3.34.56 \(\int \frac {-1576 x^4+36 x^6+e^8 (-300 x^2-80 x^3-4 x^4)+e^4 (1600 x^3+280 x^4)}{620944 x^4+370360 x^5+83593 x^6+8460 x^7+324 x^8+e^{16} (2500+2000 x+600 x^2+80 x^3+4 x^4)+e^{12} (-40000 x-30000 x^2-8400 x^3-1040 x^4-48 x^5)+e^8 (238800 x^2+167020 x^3+43552 x^4+5020 x^5+216 x^6)+e^4 (-630400 x^3-408640 x^4-99112 x^5-10680 x^6-432 x^7)} \, dx\)

Optimal. Leaf size=35 \[ \frac {x}{6+\frac {5 x}{2}-\left (-x+\frac {(5+x) \left (-e^4+4 x\right )}{x}\right )^2} \]

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Rubi [F]  time = 1.66, 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*} \int \frac {-1576 x^4+36 x^6+e^8 \left (-300 x^2-80 x^3-4 x^4\right )+e^4 \left (1600 x^3+280 x^4\right )}{620944 x^4+370360 x^5+83593 x^6+8460 x^7+324 x^8+e^{16} \left (2500+2000 x+600 x^2+80 x^3+4 x^4\right )+e^{12} \left (-40000 x-30000 x^2-8400 x^3-1040 x^4-48 x^5\right )+e^8 \left (238800 x^2+167020 x^3+43552 x^4+5020 x^5+216 x^6\right )+e^4 \left (-630400 x^3-408640 x^4-99112 x^5-10680 x^6-432 x^7\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-1576*x^4 + 36*x^6 + E^8*(-300*x^2 - 80*x^3 - 4*x^4) + E^4*(1600*x^3 + 280*x^4))/(620944*x^4 + 370360*x^5
+ 83593*x^6 + 8460*x^7 + 324*x^8 + E^16*(2500 + 2000*x + 600*x^2 + 80*x^3 + 4*x^4) + E^12*(-40000*x - 30000*x
^2 - 8400*x^3 - 1040*x^4 - 48*x^5) + E^8*(238800*x^2 + 167020*x^3 + 43552*x^4 + 5020*x^5 + 216*x^6) + E^4*(-63
0400*x^3 - 408640*x^4 - 99112*x^5 - 10680*x^6 - 432*x^7)),x]

[Out]

(2978155 - 89676*E^4 + 4860*E^8 - 432*E^12)/(11664*(50*E^8 - 20*E^4*(20 - E^4)*x + 2*(394 - 70*E^4 + E^8)*x^2
+ (235 - 12*E^4)*x^3 + 18*x^4)) - ((26857 - 600*E^4 + 72*E^8)*Defer[Int][(-50*E^8 + 20*E^4*(20 - E^4)*x - 2*(3
94 - 70*E^4 + E^8)*x^2 - (235 - 12*E^4)*x^3 - 18*x^4)^(-1), x])/162 - (5*E^4*(59563100 + 62585*E^4 + 78876*E^8
- 540*E^12 + 432*E^16)*Defer[Int][(50*E^8 - 20*E^4*(20 - E^4)*x + 2*(394 - 70*E^4 + E^8)*x^2 + (235 - 12*E^4)
*x^3 + 18*x^4)^(-2), x])/2916 + ((1173393070 - 50432794*E^4 + 988795*E^8 - 60084*E^12 + 9180*E^16 - 432*E^20)*
Defer[Int][x/(50*E^8 - 20*E^4*(20 - E^4)*x + 2*(394 - 70*E^4 + E^8)*x^2 + (235 - 12*E^4)*x^3 + 18*x^4)^2, x])/
2916 + ((191946841 + 4167000*E^4 + 100212*E^8 + 7200*E^12 + 1728*E^16)*Defer[Int][x^2/(50*E^8 - 20*E^4*(20 - E
^4)*x + 2*(394 - 70*E^4 + E^8)*x^2 + (235 - 12*E^4)*x^3 + 18*x^4)^2, x])/3888 - ((235 - 12*E^4)*Defer[Int][x/(
50*E^8 - 20*E^4*(20 - E^4)*x + 2*(394 - 70*E^4 + E^8)*x^2 + (235 - 12*E^4)*x^3 + 18*x^4), x])/9 + 2*Defer[Int]
[x^2/(50*E^8 - 20*E^4*(20 - E^4)*x + 2*(394 - 70*E^4 + E^8)*x^2 + (235 - 12*E^4)*x^3 + 18*x^4), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {-50 e^8 \left (26857-600 e^4+72 e^8\right )+40 e^4 \left (268570-14141 e^4+750 e^8-36 e^{12}\right ) x-2 \left (10581658-1270390 e^4+44125 e^8-3480 e^{12}+72 e^{16}\right ) x^2-\left (2978155-89676 e^4+4860 e^8-432 e^{12}\right ) x^3}{162 \left (50 e^8-20 e^4 \left (20-e^4\right ) x+2 \left (394-70 e^4+e^8\right ) x^2+\left (235-12 e^4\right ) x^3+18 x^4\right )^2}+\frac {26857-600 e^4+72 e^8-18 \left (235-12 e^4\right ) x+324 x^2}{162 \left (50 e^8-20 e^4 \left (20-e^4\right ) x+2 \left (394-70 e^4+e^8\right ) x^2+\left (235-12 e^4\right ) x^3+18 x^4\right )}\right ) \, dx\\ &=\frac {1}{162} \int \frac {-50 e^8 \left (26857-600 e^4+72 e^8\right )+40 e^4 \left (268570-14141 e^4+750 e^8-36 e^{12}\right ) x-2 \left (10581658-1270390 e^4+44125 e^8-3480 e^{12}+72 e^{16}\right ) x^2-\left (2978155-89676 e^4+4860 e^8-432 e^{12}\right ) x^3}{\left (50 e^8-20 e^4 \left (20-e^4\right ) x+2 \left (394-70 e^4+e^8\right ) x^2+\left (235-12 e^4\right ) x^3+18 x^4\right )^2} \, dx+\frac {1}{162} \int \frac {26857-600 e^4+72 e^8-18 \left (235-12 e^4\right ) x+324 x^2}{50 e^8-20 e^4 \left (20-e^4\right ) x+2 \left (394-70 e^4+e^8\right ) x^2+\left (235-12 e^4\right ) x^3+18 x^4} \, dx\\ &=\frac {2978155-89676 e^4+4860 e^8-432 e^{12}}{11664 \left (50 e^8-20 e^4 \left (20-e^4\right ) x+2 \left (394-70 e^4+e^8\right ) x^2+\left (235-12 e^4\right ) x^3+18 x^4\right )}+\frac {\int \frac {-20 e^4 \left (59563100+62585 e^4+78876 e^8-540 e^{12}+432 e^{16}\right )+4 \left (1173393070-50432794 e^4+988795 e^8-60084 e^{12}+9180 e^{16}-432 e^{20}\right ) x+3 \left (191946841+4167000 e^4+100212 e^8+7200 e^{12}+1728 e^{16}\right ) x^2}{\left (50 e^8-20 e^4 \left (20-e^4\right ) x+2 \left (394-70 e^4+e^8\right ) x^2+\left (235-12 e^4\right ) x^3+18 x^4\right )^2} \, dx}{11664}+\frac {1}{162} \int \left (\frac {600 e^4 \left (1-\frac {26857+72 e^8}{600 e^4}\right )}{-50 e^8+20 e^4 \left (20-e^4\right ) x-2 \left (394-70 e^4+e^8\right ) x^2-\left (235-12 e^4\right ) x^3-18 x^4}+\frac {18 \left (-235+12 e^4\right ) x}{50 e^8-20 e^4 \left (20-e^4\right ) x+2 \left (394-70 e^4+e^8\right ) x^2+\left (235-12 e^4\right ) x^3+18 x^4}+\frac {324 x^2}{50 e^8-20 e^4 \left (20-e^4\right ) x+2 \left (394-70 e^4+e^8\right ) x^2+\left (235-12 e^4\right ) x^3+18 x^4}\right ) \, dx\\ &=\frac {2978155-89676 e^4+4860 e^8-432 e^{12}}{11664 \left (50 e^8-20 e^4 \left (20-e^4\right ) x+2 \left (394-70 e^4+e^8\right ) x^2+\left (235-12 e^4\right ) x^3+18 x^4\right )}+\frac {\int \left (\frac {20 e^4 \left (-59563100-62585 e^4-78876 e^8+540 e^{12}-432 e^{16}\right )}{\left (50 e^8-20 e^4 \left (20-e^4\right ) x+2 \left (394-70 e^4+e^8\right ) x^2+\left (235-12 e^4\right ) x^3+18 x^4\right )^2}+\frac {4 \left (1173393070-50432794 e^4+988795 e^8-60084 e^{12}+9180 e^{16}-432 e^{20}\right ) x}{\left (50 e^8-20 e^4 \left (20-e^4\right ) x+2 \left (394-70 e^4+e^8\right ) x^2+\left (235-12 e^4\right ) x^3+18 x^4\right )^2}+\frac {3 \left (191946841+4167000 e^4+100212 e^8+7200 e^{12}+1728 e^{16}\right ) x^2}{\left (50 e^8-20 e^4 \left (20-e^4\right ) x+2 \left (394-70 e^4+e^8\right ) x^2+\left (235-12 e^4\right ) x^3+18 x^4\right )^2}\right ) \, dx}{11664}+2 \int \frac {x^2}{50 e^8-20 e^4 \left (20-e^4\right ) x+2 \left (394-70 e^4+e^8\right ) x^2+\left (235-12 e^4\right ) x^3+18 x^4} \, dx+\frac {1}{9} \left (-235+12 e^4\right ) \int \frac {x}{50 e^8-20 e^4 \left (20-e^4\right ) x+2 \left (394-70 e^4+e^8\right ) x^2+\left (235-12 e^4\right ) x^3+18 x^4} \, dx+\frac {1}{162} \left (-26857+600 e^4-72 e^8\right ) \int \frac {1}{-50 e^8+20 e^4 \left (20-e^4\right ) x-2 \left (394-70 e^4+e^8\right ) x^2-\left (235-12 e^4\right ) x^3-18 x^4} \, dx\\ &=\frac {2978155-89676 e^4+4860 e^8-432 e^{12}}{11664 \left (50 e^8-20 e^4 \left (20-e^4\right ) x+2 \left (394-70 e^4+e^8\right ) x^2+\left (235-12 e^4\right ) x^3+18 x^4\right )}+2 \int \frac {x^2}{50 e^8-20 e^4 \left (20-e^4\right ) x+2 \left (394-70 e^4+e^8\right ) x^2+\left (235-12 e^4\right ) x^3+18 x^4} \, dx+\frac {1}{9} \left (-235+12 e^4\right ) \int \frac {x}{50 e^8-20 e^4 \left (20-e^4\right ) x+2 \left (394-70 e^4+e^8\right ) x^2+\left (235-12 e^4\right ) x^3+18 x^4} \, dx+\frac {1}{162} \left (-26857+600 e^4-72 e^8\right ) \int \frac {1}{-50 e^8+20 e^4 \left (20-e^4\right ) x-2 \left (394-70 e^4+e^8\right ) x^2-\left (235-12 e^4\right ) x^3-18 x^4} \, dx-\frac {\left (5 e^4 \left (59563100+62585 e^4+78876 e^8-540 e^{12}+432 e^{16}\right )\right ) \int \frac {1}{\left (50 e^8-20 e^4 \left (20-e^4\right ) x+2 \left (394-70 e^4+e^8\right ) x^2+\left (235-12 e^4\right ) x^3+18 x^4\right )^2} \, dx}{2916}+\frac {\left (191946841+4167000 e^4+100212 e^8+7200 e^{12}+1728 e^{16}\right ) \int \frac {x^2}{\left (50 e^8-20 e^4 \left (20-e^4\right ) x+2 \left (394-70 e^4+e^8\right ) x^2+\left (235-12 e^4\right ) x^3+18 x^4\right )^2} \, dx}{3888}+\frac {\left (1173393070-50432794 e^4+988795 e^8-60084 e^{12}+9180 e^{16}-432 e^{20}\right ) \int \frac {x}{\left (50 e^8-20 e^4 \left (20-e^4\right ) x+2 \left (394-70 e^4+e^8\right ) x^2+\left (235-12 e^4\right ) x^3+18 x^4\right )^2} \, dx}{2916}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.12, size = 49, normalized size = 1.40 \begin {gather*} -\frac {4 x^3}{4 e^8 (5+x)^2-8 e^4 x \left (100+35 x+3 x^2\right )+2 x^2 \left (788+235 x+18 x^2\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-1576*x^4 + 36*x^6 + E^8*(-300*x^2 - 80*x^3 - 4*x^4) + E^4*(1600*x^3 + 280*x^4))/(620944*x^4 + 3703
60*x^5 + 83593*x^6 + 8460*x^7 + 324*x^8 + E^16*(2500 + 2000*x + 600*x^2 + 80*x^3 + 4*x^4) + E^12*(-40000*x - 3
0000*x^2 - 8400*x^3 - 1040*x^4 - 48*x^5) + E^8*(238800*x^2 + 167020*x^3 + 43552*x^4 + 5020*x^5 + 216*x^6) + E^
4*(-630400*x^3 - 408640*x^4 - 99112*x^5 - 10680*x^6 - 432*x^7)),x]

[Out]

(-4*x^3)/(4*E^8*(5 + x)^2 - 8*E^4*x*(100 + 35*x + 3*x^2) + 2*x^2*(788 + 235*x + 18*x^2))

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fricas [A]  time = 0.98, size = 53, normalized size = 1.51 \begin {gather*} -\frac {2 \, x^{3}}{18 \, x^{4} + 235 \, x^{3} + 788 \, x^{2} + 2 \, {\left (x^{2} + 10 \, x + 25\right )} e^{8} - 4 \, {\left (3 \, x^{3} + 35 \, x^{2} + 100 \, x\right )} e^{4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-4*x^4-80*x^3-300*x^2)*exp(4)^2+(280*x^4+1600*x^3)*exp(4)+36*x^6-1576*x^4)/((4*x^4+80*x^3+600*x^2+
2000*x+2500)*exp(4)^4+(-48*x^5-1040*x^4-8400*x^3-30000*x^2-40000*x)*exp(4)^3+(216*x^6+5020*x^5+43552*x^4+16702
0*x^3+238800*x^2)*exp(4)^2+(-432*x^7-10680*x^6-99112*x^5-408640*x^4-630400*x^3)*exp(4)+324*x^8+8460*x^7+83593*
x^6+370360*x^5+620944*x^4),x, algorithm="fricas")

[Out]

-2*x^3/(18*x^4 + 235*x^3 + 788*x^2 + 2*(x^2 + 10*x + 25)*e^8 - 4*(3*x^3 + 35*x^2 + 100*x)*e^4)

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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(((-4*x^4-80*x^3-300*x^2)*exp(4)^2+(280*x^4+1600*x^3)*exp(4)+36*x^6-1576*x^4)/((4*x^4+80*x^3+600*x^2+
2000*x+2500)*exp(4)^4+(-48*x^5-1040*x^4-8400*x^3-30000*x^2-40000*x)*exp(4)^3+(216*x^6+5020*x^5+43552*x^4+16702
0*x^3+238800*x^2)*exp(4)^2+(-432*x^7-10680*x^6-99112*x^5-408640*x^4-630400*x^3)*exp(4)+324*x^8+8460*x^7+83593*
x^6+370360*x^5+620944*x^4),x, algorithm="giac")

[Out]

Timed out

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maple [A]  time = 0.60, size = 58, normalized size = 1.66

method	result	size
risch	\(-\frac {x^{3}}{x^{2} {\mathrm e}^{8}-6 x^{3} {\mathrm e}^{4}+9 x^{4}+10 x \,{\mathrm e}^{8}-70 x^{2} {\mathrm e}^{4}+\frac {235 x^{3}}{2}+25 \,{\mathrm e}^{8}-200 x \,{\mathrm e}^{4}+394 x^{2}}\)	\(58\)
gosper	\(-\frac {2 x^{3}}{2 x^{2} {\mathrm e}^{8}-12 x^{3} {\mathrm e}^{4}+18 x^{4}+20 x \,{\mathrm e}^{8}-140 x^{2} {\mathrm e}^{4}+235 x^{3}+50 \,{\mathrm e}^{8}-400 x \,{\mathrm e}^{4}+788 x^{2}}\)	\(65\)
norman	\(-\frac {2 x^{3}}{2 x^{2} {\mathrm e}^{8}-12 x^{3} {\mathrm e}^{4}+18 x^{4}+20 x \,{\mathrm e}^{8}-140 x^{2} {\mathrm e}^{4}+235 x^{3}+50 \,{\mathrm e}^{8}-400 x \,{\mathrm e}^{4}+788 x^{2}}\)	\(65\)
default	\(-2 \left (\munderset {\textit {\_R} =\RootOf \left (324 \textit {\_Z}^{8}+\left (-432 \,{\mathrm e}^{4}+8460\right ) \textit {\_Z}^{7}+\left (-10680 \,{\mathrm e}^{4}+216 \,{\mathrm e}^{8}+83593\right ) \textit {\_Z}^{6}+\left (-48 \,{\mathrm e}^{12}-99112 \,{\mathrm e}^{4}+5020 \,{\mathrm e}^{8}+370360\right ) \textit {\_Z}^{5}+\left (-1040 \,{\mathrm e}^{12}-408640 \,{\mathrm e}^{4}+4 \,{\mathrm e}^{16}+43552 \,{\mathrm e}^{8}+620944\right ) \textit {\_Z}^{4}+\left (-8400 \,{\mathrm e}^{12}-630400 \,{\mathrm e}^{4}+80 \,{\mathrm e}^{16}+167020 \,{\mathrm e}^{8}\right ) \textit {\_Z}^{3}+\left (-30000 \,{\mathrm e}^{12}+600 \,{\mathrm e}^{16}+238800 \,{\mathrm e}^{8}\right ) \textit {\_Z}^{2}+\left (-40000 \,{\mathrm e}^{12}+2000 \,{\mathrm e}^{16}\right ) \textit {\_Z} +2500 \,{\mathrm e}^{16}\right )}{\sum }\frac {\left (9 \textit {\_R}^{6}+\left (70 \,{\mathrm e}^{4}-{\mathrm e}^{8}-394\right ) \textit {\_R}^{4}+20 \left (20 \,{\mathrm e}^{4}-{\mathrm e}^{8}\right ) \textit {\_R}^{3}-75 \textit {\_R}^{2} {\mathrm e}^{8}\right ) \ln \left (x -\textit {\_R} \right )}{-238800 \textit {\_R} \,{\mathrm e}^{8}-29610 \textit {\_R}^{6}-1296 \textit {\_R}^{7}-250779 \textit {\_R}^{5}-925900 \textit {\_R}^{4}-1241888 \textit {\_R}^{3}-600 \textit {\_R} \,{\mathrm e}^{16}+1512 \textit {\_R}^{6} {\mathrm e}^{4}-1000 \,{\mathrm e}^{16}+945600 \textit {\_R}^{2} {\mathrm e}^{4}+120 \textit {\_R}^{4} {\mathrm e}^{12}-648 \textit {\_R}^{5} {\mathrm e}^{8}-87104 \textit {\_R}^{3} {\mathrm e}^{8}-8 \textit {\_R}^{3} {\mathrm e}^{16}-250530 \textit {\_R}^{2} {\mathrm e}^{8}+12600 \textit {\_R}^{2} {\mathrm e}^{12}-12550 \textit {\_R}^{4} {\mathrm e}^{8}+2080 \textit {\_R}^{3} {\mathrm e}^{12}+30000 \textit {\_R} \,{\mathrm e}^{12}+20000 \,{\mathrm e}^{12}+817280 \textit {\_R}^{3} {\mathrm e}^{4}+247780 \textit {\_R}^{4} {\mathrm e}^{4}+32040 \textit {\_R}^{5} {\mathrm e}^{4}-120 \textit {\_R}^{2} {\mathrm e}^{16}}\right )\)	\(327\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((-4*x^4-80*x^3-300*x^2)*exp(4)^2+(280*x^4+1600*x^3)*exp(4)+36*x^6-1576*x^4)/((4*x^4+80*x^3+600*x^2+2000*x
+2500)*exp(4)^4+(-48*x^5-1040*x^4-8400*x^3-30000*x^2-40000*x)*exp(4)^3+(216*x^6+5020*x^5+43552*x^4+167020*x^3+
238800*x^2)*exp(4)^2+(-432*x^7-10680*x^6-99112*x^5-408640*x^4-630400*x^3)*exp(4)+324*x^8+8460*x^7+83593*x^6+37
0360*x^5+620944*x^4),x,method=_RETURNVERBOSE)

[Out]

-x^3/(x^2*exp(8)-6*x^3*exp(4)+9*x^4+10*x*exp(8)-70*x^2*exp(4)+235/2*x^3+25*exp(8)-200*x*exp(4)+394*x^2)

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maxima [A]  time = 0.43, size = 51, normalized size = 1.46 \begin {gather*} -\frac {2 \, x^{3}}{18 \, x^{4} - x^{3} {\left (12 \, e^{4} - 235\right )} + 2 \, x^{2} {\left (e^{8} - 70 \, e^{4} + 394\right )} + 20 \, x {\left (e^{8} - 20 \, e^{4}\right )} + 50 \, e^{8}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-4*x^4-80*x^3-300*x^2)*exp(4)^2+(280*x^4+1600*x^3)*exp(4)+36*x^6-1576*x^4)/((4*x^4+80*x^3+600*x^2+
2000*x+2500)*exp(4)^4+(-48*x^5-1040*x^4-8400*x^3-30000*x^2-40000*x)*exp(4)^3+(216*x^6+5020*x^5+43552*x^4+16702
0*x^3+238800*x^2)*exp(4)^2+(-432*x^7-10680*x^6-99112*x^5-408640*x^4-630400*x^3)*exp(4)+324*x^8+8460*x^7+83593*
x^6+370360*x^5+620944*x^4),x, algorithm="maxima")

[Out]

-2*x^3/(18*x^4 - x^3*(12*e^4 - 235) + 2*x^2*(e^8 - 70*e^4 + 394) + 20*x*(e^8 - 20*e^4) + 50*e^8)

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mupad [B]  time = 2.30, size = 54, normalized size = 1.54 \begin {gather*} -\frac {2\,x^3}{18\,x^4+\left (235-12\,{\mathrm {e}}^4\right )\,x^3+\left (2\,{\mathrm {e}}^8-140\,{\mathrm {e}}^4+788\right )\,x^2+\left (20\,{\mathrm {e}}^8-400\,{\mathrm {e}}^4\right )\,x+50\,{\mathrm {e}}^8} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(4)*(1600*x^3 + 280*x^4) - exp(8)*(300*x^2 + 80*x^3 + 4*x^4) - 1576*x^4 + 36*x^6)/(exp(8)*(238800*x^2
+ 167020*x^3 + 43552*x^4 + 5020*x^5 + 216*x^6) - exp(4)*(630400*x^3 + 408640*x^4 + 99112*x^5 + 10680*x^6 + 432
*x^7) + exp(16)*(2000*x + 600*x^2 + 80*x^3 + 4*x^4 + 2500) - exp(12)*(40000*x + 30000*x^2 + 8400*x^3 + 1040*x^
4 + 48*x^5) + 620944*x^4 + 370360*x^5 + 83593*x^6 + 8460*x^7 + 324*x^8),x)

[Out]

-(2*x^3)/(50*exp(8) + x^2*(2*exp(8) - 140*exp(4) + 788) - x^3*(12*exp(4) - 235) - x*(400*exp(4) - 20*exp(8)) +
18*x^4)

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sympy [B]  time = 6.84, size = 53, normalized size = 1.51 \begin {gather*} - \frac {2 x^{3}}{18 x^{4} + x^{3} \left (235 - 12 e^{4}\right ) + x^{2} \left (- 140 e^{4} + 788 + 2 e^{8}\right ) + x \left (- 400 e^{4} + 20 e^{8}\right ) + 50 e^{8}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-4*x**4-80*x**3-300*x**2)*exp(4)**2+(280*x**4+1600*x**3)*exp(4)+36*x**6-1576*x**4)/((4*x**4+80*x**
3+600*x**2+2000*x+2500)*exp(4)**4+(-48*x**5-1040*x**4-8400*x**3-30000*x**2-40000*x)*exp(4)**3+(216*x**6+5020*x
**5+43552*x**4+167020*x**3+238800*x**2)*exp(4)**2+(-432*x**7-10680*x**6-99112*x**5-408640*x**4-630400*x**3)*ex
p(4)+324*x**8+8460*x**7+83593*x**6+370360*x**5+620944*x**4),x)

[Out]

-2*x**3/(18*x**4 + x**3*(235 - 12*exp(4)) + x**2*(-140*exp(4) + 788 + 2*exp(8)) + x*(-400*exp(4) + 20*exp(8))
+ 50*exp(8))

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