3.12.64 \(\int \frac {8 e^4 x+e^5 (4-16 x^3)}{-x^{10}+e (-5 x^9+5 x^{12})+e^2 (-10 x^8+20 x^{11}-10 x^{14})+e^3 (-10 x^7+30 x^{10}-30 x^{13}+10 x^{16})+e^4 (-5 x^6+20 x^9-30 x^{12}+20 x^{15}-5 x^{18})+e^5 (-x^5+5 x^8-10 x^{11}+10 x^{14}-5 x^{17}+x^{20})} \, dx\)

Optimal. Leaf size=17 \[ \frac {1}{\left (x+x^2 \left (\frac {1}{e}-x^2\right )\right )^4} \]

________________________________________________________________________________________

Rubi [F]  time = 182.56, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \text {\$Aborted} \end {gather*}

Verification is not applicable to the result.

[In]

Int[(8*E^4*x + E^5*(4 - 16*x^3))/(-x^10 + E*(-5*x^9 + 5*x^12) + E^2*(-10*x^8 + 20*x^11 - 10*x^14) + E^3*(-10*x
^7 + 30*x^10 - 30*x^13 + 10*x^16) + E^4*(-5*x^6 + 20*x^9 - 30*x^12 + 20*x^15 - 5*x^18) + E^5*(-x^5 + 5*x^8 - 1
0*x^11 + 10*x^14 - 5*x^17 + x^20)),x]

[Out]

$Aborted

Rubi steps

Aborted

________________________________________________________________________________________

Mathematica [A]  time = 0.21, size = 18, normalized size = 1.06 \begin {gather*} \frac {e^4}{x^4 \left (e+x-e x^3\right )^4} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(8*E^4*x + E^5*(4 - 16*x^3))/(-x^10 + E*(-5*x^9 + 5*x^12) + E^2*(-10*x^8 + 20*x^11 - 10*x^14) + E^3*
(-10*x^7 + 30*x^10 - 30*x^13 + 10*x^16) + E^4*(-5*x^6 + 20*x^9 - 30*x^12 + 20*x^15 - 5*x^18) + E^5*(-x^5 + 5*x
^8 - 10*x^11 + 10*x^14 - 5*x^17 + x^20)),x]

[Out]

E^4/(x^4*(E + x - E*x^3)^4)

________________________________________________________________________________________

fricas [B]  time = 0.66, size = 86, normalized size = 5.06 \begin {gather*} \frac {e^{4}}{x^{8} + {\left (x^{16} - 4 \, x^{13} + 6 \, x^{10} - 4 \, x^{7} + x^{4}\right )} e^{4} - 4 \, {\left (x^{14} - 3 \, x^{11} + 3 \, x^{8} - x^{5}\right )} e^{3} + 6 \, {\left (x^{12} - 2 \, x^{9} + x^{6}\right )} e^{2} - 4 \, {\left (x^{10} - x^{7}\right )} e} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-16*x^3+4)*exp(1)^5+8*x*exp(1)^4)/((x^20-5*x^17+10*x^14-10*x^11+5*x^8-x^5)*exp(1)^5+(-5*x^18+20*x^
15-30*x^12+20*x^9-5*x^6)*exp(1)^4+(10*x^16-30*x^13+30*x^10-10*x^7)*exp(1)^3+(-10*x^14+20*x^11-10*x^8)*exp(1)^2
+(5*x^12-5*x^9)*exp(1)-x^10),x, algorithm="fricas")

[Out]

e^4/(x^8 + (x^16 - 4*x^13 + 6*x^10 - 4*x^7 + x^4)*e^4 - 4*(x^14 - 3*x^11 + 3*x^8 - x^5)*e^3 + 6*(x^12 - 2*x^9
+ x^6)*e^2 - 4*(x^10 - x^7)*e)

________________________________________________________________________________________

giac [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-16*x^3+4)*exp(1)^5+8*x*exp(1)^4)/((x^20-5*x^17+10*x^14-10*x^11+5*x^8-x^5)*exp(1)^5+(-5*x^18+20*x^
15-30*x^12+20*x^9-5*x^6)*exp(1)^4+(10*x^16-30*x^13+30*x^10-10*x^7)*exp(1)^3+(-10*x^14+20*x^11-10*x^8)*exp(1)^2
+(5*x^12-5*x^9)*exp(1)-x^10),x, algorithm="giac")

[Out]

Timed out

________________________________________________________________________________________

maple [A]  time = 1.18, size = 25, normalized size = 1.47

method	result	size
norman	\(\frac {{\mathrm e}^{4}}{x^{4} \left (x^{3} {\mathrm e}-{\mathrm e}-x \right )^{4}}\)	\(25\)
risch	\(\frac {{\mathrm e}^{4}}{x^{4} \left ({\mathrm e}^{4} x^{12}-4 x^{9} {\mathrm e}^{4}-4 \,{\mathrm e}^{3} x^{10}+6 x^{6} {\mathrm e}^{4}+12 x^{7} {\mathrm e}^{3}+6 x^{8} {\mathrm e}^{2}-4 x^{3} {\mathrm e}^{4}-12 x^{4} {\mathrm e}^{3}-12 \,{\mathrm e}^{2} x^{5}-4 x^{6} {\mathrm e}+{\mathrm e}^{4}+4 x \,{\mathrm e}^{3}+6 x^{2} {\mathrm e}^{2}+4 x^{3} {\mathrm e}+x^{4}\right )}\)	\(103\)
gosper	\(\frac {{\mathrm e}^{4}}{x^{4} \left ({\mathrm e}^{4} x^{12}-4 x^{9} {\mathrm e}^{4}-4 \,{\mathrm e}^{3} x^{10}+6 x^{6} {\mathrm e}^{4}+12 x^{7} {\mathrm e}^{3}+6 x^{8} {\mathrm e}^{2}-4 x^{3} {\mathrm e}^{4}-12 x^{4} {\mathrm e}^{3}-12 \,{\mathrm e}^{2} x^{5}-4 x^{6} {\mathrm e}+{\mathrm e}^{4}+4 x \,{\mathrm e}^{3}+6 x^{2} {\mathrm e}^{2}+4 x^{3} {\mathrm e}+x^{4}\right )}\)	\(129\)
default	\(4 \,{\mathrm e}^{4} \left (\frac {{\mathrm e}^{-25} \left ({\mathrm e}^{21}-5 \,{\mathrm e}^{18}\right )}{x}+\frac {{\mathrm e}^{21} {\mathrm e}^{-25}}{4 x^{4}}+\frac {5 \,{\mathrm e}^{-25} {\mathrm e}^{19}}{2 x^{2}}-\frac {{\mathrm e}^{-25} {\mathrm e}^{20}}{x^{3}}-\frac {{\mathrm e}^{-25} \left (\munderset {\textit {\_R} =\RootOf \left ({\mathrm e}^{5} \textit {\_Z}^{15}-5 \,{\mathrm e}^{4} \textit {\_Z}^{13}-5 \,{\mathrm e}^{5} \textit {\_Z}^{12}+10 \,{\mathrm e}^{3} \textit {\_Z}^{11}+20 \,{\mathrm e}^{4} \textit {\_Z}^{10}+\left (10 \,{\mathrm e}^{5}-10 \,{\mathrm e}^{2}\right ) \textit {\_Z}^{9}-30 \,{\mathrm e}^{3} \textit {\_Z}^{8}+\left (-30 \,{\mathrm e}^{4}+5 \,{\mathrm e}\right ) \textit {\_Z}^{7}+\left (-10 \,{\mathrm e}^{5}+20 \,{\mathrm e}^{2}\right ) \textit {\_Z}^{6}+\left (30 \,{\mathrm e}^{3}-1\right ) \textit {\_Z}^{5}+\left (20 \,{\mathrm e}^{4}-5 \,{\mathrm e}\right ) \textit {\_Z}^{4}+\left (5 \,{\mathrm e}^{5}-10 \,{\mathrm e}^{2}\right ) \textit {\_Z}^{3}-10 \textit {\_Z}^{2} {\mathrm e}^{3}-5 \textit {\_Z} \,{\mathrm e}^{4}-{\mathrm e}^{5}\right )}{\sum }\frac {\left (\left (-{\mathrm e}^{26}+5 \,{\mathrm e}^{23}\right ) \textit {\_R}^{13}-5 \textit {\_R}^{12} {\mathrm e}^{24}+\left (8 \,{\mathrm e}^{25}-25 \,{\mathrm e}^{22}\right ) \textit {\_R}^{11}+4 \textit {\_R}^{10} {\mathrm e}^{26}+50 \textit {\_R}^{9} {\mathrm e}^{21}+10 \left (-3 \,{\mathrm e}^{25}+5 \,{\mathrm e}^{22}\right ) \textit {\_R}^{8}+5 \left (-{\mathrm e}^{26}-2 \,{\mathrm e}^{23}-10 \,{\mathrm e}^{20}\right ) \textit {\_R}^{7}+10 \left (-10 \,{\mathrm e}^{21}+3 \,{\mathrm e}^{24}\right ) \textit {\_R}^{6}+5 \left (8 \,{\mathrm e}^{25}-7 \,{\mathrm e}^{22}+5 \,{\mathrm e}^{19}\right ) \textit {\_R}^{5}+75 \textit {\_R}^{4} {\mathrm e}^{20}+\left (66 \,{\mathrm e}^{21}-40 \,{\mathrm e}^{24}-5 \,{\mathrm e}^{18}\right ) \textit {\_R}^{3}+10 \left (-2 \,{\mathrm e}^{25}+{\mathrm e}^{22}-2 \,{\mathrm e}^{19}\right ) \textit {\_R}^{2}+\left (5 \,{\mathrm e}^{26}+5 \,{\mathrm e}^{23}-28 \,{\mathrm e}^{20}\right ) \textit {\_R} -14 \,{\mathrm e}^{21}+15 \,{\mathrm e}^{24}\right ) \ln \left (x -\textit {\_R} \right )}{3 \textit {\_R}^{14} {\mathrm e}^{5}-12 \,{\mathrm e}^{5} \textit {\_R}^{11}-13 \,{\mathrm e}^{4} \textit {\_R}^{12}+18 \textit {\_R}^{8} {\mathrm e}^{5}+40 \textit {\_R}^{9} {\mathrm e}^{4}+22 \,{\mathrm e}^{3} \textit {\_R}^{10}-12 \textit {\_R}^{5} {\mathrm e}^{5}-42 \textit {\_R}^{6} {\mathrm e}^{4}-48 \textit {\_R}^{7} {\mathrm e}^{3}-18 \textit {\_R}^{8} {\mathrm e}^{2}+3 \textit {\_R}^{2} {\mathrm e}^{5}+16 \textit {\_R}^{3} {\mathrm e}^{4}+30 \textit {\_R}^{4} {\mathrm e}^{3}+24 \,{\mathrm e}^{2} \textit {\_R}^{5}+7 \textit {\_R}^{6} {\mathrm e}-{\mathrm e}^{4}-4 \textit {\_R} \,{\mathrm e}^{3}-6 \textit {\_R}^{2} {\mathrm e}^{2}-4 \textit {\_R}^{3} {\mathrm e}-\textit {\_R}^{4}}\right )}{5}\right )\)	\(507\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((-16*x^3+4)*exp(1)^5+8*x*exp(1)^4)/((x^20-5*x^17+10*x^14-10*x^11+5*x^8-x^5)*exp(1)^5+(-5*x^18+20*x^15-30*
x^12+20*x^9-5*x^6)*exp(1)^4+(10*x^16-30*x^13+30*x^10-10*x^7)*exp(1)^3+(-10*x^14+20*x^11-10*x^8)*exp(1)^2+(5*x^
12-5*x^9)*exp(1)-x^10),x,method=_RETURNVERBOSE)

[Out]

exp(1)^4/x^4/(x^3*exp(1)-exp(1)-x)^4

________________________________________________________________________________________

maxima [B]  time = 0.40, size = 104, normalized size = 6.12 \begin {gather*} \frac {e^{4}}{x^{16} e^{4} - 4 \, x^{14} e^{3} - 4 \, x^{13} e^{4} + 6 \, x^{12} e^{2} + 12 \, x^{11} e^{3} + 2 \, x^{10} {\left (3 \, e^{4} - 2 \, e\right )} - 12 \, x^{9} e^{2} - x^{8} {\left (12 \, e^{3} - 1\right )} - 4 \, x^{7} {\left (e^{4} - e\right )} + 6 \, x^{6} e^{2} + 4 \, x^{5} e^{3} + x^{4} e^{4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-16*x^3+4)*exp(1)^5+8*x*exp(1)^4)/((x^20-5*x^17+10*x^14-10*x^11+5*x^8-x^5)*exp(1)^5+(-5*x^18+20*x^
15-30*x^12+20*x^9-5*x^6)*exp(1)^4+(10*x^16-30*x^13+30*x^10-10*x^7)*exp(1)^3+(-10*x^14+20*x^11-10*x^8)*exp(1)^2
+(5*x^12-5*x^9)*exp(1)-x^10),x, algorithm="maxima")

[Out]

e^4/(x^16*e^4 - 4*x^14*e^3 - 4*x^13*e^4 + 6*x^12*e^2 + 12*x^11*e^3 + 2*x^10*(3*e^4 - 2*e) - 12*x^9*e^2 - x^8*(
12*e^3 - 1) - 4*x^7*(e^4 - e) + 6*x^6*e^2 + 4*x^5*e^3 + x^4*e^4)

________________________________________________________________________________________

mupad [B]  time = 2.27, size = 105, normalized size = 6.18 \begin {gather*} \frac {{\mathrm {e}}^4}{{\mathrm {e}}^4\,x^{16}-4\,{\mathrm {e}}^3\,x^{14}-4\,{\mathrm {e}}^4\,x^{13}+6\,{\mathrm {e}}^2\,x^{12}+12\,{\mathrm {e}}^3\,x^{11}+\left (6\,{\mathrm {e}}^4-4\,\mathrm {e}\right )\,x^{10}-12\,{\mathrm {e}}^2\,x^9+\left (1-12\,{\mathrm {e}}^3\right )\,x^8+\left (4\,\mathrm {e}-4\,{\mathrm {e}}^4\right )\,x^7+6\,{\mathrm {e}}^2\,x^6+4\,{\mathrm {e}}^3\,x^5+{\mathrm {e}}^4\,x^4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(8*x*exp(4) - exp(5)*(16*x^3 - 4))/(exp(5)*(x^5 - 5*x^8 + 10*x^11 - 10*x^14 + 5*x^17 - x^20) + exp(4)*(5*
x^6 - 20*x^9 + 30*x^12 - 20*x^15 + 5*x^18) + exp(1)*(5*x^9 - 5*x^12) + exp(2)*(10*x^8 - 20*x^11 + 10*x^14) + x
^10 + exp(3)*(10*x^7 - 30*x^10 + 30*x^13 - 10*x^16)),x)

[Out]

exp(4)/(x^7*(4*exp(1) - 4*exp(4)) - x^10*(4*exp(1) - 6*exp(4)) - x^8*(12*exp(3) - 1) + x^4*exp(4) + 4*x^5*exp(
3) + 6*x^6*exp(2) - 12*x^9*exp(2) + 12*x^11*exp(3) + 6*x^12*exp(2) - 4*x^13*exp(4) - 4*x^14*exp(3) + x^16*exp(
4))

________________________________________________________________________________________

sympy [B]  time = 3.29, size = 112, normalized size = 6.59 \begin {gather*} \frac {e^{4}}{x^{16} e^{4} - 4 x^{14} e^{3} - 4 x^{13} e^{4} + 6 x^{12} e^{2} + 12 x^{11} e^{3} + x^{10} \left (- 4 e + 6 e^{4}\right ) - 12 x^{9} e^{2} + x^{8} \left (1 - 12 e^{3}\right ) + x^{7} \left (- 4 e^{4} + 4 e\right ) + 6 x^{6} e^{2} + 4 x^{5} e^{3} + x^{4} e^{4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-16*x**3+4)*exp(1)**5+8*x*exp(1)**4)/((x**20-5*x**17+10*x**14-10*x**11+5*x**8-x**5)*exp(1)**5+(-5*
x**18+20*x**15-30*x**12+20*x**9-5*x**6)*exp(1)**4+(10*x**16-30*x**13+30*x**10-10*x**7)*exp(1)**3+(-10*x**14+20
*x**11-10*x**8)*exp(1)**2+(5*x**12-5*x**9)*exp(1)-x**10),x)

[Out]

exp(4)/(x**16*exp(4) - 4*x**14*exp(3) - 4*x**13*exp(4) + 6*x**12*exp(2) + 12*x**11*exp(3) + x**10*(-4*E + 6*ex
p(4)) - 12*x**9*exp(2) + x**8*(1 - 12*exp(3)) + x**7*(-4*exp(4) + 4*E) + 6*x**6*exp(2) + 4*x**5*exp(3) + x**4*
exp(4))

________________________________________________________________________________________