\(\int \frac {960+480 x+2520 x^2+360 e^3 x^2}{400-320 x-16 x^2-248 x^3+116 x^4+28 x^5+49 x^6+e^6 x^6+e^3 (-40 x^3+16 x^4+4 x^5+14 x^6)} \, dx\) [6722]

Optimal result

Integrand size = 83, antiderivative size = 34 \[ \int \frac {960+480 x+2520 x^2+360 e^3 x^2}{400-320 x-16 x^2-248 x^3+116 x^4+28 x^5+49 x^6+e^6 x^6+e^3 \left (-40 x^3+16 x^4+4 x^5+14 x^6\right )} \, dx=\frac {12}{x \left (\frac {2}{x}+\frac {1}{5} \left (-4-x-\frac {1}{2} \left (7+e^3\right ) x^2\right )\right )} \]

[Out]

12/(2/x-1/10*(7+exp(3))*x^2-4/5-1/5*x)/x

Rubi [F(-1)]

Timed out. \[ \int \frac {960+480 x+2520 x^2+360 e^3 x^2}{400-320 x-16 x^2-248 x^3+116 x^4+28 x^5+49 x^6+e^6 x^6+e^3 \left (-40 x^3+16 x^4+4 x^5+14 x^6\right )} \, dx=\text {\$Aborted} \]

[In]

Int[(960 + 480*x + 2520*x^2 + 360*E^3*x^2)/(400 - 320*x - 16*x^2 - 248*x^3 + 116*x^4 + 28*x^5 + 49*x^6 + E^6*x
^6 + E^3*(-40*x^3 + 16*x^4 + 4*x^5 + 14*x^6)),x]

[Out]

$Aborted

Rubi steps Aborted

Mathematica [A] (verified)

Time = 0.02 (sec) , antiderivative size = 23, normalized size of antiderivative = 0.68 \[ \int \frac {960+480 x+2520 x^2+360 e^3 x^2}{400-320 x-16 x^2-248 x^3+116 x^4+28 x^5+49 x^6+e^6 x^6+e^3 \left (-40 x^3+16 x^4+4 x^5+14 x^6\right )} \, dx=-\frac {120}{-20+8 x+2 x^2+\left (7+e^3\right ) x^3} \]

[In]

Integrate[(960 + 480*x + 2520*x^2 + 360*E^3*x^2)/(400 - 320*x - 16*x^2 - 248*x^3 + 116*x^4 + 28*x^5 + 49*x^6 +
E^6*x^6 + E^3*(-40*x^3 + 16*x^4 + 4*x^5 + 14*x^6)),x]

[Out]

-120/(-20 + 8*x + 2*x^2 + (7 + E^3)*x^3)

Maple [A] (verified)

Time = 0.40 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.76

method	result	size
gosper	\(-\frac {120}{x^{3} {\mathrm e}^{3}+7 x^{3}+2 x^{2}+8 x -20}\)	\(26\)
norman	\(-\frac {120}{x^{3} {\mathrm e}^{3}+7 x^{3}+2 x^{2}+8 x -20}\)	\(26\)
risch	\(-\frac {120}{x^{3} {\mathrm e}^{3}+7 x^{3}+2 x^{2}+8 x -20}\)	\(26\)
parallelrisch	\(-\frac {120}{x^{3} {\mathrm e}^{3}+7 x^{3}+2 x^{2}+8 x -20}\)	\(26\)
default	\(60 \left (\munderset {\textit {\_R} =\operatorname {RootOf}\left (400+\left ({\mathrm e}^{6}+14 \,{\mathrm e}^{3}+49\right ) \textit {\_Z}^{6}+\left (4 \,{\mathrm e}^{3}+28\right ) \textit {\_Z}^{5}+\left (16 \,{\mathrm e}^{3}+116\right ) \textit {\_Z}^{4}+\left (-40 \,{\mathrm e}^{3}-248\right ) \textit {\_Z}^{3}-16 \textit {\_Z}^{2}-320 \textit {\_Z} \right )}{\sum }\frac {\left (8+3 \left (7+{\mathrm e}^{3}\right ) \textit {\_R}^{2}+4 \textit {\_R} \right ) \ln \left (x -\textit {\_R} \right )}{-160+3 \textit {\_R}^{5} {\mathrm e}^{6}+42 \textit {\_R}^{5} {\mathrm e}^{3}+10 \textit {\_R}^{4} {\mathrm e}^{3}+147 \textit {\_R}^{5}+32 \textit {\_R}^{3} {\mathrm e}^{3}+70 \textit {\_R}^{4}-60 \textit {\_R}^{2} {\mathrm e}^{3}+232 \textit {\_R}^{3}-372 \textit {\_R}^{2}-16 \textit {\_R}}\right )\)	\(142\)

[In]

int((360*x^2*exp(3)+2520*x^2+480*x+960)/(x^6*exp(3)^2+(14*x^6+4*x^5+16*x^4-40*x^3)*exp(3)+49*x^6+28*x^5+116*x^
4-248*x^3-16*x^2-320*x+400),x,method=_RETURNVERBOSE)

[Out]

-120/(x^3*exp(3)+7*x^3+2*x^2+8*x-20)

Fricas [A] (verification not implemented)

none

Time = 0.29 (sec) , antiderivative size = 25, normalized size of antiderivative = 0.74 \[ \int \frac {960+480 x+2520 x^2+360 e^3 x^2}{400-320 x-16 x^2-248 x^3+116 x^4+28 x^5+49 x^6+e^6 x^6+e^3 \left (-40 x^3+16 x^4+4 x^5+14 x^6\right )} \, dx=-\frac {120}{x^{3} e^{3} + 7 \, x^{3} + 2 \, x^{2} + 8 \, x - 20} \]

[In]

integrate((360*x^2*exp(3)+2520*x^2+480*x+960)/(x^6*exp(3)^2+(14*x^6+4*x^5+16*x^4-40*x^3)*exp(3)+49*x^6+28*x^5+
116*x^4-248*x^3-16*x^2-320*x+400),x, algorithm="fricas")

[Out]

-120/(x^3*e^3 + 7*x^3 + 2*x^2 + 8*x - 20)

Sympy [A] (verification not implemented)

Time = 1.18 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.59 \[ \int \frac {960+480 x+2520 x^2+360 e^3 x^2}{400-320 x-16 x^2-248 x^3+116 x^4+28 x^5+49 x^6+e^6 x^6+e^3 \left (-40 x^3+16 x^4+4 x^5+14 x^6\right )} \, dx=- \frac {120}{x^{3} \cdot \left (7 + e^{3}\right ) + 2 x^{2} + 8 x - 20} \]

[In]

integrate((360*x**2*exp(3)+2520*x**2+480*x+960)/(x**6*exp(3)**2+(14*x**6+4*x**5+16*x**4-40*x**3)*exp(3)+49*x**
6+28*x**5+116*x**4-248*x**3-16*x**2-320*x+400),x)

[Out]

-120/(x**3*(7 + exp(3)) + 2*x**2 + 8*x - 20)

Maxima [A] (verification not implemented)

none

Time = 0.21 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.65 \[ \int \frac {960+480 x+2520 x^2+360 e^3 x^2}{400-320 x-16 x^2-248 x^3+116 x^4+28 x^5+49 x^6+e^6 x^6+e^3 \left (-40 x^3+16 x^4+4 x^5+14 x^6\right )} \, dx=-\frac {120}{x^{3} {\left (e^{3} + 7\right )} + 2 \, x^{2} + 8 \, x - 20} \]

[In]

integrate((360*x^2*exp(3)+2520*x^2+480*x+960)/(x^6*exp(3)^2+(14*x^6+4*x^5+16*x^4-40*x^3)*exp(3)+49*x^6+28*x^5+
116*x^4-248*x^3-16*x^2-320*x+400),x, algorithm="maxima")

[Out]

-120/(x^3*(e^3 + 7) + 2*x^2 + 8*x - 20)

Giac [A] (verification not implemented)

none

Time = 0.28 (sec) , antiderivative size = 25, normalized size of antiderivative = 0.74 \[ \int \frac {960+480 x+2520 x^2+360 e^3 x^2}{400-320 x-16 x^2-248 x^3+116 x^4+28 x^5+49 x^6+e^6 x^6+e^3 \left (-40 x^3+16 x^4+4 x^5+14 x^6\right )} \, dx=-\frac {120}{x^{3} e^{3} + 7 \, x^{3} + 2 \, x^{2} + 8 \, x - 20} \]

[In]

integrate((360*x^2*exp(3)+2520*x^2+480*x+960)/(x^6*exp(3)^2+(14*x^6+4*x^5+16*x^4-40*x^3)*exp(3)+49*x^6+28*x^5+
116*x^4-248*x^3-16*x^2-320*x+400),x, algorithm="giac")

[Out]

-120/(x^3*e^3 + 7*x^3 + 2*x^2 + 8*x - 20)

Mupad [B] (verification not implemented)

Time = 0.19 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.65 \[ \int \frac {960+480 x+2520 x^2+360 e^3 x^2}{400-320 x-16 x^2-248 x^3+116 x^4+28 x^5+49 x^6+e^6 x^6+e^3 \left (-40 x^3+16 x^4+4 x^5+14 x^6\right )} \, dx=-\frac {120}{\left ({\mathrm {e}}^3+7\right )\,x^3+2\,x^2+8\,x-20} \]

[In]

int((480*x + 360*x^2*exp(3) + 2520*x^2 + 960)/(x^6*exp(6) - 320*x - 16*x^2 - 248*x^3 + 116*x^4 + 28*x^5 + 49*x
^6 + exp(3)*(16*x^4 - 40*x^3 + 4*x^5 + 14*x^6) + 400),x)

[Out]

-120/(8*x + 2*x^2 + x^3*(exp(3) + 7) - 20)