Дано
$$- 6 log{left (x right )} + 34 log{left (x + 2 right )} + frac{1}{12} left(- 168 x + 42 x^{2} + 3 x^{4} – 8 x^{3}right)$$
Подстановка условия
$$- 6 log{left (x right )} + 34 log{left (x + 2 right )} + frac{1}{12} left(- 168 x + 42 x^{2} + 3 x^{4} – 8 x^{3}right)$$
34*log((3/2) + 2) – 6*log((3/2)) + (3*(3/2)^4 – 8*(3/2)^3 + 42*(3/2)^2 – 168*(3/2))/12
$$- 6 log{left ((3/2) right )} + 34 log{left ((3/2) + 2 right )} + frac{1}{12} left(- 168 (3/2) + 42 (3/2)^{2} + 3 (3/2)^{4} – 8 (3/2)^{3}right)$$
34*log(3/2 + 2) – 6*log(3/2) + (3*(3/2)^4 – 8*(3/2)^3 + 42*(3/2)^2 – 168*3/2)/12
$$frac{1}{12} left(- 252 + – 27 + 3 left(frac{3}{2}right)^{4} + 42 left(frac{3}{2}right)^{2}right) + – 6 log{left (frac{3}{2} right )} + 34 log{left (frac{3}{2} + 2 right )}$$
-903/64 – 28*log(2) – 6*log(3) + 34*log(7)
$$- 28 log{left (2 right )} – frac{903}{64} – 6 log{left (3 right )} + 34 log{left (7 right )}$$
Степени
$$frac{x^{4}}{4} – frac{2 x^{3}}{3} + frac{7 x^{2}}{2} – 14 x – 6 log{left (x right )} + 34 log{left (x + 2 right )}$$
Численный ответ
0.25*x^4 + 3.5*x^2 + 34.0*log(x + 2) – 6.0*log(x) – 14.0*x – 0.666666666666667*x^3
Рациональный знаменатель
$$frac{1}{12} left(3 x^{4} – 8 x^{3} + 42 x^{2} – 168 x – 72 log{left (x right )} + 408 log{left (x + 2 right )}right)$$
Объединение рациональных выражений
$$frac{1}{12} left(x left(x left(x left(3 x – 8right) + 42right) – 168right) – 72 log{left (x right )} + 408 log{left (x + 2 right )}right)$$
Общее упрощение
3 4 2
2*x x 7*x
-14*x – 6*log(x) + 34*log(2 + x) – —- + — + —-
3 4 2
$$frac{x^{4}}{4} – frac{2 x^{3}}{3} + frac{7 x^{2}}{2} – 14 x – 6 log{left (x right )} + 34 log{left (x + 2 right )}$$
Соберем выражение
$$frac{x^{4}}{4} – frac{2 x^{3}}{3} + frac{7 x^{2}}{2} – 14 x + log{left (frac{1}{x^{6}} left(x + 2right)^{34} right )}$$
4 3 2
3*x – 8*x + 42*x – 168*x
34*log(x + 2) + ————————— – 6*log(x)
12
$$frac{1}{12} left(- 168 x + 42 x^{2} + 3 x^{4} – 8 x^{3}right) – 6 log{left (x right )} + 34 log{left (x + 2 right )}$$
Общий знаменатель
3 4 2
2*x x 7*x
-14*x – 6*log(x) + 34*log(2 + x) – —- + — + —-
3 4 2
$$frac{x^{4}}{4} – frac{2 x^{3}}{3} + frac{7 x^{2}}{2} – 14 x – 6 log{left (x right )} + 34 log{left (x + 2 right )}$$
Комбинаторика
3 4 2
-168*x – 72*log(x) – 8*x + 3*x + 42*x + 408*log(2 + x)
———————————————————
12
$$frac{1}{12} left(3 x^{4} – 8 x^{3} + 42 x^{2} – 168 x – 72 log{left (x right )} + 408 log{left (x + 2 right )}right)$$
Раскрыть выражение
3 4 2
2*x x 7*x
-14*x – 6*log(x) + 34*log(2 + x) – —- + — + —-
3 4 2
$$frac{x^{4}}{4} – frac{2 x^{3}}{3} + frac{7 x^{2}}{2} – 14 x – 6 log{left (x right )} + 34 log{left (x + 2 right )}$$
