Дано
$$frac{1}{128} left(-1 cdot 3 log{left (x^{2} + 2 x + 5 right )}right) – frac{7}{128} {atan}{left (frac{1}{4} left(2 x + 2right) right )} + frac{3}{64} log{left (x + 3 right )} – frac{13 x^{2} + 40 x + 75}{64 x^{3} + 320 x^{2} + 704 x + 960}$$
Подстановка условия
$$frac{1}{128} left(-1 cdot 3 log{left (x^{2} + 2 x + 5 right )}right) – frac{7}{128} {atan}{left (frac{1}{4} left(2 x + 2right) right )} + frac{3}{64} log{left (x + 3 right )} – frac{13 x^{2} + 40 x + 75}{64 x^{3} + 320 x^{2} + 704 x + 960}$$
(-3*log((1/3)^2 + 2*(1/3) + 5))/128 – 7*atan((2*(1/3) + 2)/4)/128 + (3*log((1/3) + 3))/64 – (13*(1/3)^2 + 40*(1/3) + 75)/(960 + 704*(1/3) + 320*(1/3)^2 + 64*(1/3)^3)
$$frac{1}{128} left(-1 cdot 3 log{left ((1/3)^{2} + 2 (1/3) + 5 right )}right) – frac{7}{128} {atan}{left (frac{1}{4} left(2 (1/3) + 2right) right )} + frac{3}{64} log{left ((1/3) + 3 right )} – frac{13 (1/3)^{2} + 40 (1/3) + 75}{64 (1/3)^{3} + 320 (1/3)^{2} + 704 (1/3) + 960}$$
(-3*log((1/3)^2 + 2/3 + 5))/128 – 7*atan((2/3 + 2)/4)/128 + (3*log(1/3 + 3))/64 – (13*(1/3)^2 + 40/3 + 75)/(960 + 704/3 + 320*(1/3)^2 + 64*(1/3)^3)
$$- frac{frac{13}{9} + frac{40}{3} + 75}{frac{64}{27} + frac{320}{9} + frac{704}{3} + 960} + frac{1}{128} left(-1 cdot 3 log{left (left(frac{1}{3}right)^{2} + frac{2}{3} + 5 right )}right) – frac{7}{128} {atan}{left (frac{1}{4} left(frac{2}{3} + 2right) right )} + frac{3}{64} log{left (frac{1}{3} + 3 right )}$$
-303/4160 – 7*atan(2/3)/128 – 3*log(3)/64 – 3*log(52)/128 + 3*log(10)/64 + 3*log(9)/128
$$- frac{3}{128} log{left (52 right )} – frac{303}{4160} – frac{3}{64} log{left (3 right )} – frac{7}{128} {atan}{left (frac{2}{3} right )} + frac{3}{128} log{left (9 right )} + frac{3}{64} log{left (10 right )}$$
Степени
$$frac{- 13 x^{2} – 40 x – 75}{64 x^{3} + 320 x^{2} + 704 x + 960} + frac{3}{64} log{left (x + 3 right )} – frac{3}{128} log{left (x^{2} + 2 x + 5 right )} – frac{7}{128} {atan}{left (frac{x}{2} + frac{1}{2} right )}$$
/1 x
7*atan|- + -| / 2 2
2 2/ 3*log5 + x + 2*x/ 3*log(3 + x) 75 + 13*x + 40*x
– ————- – ——————- + ———— – —————————-
128 128 64 3 2
960 + 64*x + 320*x + 704*x
$$- frac{13 x^{2} + 40 x + 75}{64 x^{3} + 320 x^{2} + 704 x + 960} + frac{3}{64} log{left (x + 3 right )} – frac{3}{128} log{left (x^{2} + 2 x + 5 right )} – frac{7}{128} {atan}{left (frac{x}{2} + frac{1}{2} right )}$$
Численный ответ
0.046875*log(x + 3) – 0.0234375*log(x^2 + 2*x + 5) – 0.0546875*atan((2*x + 2)/4) – (75.0 + 40.0*x + 13.0*x^2)/(960.0 + 64.0*x^3 + 320.0*x^2 + 704.0*x)
Рациональный знаменатель
$$frac{1}{128 x^{3} + 640 x^{2} + 1408 x + 1920} left(6 x^{3} log{left (x + 3 right )} – 3 x^{3} log{left (x^{2} + 2 x + 5 right )} – 7 x^{3} {atan}{left (frac{x}{2} + frac{1}{2} right )} + 30 x^{2} log{left (x + 3 right )} – 15 x^{2} log{left (x^{2} + 2 x + 5 right )} – 35 x^{2} {atan}{left (frac{x}{2} + frac{1}{2} right )} – 26 x^{2} + 66 x log{left (x + 3 right )} – 33 x log{left (x^{2} + 2 x + 5 right )} – 77 x {atan}{left (frac{x}{2} + frac{1}{2} right )} – 80 x + 90 log{left (x + 3 right )} – 45 log{left (x^{2} + 2 x + 5 right )} – 105 {atan}{left (frac{x}{2} + frac{1}{2} right )} – 150right)$$
Объединение рациональных выражений
$$frac{1}{128 x^{3} + 640 x^{2} + 1408 x + 1920} left(- 2 x left(13 x + 40right) + left(6 log{left (x + 3 right )} – 3 log{left (x left(x + 2right) + 5 right )} – 7 {atan}{left (frac{1}{2} left(x + 1right) right )}right) left(x^{3} + 5 x^{2} + 11 x + 15right) – 150right)$$
Общее упрощение
2 / /1 x / 2 / 3 2
-150 – 80*x – 26*x + |- 7*atan|- + -| – 3*log5 + x + 2*x/ + 6*log(3 + x)|*15 + x + 5*x + 11*x/
2 2/ /
—————————————————————————————————-
/ 3 2
128*15 + x + 5*x + 11*x/
$$frac{1}{128 x^{3} + 640 x^{2} + 1408 x + 1920} left(- 26 x^{2} – 80 x + left(6 log{left (x + 3 right )} – 3 log{left (x^{2} + 2 x + 5 right )} – 7 {atan}{left (frac{x}{2} + frac{1}{2} right )}right) left(x^{3} + 5 x^{2} + 11 x + 15right) – 150right)$$
Соберем выражение
$$frac{3}{64} log{left (x + 3 right )} + frac{1}{128} left(-1 cdot 3 log{left (x^{2} + 2 x + 5 right )}right) – frac{7}{128} {atan}{left (frac{1}{4} left(2 x + 2right) right )} – frac{13 x^{2} + 40 x + 75}{64 x^{3} + 320 x^{2} + 704 x + 960}$$
/1 x
7*atan|- + -| / 2 2
2 2/ 3*log5 + x + 2*x/ 3*log(3 + x) -75 – 40*x – 13*x
– ————- – ——————- + ———— + —————————-
128 128 64 3 2
960 + 64*x + 320*x + 704*x
$$frac{- 13 x^{2} – 40 x – 75}{64 x^{3} + 320 x^{2} + 704 x + 960} + frac{3}{64} log{left (x + 3 right )} – frac{3}{128} log{left (x^{2} + 2 x + 5 right )} – frac{7}{128} {atan}{left (frac{x}{2} + frac{1}{2} right )}$$
Общий знаменатель
/1 x
7*atan|- + -| / 2 2
2 2/ 3*log5 + x + 2*x/ 3*log(3 + x) 75 + 13*x + 40*x
– ————- – ——————- + ———— – —————————-
128 128 64 3 2
960 + 64*x + 320*x + 704*x
$$- frac{13 x^{2} + 40 x + 75}{64 x^{3} + 320 x^{2} + 704 x + 960} + frac{3}{64} log{left (x + 3 right )} – frac{3}{128} log{left (x^{2} + 2 x + 5 right )} – frac{7}{128} {atan}{left (frac{x}{2} + frac{1}{2} right )}$$
Комбинаторика
/ 2 / 2 /1 x 2 3 3 / 2 3 /1 x 2 / 2 / 2 2 /1 x /1 x
-|150 – 90*log(3 + x) + 26*x + 45*log5 + x + 2*x/ + 80*x + 105*atan|- + -| – 66*x*log(3 + x) – 30*x *log(3 + x) – 6*x *log(3 + x) + 3*x *log5 + x + 2*x/ + 7*x *atan|- + -| + 15*x *log5 + x + 2*x/ + 33*x*log5 + x + 2*x/ + 35*x *atan|- + -| + 77*x*atan|- + -||
2 2/ 2 2/ 2 2/ 2 2//
—————————————————————————————————————————————————————————————————————————————————————————-
/ 2
128*(3 + x)*5 + x + 2*x/
$$- frac{1}{128 left(x + 3right) left(x^{2} + 2 x + 5right)} left(- 6 x^{3} log{left (x + 3 right )} + 3 x^{3} log{left (x^{2} + 2 x + 5 right )} + 7 x^{3} {atan}{left (frac{x}{2} + frac{1}{2} right )} – 30 x^{2} log{left (x + 3 right )} + 15 x^{2} log{left (x^{2} + 2 x + 5 right )} + 35 x^{2} {atan}{left (frac{x}{2} + frac{1}{2} right )} + 26 x^{2} – 66 x log{left (x + 3 right )} + 33 x log{left (x^{2} + 2 x + 5 right )} + 77 x {atan}{left (frac{x}{2} + frac{1}{2} right )} + 80 x – 90 log{left (x + 3 right )} + 45 log{left (x^{2} + 2 x + 5 right )} + 105 {atan}{left (frac{x}{2} + frac{1}{2} right )} + 150right)$$
Раскрыть выражение
/1 x
7*atan|- + -| / 2 2
2 2/ 3*log5 + x + 2*x/ 3*log(3 + x) -75 – 40*x – 13*x
– ————- – ——————- + ———— + —————————-
128 128 64 3 2
960 + 64*x + 320*x + 704*x
$$frac{- 13 x^{2} – 40 x – 75}{64 x^{3} + 320 x^{2} + 704 x + 960} + frac{3}{64} log{left (x + 3 right )} – frac{3}{128} log{left (x^{2} + 2 x + 5 right )} – frac{7}{128} {atan}{left (frac{x}{2} + frac{1}{2} right )}$$
