Дано
$$frac{1}{log{left (2 right )}} left(frac{x^{3}}{3} log{left (8 x + 7 right )} – frac{x^{3}}{9} – frac{7 x^{2}}{48} + frac{49 x}{192} – frac{343}{1536} log{left (8 x + 7 right )}right)$$
Подстановка условия
$$frac{1}{log{left (2 right )}} left(frac{x^{3}}{3} log{left (8 x + 7 right )} – frac{x^{3}}{9} – frac{7 x^{2}}{48} + frac{49 x}{192} – frac{343}{1536} log{left (8 x + 7 right )}right)$$
(((-3)^3*log(8*(-3) + 7))/3 – 8*((64*(-3)^3 – 84*(-3)^2 + 147*(-3))/1536 – 343*log(8*(-3) + 7)/4096)/3)/log(2)
$$frac{1}{log{left (2 right )}} left(frac{(-3)^{3}}{3} log{left (8 (-3) + 7 right )} – frac{(-3)^{3}}{9} – frac{7 (-3)^{2}}{48} + frac{49 (-3)}{192} – frac{343}{1536} log{left (8 (-3) + 7 right )}right)$$
(((-3)^3*log(8*(-3) + 7))/3 – 8*((64*(-3)^3 – 84*(-3)^2 + 147*(-3))/1536 – 343*log(8*(-3) + 7)/4096)/3)/log(2)
$$frac{1}{log{left (2 right )}} left(frac{left(-3right)^{3}}{3} log{left (-3 cdot 8 + 7 right )} – – frac{241}{64} – frac{21}{16} – frac{343}{1536} log{left (-3 cdot 8 + 7 right )}right)$$
(325/64 – 13481*log(17)/1536 – 13481*pi*i/1536)/log(2)
$$frac{1}{log{left (2 right )}} left(- frac{13481}{1536} log{left (17 right )} + frac{325}{64} – frac{13481 pi}{1536} iright)$$
Степени
$$frac{1}{log{left (2 right )}} left(frac{x^{3}}{3} log{left (8 x + 7 right )} – frac{x^{3}}{9} + frac{7 x^{2}}{48} – frac{49 x}{192} + frac{343}{1536} log{left (8 x + 7 right )}right)$$
Численный ответ
0.322164322281845*log(8*x + 7) + 0.210393026796307*x^2 – 0.160299448987663*x^3 – 0.368187796893537*x + 0.480898346962988*x^3*log(8*x + 7)
Рациональный знаменатель
$$frac{1}{56623104 log{left (2 right )}} left(18874368 x^{3} log{left (8 x + 7 right )} – 6291456 x^{3} + 8257536 x^{2} – 14450688 x + 12644352 log{left (8 x + 7 right )}right)$$
Объединение рациональных выражений
$$frac{1}{4608 log{left (2 right )}} left(1536 x^{3} log{left (8 x + 7 right )} – 8 x left(4 x left(16 x – 21right) + 147right) + 1029 log{left (8 x + 7 right )}right)$$
Общее упрощение
3 2 3
-1176*x – 512*x + 672*x + 1029*log(7 + 8*x) + 1536*x *log(7 + 8*x)
——————————————————————–
4608*log(2)
$$frac{1}{4608 log{left (2 right )}} left(1536 x^{3} log{left (8 x + 7 right )} – 512 x^{3} + 672 x^{2} – 1176 x + 1029 log{left (8 x + 7 right )}right)$$
Соберем выражение
$$frac{1}{4608 log{left (2 right )}} left(x^{3} left(log{left (left(8 x + 7right)^{1536} right )} – 512right) + 672 x^{2} – 1176 x + log{left (left(8 x + 7right)^{1029} right )}right)$$
Общий знаменатель
3 2 3
-1176*x – 512*x + 672*x + 1029*log(7 + 8*x) + 1536*x *log(7 + 8*x)
——————————————————————–
4608*log(2)
$$frac{1}{4608 log{left (2 right )}} left(1536 x^{3} log{left (8 x + 7 right )} – 512 x^{3} + 672 x^{2} – 1176 x + 1029 log{left (8 x + 7 right )}right)$$
Комбинаторика
3 2 3
-1176*x – 512*x + 672*x + 1029*log(7 + 8*x) + 1536*x *log(7 + 8*x)
——————————————————————–
4608*log(2)
$$frac{1}{4608 log{left (2 right )}} left(1536 x^{3} log{left (8 x + 7 right )} – 512 x^{3} + 672 x^{2} – 1176 x + 1029 log{left (8 x + 7 right )}right)$$
Раскрыть выражение
3 2 3
49*x x 7*x 343*log(7 + 8*x) x *log(7 + 8*x)
– —- – — + —- + —————- + —————
192 9 48 1536 3
——————————————————-
log(2)
$$frac{1}{log{left (2 right )}} left(frac{x^{3}}{3} log{left (8 x + 7 right )} – frac{x^{3}}{9} + frac{7 x^{2}}{48} – frac{49 x}{192} + frac{343}{1536} log{left (8 x + 7 right )}right)$$
