Дано
$$3 left(- 27 log{left (x right )} + 27 log{left (3 x – 1 right )} + frac{1}{6 x^{3}} left(54 x^{2} + 9 x + 2right)right)$$
Подстановка условия
$$3 left(- 27 log{left (x right )} + 27 log{left (3 x – 1 right )} + frac{1}{6 x^{3}} left(54 x^{2} + 9 x + 2right)right)$$
3*(27*log(3*(2) – 1) – 27*log((2)) + (54*(2)^2 + 9*(2) + 2)/(6*(2)^3))
$$3 left(- 27 log{left ((2) right )} + 27 log{left (3 (2) – 1 right )} + frac{1}{6 (2)^{3}} left(54 (2)^{2} + 9 (2) + 2right)right)$$
3*(27*log(3*2 – 1) – 27*log(2) + (54*2^2 + 9*2 + 2)/(6*2^3))
$$3 left(frac{1}{6 cdot 2^{3}} left(2 + 2 cdot 9 + 54 cdot 2^{2}right) + – 27 log{left (2 right )} + 27 log{left (-1 + 2 cdot 3 right )}right)$$
59/4 – 81*log(2) + 81*log(5)
$$- 81 log{left (2 right )} + frac{59}{4} + 81 log{left (5 right )}$$
Степени
$$- 81 log{left (x right )} + 81 log{left (3 x – 1 right )} + frac{1}{x^{3}} left(27 x^{2} + frac{9 x}{2} + 1right)$$
2
2 + 9*x + 54*x
-81*log(x) + 81*log(-1 + 3*x) + —————
3
2*x
$$- 81 log{left (x right )} + 81 log{left (3 x – 1 right )} + frac{1}{2 x^{3}} left(54 x^{2} + 9 x + 2right)$$
Численный ответ
81.0*log(3*x – 1) – 81.0*log(x) + 0.5*(2.0 + 9.0*x + 54.0*x^2)/x^3
Рациональный знаменатель
$$frac{1}{6 x^{3}} left(- 486 x^{3} log{left (x right )} + 486 x^{3} log{left (3 x – 1 right )} + 162 x^{2} + 27 x + 6right)$$
Объединение рациональных выражений
$$frac{1}{2 x^{3}} left(162 x^{3} left(- log{left (x right )} + log{left (3 x – 1 right )}right) + 9 x left(6 x + 1right) + 2right)$$
Общее упрощение
1 27 9
— – 81*log(x) + — + 81*log(-1 + 3*x) + —-
3 x 2
x 2*x
$$- 81 log{left (x right )} + 81 log{left (3 x – 1 right )} + frac{27}{x} + frac{9}{2 x^{2}} + frac{1}{x^{3}}$$
Соберем выражение
$$frac{1}{2 x^{3}} left(- x^{3} log{left (frac{x^{162}}{left(3 x – 1right)^{162}} right )} + 54 x^{2} + 9 x + 2right)$$
/ 2
3*54*x + 9*x + 2/
81*log(3*x – 1) – 3*27*log(x) + ——————-
3
6*x
$$- 81 log{left (x right )} + 81 log{left (3 x – 1 right )} + frac{1}{6 x^{3}} left(3 left(54 x^{2} + 9 xright) + 6right)$$
Общий знаменатель
2
2 + 9*x + 54*x
-81*log(x) + 81*log(-1 + 3*x) + —————
3
2*x
$$- 81 log{left (x right )} + 81 log{left (3 x – 1 right )} + frac{1}{2 x^{3}} left(54 x^{2} + 9 x + 2right)$$
Комбинаторика
2 3 3
2 + 9*x + 54*x – 162*x *log(x) + 162*x *log(-1 + 3*x)
——————————————————
3
2*x
$$frac{1}{2 x^{3}} left(- 162 x^{3} log{left (x right )} + 162 x^{3} log{left (3 x – 1 right )} + 54 x^{2} + 9 x + 2right)$$
Раскрыть выражение
2
54*x + 9*x + 2
81*log(3*x – 1) + ————— – 3*27*log(x)
3
2*x
$$- 81 log{left (x right )} + 81 log{left (3 x – 1 right )} + frac{1}{2 x^{3}} left(54 x^{2} + 9 x + 2right)$$
2
2 + 9*x + 54*x
-81*log(x) + 81*log(-1 + 3*x) + —————
3
2*x
$$- 81 log{left (x right )} + 81 log{left (3 x – 1 right )} + frac{1}{2 x^{3}} left(54 x^{2} + 9 x + 2right)$$
