\(\int -\frac {100 e^{\frac {-20711+6912 x-864 x^2+48 x^3-x^4}{20736-6912 x+864 x^2-48 x^3+x^4}}}{-248832+103680 x-17280 x^2+1440 x^3-60 x^4+x^5} \, dx\) [6697]

Optimal result

Integrand size = 70, antiderivative size = 11 \[ \int -\frac {100 e^{\frac {-20711+6912 x-864 x^2+48 x^3-x^4}{20736-6912 x+864 x^2-48 x^3+x^4}}}{-248832+103680 x-17280 x^2+1440 x^3-60 x^4+x^5} \, dx=e^{-1+\frac {25}{(-12+x)^4}} \]

[Out]

exp(25/(x-12)^4-1)

Rubi [F]

\[ \int -\frac {100 e^{\frac {-20711+6912 x-864 x^2+48 x^3-x^4}{20736-6912 x+864 x^2-48 x^3+x^4}}}{-248832+103680 x-17280 x^2+1440 x^3-60 x^4+x^5} \, dx=\int -\frac {100 \exp \left (\frac {-20711+6912 x-864 x^2+48 x^3-x^4}{20736-6912 x+864 x^2-48 x^3+x^4}\right )}{-248832+103680 x-17280 x^2+1440 x^3-60 x^4+x^5} \, dx \]

[In]

Int[(-100*E^((-20711 + 6912*x - 864*x^2 + 48*x^3 - x^4)/(20736 - 6912*x + 864*x^2 - 48*x^3 + x^4)))/(-248832 +
103680*x - 17280*x^2 + 1440*x^3 - 60*x^4 + x^5),x]

[Out]

-100*Defer[Int][1/(E^((20711 - 6912*x + 864*x^2 - 48*x^3 + x^4)/(-12 + x)^4)*(-12 + x)^5), x]

Rubi steps \begin{align*} \text {integral}& = -\left (100 \int \frac {\exp \left (\frac {-20711+6912 x-864 x^2+48 x^3-x^4}{20736-6912 x+864 x^2-48 x^3+x^4}\right )}{-248832+103680 x-17280 x^2+1440 x^3-60 x^4+x^5} \, dx\right ) \\ & = -\left (100 \int \frac {e^{-\frac {20711-6912 x+864 x^2-48 x^3+x^4}{(-12+x)^4}}}{(-12+x)^5} \, dx\right ) \\ \end{align*}

Mathematica [A] (verified)

Time = 0.13 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.00 \[ \int -\frac {100 e^{\frac {-20711+6912 x-864 x^2+48 x^3-x^4}{20736-6912 x+864 x^2-48 x^3+x^4}}}{-248832+103680 x-17280 x^2+1440 x^3-60 x^4+x^5} \, dx=e^{-1+\frac {25}{(-12+x)^4}} \]

[In]

Integrate[(-100*E^((-20711 + 6912*x - 864*x^2 + 48*x^3 - x^4)/(20736 - 6912*x + 864*x^2 - 48*x^3 + x^4)))/(-24
8832 + 103680*x - 17280*x^2 + 1440*x^3 - 60*x^4 + x^5),x]

[Out]

E^(-1 + 25/(-12 + x)^4)

Maple [A] (verified)

Time = 0.28 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.09

method	result	size
derivativedivides	\({\mathrm e}^{\frac {25}{\left (x -12\right )^{4}}} {\mathrm e}^{-1}\)	\(12\)
default	\({\mathrm e}^{\frac {25}{\left (x -12\right )^{4}}} {\mathrm e}^{-1}\)	\(12\)
risch	\({\mathrm e}^{-\frac {\left (x^{2}-24 x +149\right ) \left (x^{2}-24 x +139\right )}{\left (x -12\right )^{4}}}\)	\(25\)
gosper	\({\mathrm e}^{-\frac {x^{4}-48 x^{3}+864 x^{2}-6912 x +20711}{x^{4}-48 x^{3}+864 x^{2}-6912 x +20736}}\)	\(42\)
parallelrisch	\({\mathrm e}^{-\frac {x^{4}-48 x^{3}+864 x^{2}-6912 x +20711}{x^{4}-48 x^{3}+864 x^{2}-6912 x +20736}}\)	\(42\)
norman	\(\frac {x^{4} {\mathrm e}^{\frac {-x^{4}+48 x^{3}-864 x^{2}+6912 x -20711}{x^{4}-48 x^{3}+864 x^{2}-6912 x +20736}}-6912 x \,{\mathrm e}^{\frac {-x^{4}+48 x^{3}-864 x^{2}+6912 x -20711}{x^{4}-48 x^{3}+864 x^{2}-6912 x +20736}}+864 x^{2} {\mathrm e}^{\frac {-x^{4}+48 x^{3}-864 x^{2}+6912 x -20711}{x^{4}-48 x^{3}+864 x^{2}-6912 x +20736}}-48 x^{3} {\mathrm e}^{\frac {-x^{4}+48 x^{3}-864 x^{2}+6912 x -20711}{x^{4}-48 x^{3}+864 x^{2}-6912 x +20736}}+20736 \,{\mathrm e}^{\frac {-x^{4}+48 x^{3}-864 x^{2}+6912 x -20711}{x^{4}-48 x^{3}+864 x^{2}-6912 x +20736}}}{\left (x -12\right )^{4}}\)	\(237\)

[In]

int(-100*exp((-x^4+48*x^3-864*x^2+6912*x-20711)/(x^4-48*x^3+864*x^2-6912*x+20736))/(x^5-60*x^4+1440*x^3-17280*
x^2+103680*x-248832),x,method=_RETURNVERBOSE)

[Out]

exp(1/(x-12)^4)^25*exp(-1)

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 41 vs. \(2 (10) = 20\).

Time = 0.30 (sec) , antiderivative size = 41, normalized size of antiderivative = 3.73 \[ \int -\frac {100 e^{\frac {-20711+6912 x-864 x^2+48 x^3-x^4}{20736-6912 x+864 x^2-48 x^3+x^4}}}{-248832+103680 x-17280 x^2+1440 x^3-60 x^4+x^5} \, dx=e^{\left (-\frac {x^{4} - 48 \, x^{3} + 864 \, x^{2} - 6912 \, x + 20711}{x^{4} - 48 \, x^{3} + 864 \, x^{2} - 6912 \, x + 20736}\right )} \]

[In]

integrate(-100*exp((-x^4+48*x^3-864*x^2+6912*x-20711)/(x^4-48*x^3+864*x^2-6912*x+20736))/(x^5-60*x^4+1440*x^3-
17280*x^2+103680*x-248832),x, algorithm="fricas")

[Out]

e^(-(x^4 - 48*x^3 + 864*x^2 - 6912*x + 20711)/(x^4 - 48*x^3 + 864*x^2 - 6912*x + 20736))

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 37 vs. \(2 (8) = 16\).

Time = 0.11 (sec) , antiderivative size = 37, normalized size of antiderivative = 3.36 \[ \int -\frac {100 e^{\frac {-20711+6912 x-864 x^2+48 x^3-x^4}{20736-6912 x+864 x^2-48 x^3+x^4}}}{-248832+103680 x-17280 x^2+1440 x^3-60 x^4+x^5} \, dx=e^{\frac {- x^{4} + 48 x^{3} - 864 x^{2} + 6912 x - 20711}{x^{4} - 48 x^{3} + 864 x^{2} - 6912 x + 20736}} \]

[In]

integrate(-100*exp((-x**4+48*x**3-864*x**2+6912*x-20711)/(x**4-48*x**3+864*x**2-6912*x+20736))/(x**5-60*x**4+1
440*x**3-17280*x**2+103680*x-248832),x)

[Out]

exp((-x**4 + 48*x**3 - 864*x**2 + 6912*x - 20711)/(x**4 - 48*x**3 + 864*x**2 - 6912*x + 20736))

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 25 vs. \(2 (10) = 20\).

Time = 0.22 (sec) , antiderivative size = 25, normalized size of antiderivative = 2.27 \[ \int -\frac {100 e^{\frac {-20711+6912 x-864 x^2+48 x^3-x^4}{20736-6912 x+864 x^2-48 x^3+x^4}}}{-248832+103680 x-17280 x^2+1440 x^3-60 x^4+x^5} \, dx=e^{\left (\frac {25}{x^{4} - 48 \, x^{3} + 864 \, x^{2} - 6912 \, x + 20736} - 1\right )} \]

[In]

integrate(-100*exp((-x^4+48*x^3-864*x^2+6912*x-20711)/(x^4-48*x^3+864*x^2-6912*x+20736))/(x^5-60*x^4+1440*x^3-
17280*x^2+103680*x-248832),x, algorithm="maxima")

[Out]

e^(25/(x^4 - 48*x^3 + 864*x^2 - 6912*x + 20736) - 1)

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 122 vs. \(2 (10) = 20\).

Time = 0.29 (sec) , antiderivative size = 122, normalized size of antiderivative = 11.09 \[ \int -\frac {100 e^{\frac {-20711+6912 x-864 x^2+48 x^3-x^4}{20736-6912 x+864 x^2-48 x^3+x^4}}}{-248832+103680 x-17280 x^2+1440 x^3-60 x^4+x^5} \, dx=e^{\left (-\frac {x^{4}}{x^{4} - 48 \, x^{3} + 864 \, x^{2} - 6912 \, x + 20736} + \frac {48 \, x^{3}}{x^{4} - 48 \, x^{3} + 864 \, x^{2} - 6912 \, x + 20736} - \frac {864 \, x^{2}}{x^{4} - 48 \, x^{3} + 864 \, x^{2} - 6912 \, x + 20736} + \frac {6912 \, x}{x^{4} - 48 \, x^{3} + 864 \, x^{2} - 6912 \, x + 20736} - \frac {20711}{x^{4} - 48 \, x^{3} + 864 \, x^{2} - 6912 \, x + 20736}\right )} \]

[In]

integrate(-100*exp((-x^4+48*x^3-864*x^2+6912*x-20711)/(x^4-48*x^3+864*x^2-6912*x+20736))/(x^5-60*x^4+1440*x^3-
17280*x^2+103680*x-248832),x, algorithm="giac")

[Out]

e^(-x^4/(x^4 - 48*x^3 + 864*x^2 - 6912*x + 20736) + 48*x^3/(x^4 - 48*x^3 + 864*x^2 - 6912*x + 20736) - 864*x^2
/(x^4 - 48*x^3 + 864*x^2 - 6912*x + 20736) + 6912*x/(x^4 - 48*x^3 + 864*x^2 - 6912*x + 20736) - 20711/(x^4 - 4
8*x^3 + 864*x^2 - 6912*x + 20736))

Mupad [B] (verification not implemented)

Time = 11.70 (sec) , antiderivative size = 126, normalized size of antiderivative = 11.45 \[ \int -\frac {100 e^{\frac {-20711+6912 x-864 x^2+48 x^3-x^4}{20736-6912 x+864 x^2-48 x^3+x^4}}}{-248832+103680 x-17280 x^2+1440 x^3-60 x^4+x^5} \, dx={\mathrm {e}}^{\frac {6912\,x}{x^4-48\,x^3+864\,x^2-6912\,x+20736}}\,{\mathrm {e}}^{-\frac {x^4}{x^4-48\,x^3+864\,x^2-6912\,x+20736}}\,{\mathrm {e}}^{\frac {48\,x^3}{x^4-48\,x^3+864\,x^2-6912\,x+20736}}\,{\mathrm {e}}^{-\frac {864\,x^2}{x^4-48\,x^3+864\,x^2-6912\,x+20736}}\,{\mathrm {e}}^{-\frac {20711}{x^4-48\,x^3+864\,x^2-6912\,x+20736}} \]

[In]

int(-(100*exp(-(864*x^2 - 6912*x - 48*x^3 + x^4 + 20711)/(864*x^2 - 6912*x - 48*x^3 + x^4 + 20736)))/(103680*x
- 17280*x^2 + 1440*x^3 - 60*x^4 + x^5 - 248832),x)

[Out]

exp((6912*x)/(864*x^2 - 6912*x - 48*x^3 + x^4 + 20736))*exp(-x^4/(864*x^2 - 6912*x - 48*x^3 + x^4 + 20736))*ex
p((48*x^3)/(864*x^2 - 6912*x - 48*x^3 + x^4 + 20736))*exp(-(864*x^2)/(864*x^2 - 6912*x - 48*x^3 + x^4 + 20736)
)*exp(-20711/(864*x^2 - 6912*x - 48*x^3 + x^4 + 20736))