left(49 log^{2}{left (x right )} – 84 log{left (x right )} + 72right)$$
Соберем выражение
$$frac{x^{frac{7}{6}}}{343} left(294 log^{2}{left (x right )} – log{left (x^{504} right )} + 432right)$$
Общий знаменатель
7/6 7/6 7/6 2
432*x 72*x *log(x) 6*x *log (x)
——– – ————– + ————–
343 49 7
$$frac{6 x^{frac{7}{6}}}{7} log^{2}{left (x right )} – frac{72 x^{frac{7}{6}}}{49} log{left (x right )} + frac{432 x^{frac{7}{6}}}{343}$$
Комбинаторика
7/6 / 2
6*x *72 – 84*log(x) + 49*log (x)/
————————————
343
$$frac{6 x^{frac{7}{6}}}{343} left(49 log^{2}{left (x right )} – 84 log{left (x right )} + 72right)$$
Раскрыть выражение
/ 2
7/6 | 7*log(x) 49*log (x)|
216*x *|2 – ——– + ———-|
3 36 /
————————————
343
$$frac{216 x^{frac{7}{6}}}{343} left(frac{49}{36} log^{2}{left (x right )} – frac{7}{3} log{left (x right )} + 2right)$$
