3.93.53 \(\int \frac {e^{\frac {28561-3042 e x+81 e^2 x^2+e^{30/x} (2426112-11664 e x-8748 e^2 x^2)+e^{10/x} (316368+1404 e x-972 e^2 x^2)+e^{20/x} (1314144+50382 e x+4374 e^2 x^2)+e^{40/x} (1679616-209952 e x+6561 e^2 x^2)}{81-972 e^{10/x}+4374 e^{20/x}-8748 e^{30/x}+6561 e^{40/x}}} (1014 e x^2-54 e^2 x^3+e^{50/x} (-209952 e x^2+13122 e^2 x^3)+e^{20/x} (18252000-4860 e^2 x^3+e (378000 x-15390 x^2))+e^{10/x} (2197000+810 e^2 x^3+e (-117000 x-3510 x^2))+e^{30/x} (50544000+14580 e^2 x^3+e (891000 x+54270 x^2))+e^{40/x} (46656000-21870 e^2 x^3+e (-2916000 x+58320 x^2)))}{-27 x^2+405 e^{10/x} x^2-2430 e^{20/x} x^2+7290 e^{30/x} x^2-10935 e^{40/x} x^2+6561 e^{50/x} x^2} \, dx\)

Optimal. Leaf size=30 \[ e^{\left (\left (4-\frac {25}{3 \left (1-3 e^{10/x}\right )}\right )^2-e x\right )^2} \]

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Rubi [F]  time = 76.78, 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 {\exp \left (\frac {28561-3042 e x+81 e^2 x^2+e^{30/x} \left (2426112-11664 e x-8748 e^2 x^2\right )+e^{10/x} \left (316368+1404 e x-972 e^2 x^2\right )+e^{20/x} \left (1314144+50382 e x+4374 e^2 x^2\right )+e^{40/x} \left (1679616-209952 e x+6561 e^2 x^2\right )}{81-972 e^{10/x}+4374 e^{20/x}-8748 e^{30/x}+6561 e^{40/x}}\right ) \left (1014 e x^2-54 e^2 x^3+e^{50/x} \left (-209952 e x^2+13122 e^2 x^3\right )+e^{20/x} \left (18252000-4860 e^2 x^3+e \left (378000 x-15390 x^2\right )\right )+e^{10/x} \left (2197000+810 e^2 x^3+e \left (-117000 x-3510 x^2\right )\right )+e^{30/x} \left (50544000+14580 e^2 x^3+e \left (891000 x+54270 x^2\right )\right )+e^{40/x} \left (46656000-21870 e^2 x^3+e \left (-2916000 x+58320 x^2\right )\right )\right )}{-27 x^2+405 e^{10/x} x^2-2430 e^{20/x} x^2+7290 e^{30/x} x^2-10935 e^{40/x} x^2+6561 e^{50/x} x^2} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^((28561 - 3042*E*x + 81*E^2*x^2 + E^(30/x)*(2426112 - 11664*E*x - 8748*E^2*x^2) + E^(10/x)*(316368 + 14
04*E*x - 972*E^2*x^2) + E^(20/x)*(1314144 + 50382*E*x + 4374*E^2*x^2) + E^(40/x)*(1679616 - 209952*E*x + 6561*
E^2*x^2))/(81 - 972*E^(10/x) + 4374*E^(20/x) - 8748*E^(30/x) + 6561*E^(40/x)))*(1014*E*x^2 - 54*E^2*x^3 + E^(5
0/x)*(-209952*E*x^2 + 13122*E^2*x^3) + E^(20/x)*(18252000 - 4860*E^2*x^3 + E*(378000*x - 15390*x^2)) + E^(10/x
)*(2197000 + 810*E^2*x^3 + E*(-117000*x - 3510*x^2)) + E^(30/x)*(50544000 + 14580*E^2*x^3 + E*(891000*x + 5427
0*x^2)) + E^(40/x)*(46656000 - 21870*E^2*x^3 + E*(-2916000*x + 58320*x^2))))/(-27*x^2 + 405*E^(10/x)*x^2 - 243
0*E^(20/x)*x^2 + 7290*E^(30/x)*x^2 - 10935*E^(40/x)*x^2 + 6561*E^(50/x)*x^2),x]

[Out]

-32*Defer[Int][E^(1 + (-169 - 936*E^(10/x) - 1296*E^(20/x) + 9*E*x - 54*E^(1 + 10/x)*x + 81*E^(1 + 20/x)*x)^2/
(81*(-1 + 3*E^(10/x))^4)), x] - (1250*Defer[Int][E^(1 + (-169 - 936*E^(10/x) - 1296*E^(20/x) + 9*E*x - 54*E^(1
+ 10/x)*x + 81*E^(1 + 20/x)*x)^2/(81*(-1 + 3*E^(10/x))^4))/(-1 + 3*E^(10/x))^2, x])/9 - (400*Defer[Int][E^(1
+ (-169 - 936*E^(10/x) - 1296*E^(20/x) + 9*E*x - 54*E^(1 + 10/x)*x + 81*E^(1 + 20/x)*x)^2/(81*(-1 + 3*E^(10/x)
)^4))/(-1 + 3*E^(10/x)), x])/3 + (15625000*Defer[Int][E^((-169 - 936*E^(10/x) - 1296*E^(20/x) + 9*E*x - 54*E^(
1 + 10/x)*x + 81*E^(1 + 20/x)*x)^2/(81*(-1 + 3*E^(10/x))^4))/((-1 + 3*E^(10/x))^5*x^2), x])/81 + (38125000*Def
er[Int][E^((-169 - 936*E^(10/x) - 1296*E^(20/x) + 9*E*x - 54*E^(1 + 10/x)*x + 81*E^(1 + 20/x)*x)^2/(81*(-1 + 3
*E^(10/x))^4))/((-1 + 3*E^(10/x))^4*x^2), x])/81 + (3700000*Defer[Int][E^((-169 - 936*E^(10/x) - 1296*E^(20/x)
+ 9*E*x - 54*E^(1 + 10/x)*x + 81*E^(1 + 20/x)*x)^2/(81*(-1 + 3*E^(10/x))^4))/((-1 + 3*E^(10/x))^3*x^2), x])/9
+ (464000*Defer[Int][E^((-169 - 936*E^(10/x) - 1296*E^(20/x) + 9*E*x - 54*E^(1 + 10/x)*x + 81*E^(1 + 20/x)*x)
^2/(81*(-1 + 3*E^(10/x))^4))/((-1 + 3*E^(10/x))^2*x^2), x])/3 + (64000*Defer[Int][E^((-169 - 936*E^(10/x) - 12
96*E^(20/x) + 9*E*x - 54*E^(1 + 10/x)*x + 81*E^(1 + 20/x)*x)^2/(81*(-1 + 3*E^(10/x))^4))/((-1 + 3*E^(10/x))*x^
2), x])/3 - (25000*Defer[Int][E^(1 + (-169 - 936*E^(10/x) - 1296*E^(20/x) + 9*E*x - 54*E^(1 + 10/x)*x + 81*E^(
1 + 20/x)*x)^2/(81*(-1 + 3*E^(10/x))^4))/((-1 + 3*E^(10/x))^3*x), x])/9 - (37000*Defer[Int][E^(1 + (-169 - 936
*E^(10/x) - 1296*E^(20/x) + 9*E*x - 54*E^(1 + 10/x)*x + 81*E^(1 + 20/x)*x)^2/(81*(-1 + 3*E^(10/x))^4))/((-1 +
3*E^(10/x))^2*x), x])/9 - (4000*Defer[Int][E^(1 + (-169 - 936*E^(10/x) - 1296*E^(20/x) + 9*E*x - 54*E^(1 + 10/
x)*x + 81*E^(1 + 20/x)*x)^2/(81*(-1 + 3*E^(10/x))^4))/((-1 + 3*E^(10/x))*x), x])/3 + 2*Defer[Int][E^(2 + (-169
- 936*E^(10/x) - 1296*E^(20/x) + 9*E*x - 54*E^(1 + 10/x)*x + 81*E^(1 + 20/x)*x)^2/(81*(-1 + 3*E^(10/x))^4))*x
, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {\exp \left (\frac {\left (-169-936 e^{10/x}-1296 e^{20/x}+9 e x-54 e^{1+\frac {10}{x}} x+81 e^{1+\frac {20}{x}} x\right )^2}{81 \left (-1+3 e^{10/x}\right )^4}\right ) \left (-1014 e x^2+54 e^2 x^3-e^{50/x} \left (-209952 e x^2+13122 e^2 x^3\right )-e^{20/x} \left (18252000-4860 e^2 x^3+e \left (378000 x-15390 x^2\right )\right )-e^{10/x} \left (2197000+810 e^2 x^3+e \left (-117000 x-3510 x^2\right )\right )-e^{30/x} \left (50544000+14580 e^2 x^3+e \left (891000 x+54270 x^2\right )\right )-e^{40/x} \left (46656000-21870 e^2 x^3+e \left (-2916000 x+58320 x^2\right )\right )\right )}{27 \left (1-3 e^{10/x}\right )^5 x^2} \, dx\\ &=\frac {1}{27} \int \frac {\exp \left (\frac {\left (-169-936 e^{10/x}-1296 e^{20/x}+9 e x-54 e^{1+\frac {10}{x}} x+81 e^{1+\frac {20}{x}} x\right )^2}{81 \left (-1+3 e^{10/x}\right )^4}\right ) \left (-1014 e x^2+54 e^2 x^3-e^{50/x} \left (-209952 e x^2+13122 e^2 x^3\right )-e^{20/x} \left (18252000-4860 e^2 x^3+e \left (378000 x-15390 x^2\right )\right )-e^{10/x} \left (2197000+810 e^2 x^3+e \left (-117000 x-3510 x^2\right )\right )-e^{30/x} \left (50544000+14580 e^2 x^3+e \left (891000 x+54270 x^2\right )\right )-e^{40/x} \left (46656000-21870 e^2 x^3+e \left (-2916000 x+58320 x^2\right )\right )\right )}{\left (1-3 e^{10/x}\right )^5 x^2} \, dx\\ &=\frac {1}{27} \int \left (\frac {15625000 \exp \left (\frac {\left (-169-936 e^{10/x}-1296 e^{20/x}+9 e x-54 e^{1+\frac {10}{x}} x+81 e^{1+\frac {20}{x}} x\right )^2}{81 \left (-1+3 e^{10/x}\right )^4}\right )}{3 \left (-1+3 e^{10/x}\right )^5 x^2}+\frac {38125000 \exp \left (\frac {\left (-169-936 e^{10/x}-1296 e^{20/x}+9 e x-54 e^{1+\frac {10}{x}} x+81 e^{1+\frac {20}{x}} x\right )^2}{81 \left (-1+3 e^{10/x}\right )^4}\right )}{3 \left (-1+3 e^{10/x}\right )^4 x^2}-\frac {75000 \exp \left (\frac {\left (-169-936 e^{10/x}-1296 e^{20/x}+9 e x-54 e^{1+\frac {10}{x}} x+81 e^{1+\frac {20}{x}} x\right )^2}{81 \left (-1+3 e^{10/x}\right )^4}\right ) (-148+e x)}{\left (-1+3 e^{10/x}\right )^3 x^2}+54 \exp \left (1+\frac {\left (-169-936 e^{10/x}-1296 e^{20/x}+9 e x-54 e^{1+\frac {10}{x}} x+81 e^{1+\frac {20}{x}} x\right )^2}{81 \left (-1+3 e^{10/x}\right )^4}\right ) (-16+e x)-\frac {3600 \exp \left (\frac {\left (-169-936 e^{10/x}-1296 e^{20/x}+9 e x-54 e^{1+\frac {10}{x}} x+81 e^{1+\frac {20}{x}} x\right )^2}{81 \left (-1+3 e^{10/x}\right )^4}\right ) \left (-160+10 e x+e x^2\right )}{\left (-1+3 e^{10/x}\right ) x^2}-\frac {750 \exp \left (\frac {\left (-169-936 e^{10/x}-1296 e^{20/x}+9 e x-54 e^{1+\frac {10}{x}} x+81 e^{1+\frac {20}{x}} x\right )^2}{81 \left (-1+3 e^{10/x}\right )^4}\right ) \left (-5568+148 e x+5 e x^2\right )}{\left (-1+3 e^{10/x}\right )^2 x^2}\right ) \, dx\\ &=2 \int \exp \left (1+\frac {\left (-169-936 e^{10/x}-1296 e^{20/x}+9 e x-54 e^{1+\frac {10}{x}} x+81 e^{1+\frac {20}{x}} x\right )^2}{81 \left (-1+3 e^{10/x}\right )^4}\right ) (-16+e x) \, dx-\frac {250}{9} \int \frac {\exp \left (\frac {\left (-169-936 e^{10/x}-1296 e^{20/x}+9 e x-54 e^{1+\frac {10}{x}} x+81 e^{1+\frac {20}{x}} x\right )^2}{81 \left (-1+3 e^{10/x}\right )^4}\right ) \left (-5568+148 e x+5 e x^2\right )}{\left (-1+3 e^{10/x}\right )^2 x^2} \, dx-\frac {400}{3} \int \frac {\exp \left (\frac {\left (-169-936 e^{10/x}-1296 e^{20/x}+9 e x-54 e^{1+\frac {10}{x}} x+81 e^{1+\frac {20}{x}} x\right )^2}{81 \left (-1+3 e^{10/x}\right )^4}\right ) \left (-160+10 e x+e x^2\right )}{\left (-1+3 e^{10/x}\right ) x^2} \, dx-\frac {25000}{9} \int \frac {\exp \left (\frac {\left (-169-936 e^{10/x}-1296 e^{20/x}+9 e x-54 e^{1+\frac {10}{x}} x+81 e^{1+\frac {20}{x}} x\right )^2}{81 \left (-1+3 e^{10/x}\right )^4}\right ) (-148+e x)}{\left (-1+3 e^{10/x}\right )^3 x^2} \, dx+\frac {15625000}{81} \int \frac {\exp \left (\frac {\left (-169-936 e^{10/x}-1296 e^{20/x}+9 e x-54 e^{1+\frac {10}{x}} x+81 e^{1+\frac {20}{x}} x\right )^2}{81 \left (-1+3 e^{10/x}\right )^4}\right )}{\left (-1+3 e^{10/x}\right )^5 x^2} \, dx+\frac {38125000}{81} \int \frac {\exp \left (\frac {\left (-169-936 e^{10/x}-1296 e^{20/x}+9 e x-54 e^{1+\frac {10}{x}} x+81 e^{1+\frac {20}{x}} x\right )^2}{81 \left (-1+3 e^{10/x}\right )^4}\right )}{\left (-1+3 e^{10/x}\right )^4 x^2} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [B]  time = 0.50, size = 69, normalized size = 2.30 \begin {gather*} e^{\frac {\left (169+936 e^{10/x}+1296 e^{20/x}-9 e x+54 e^{1+\frac {10}{x}} x-81 e^{1+\frac {20}{x}} x\right )^2}{81 \left (1-3 e^{10/x}\right )^4}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^((28561 - 3042*E*x + 81*E^2*x^2 + E^(30/x)*(2426112 - 11664*E*x - 8748*E^2*x^2) + E^(10/x)*(31636
8 + 1404*E*x - 972*E^2*x^2) + E^(20/x)*(1314144 + 50382*E*x + 4374*E^2*x^2) + E^(40/x)*(1679616 - 209952*E*x +
6561*E^2*x^2))/(81 - 972*E^(10/x) + 4374*E^(20/x) - 8748*E^(30/x) + 6561*E^(40/x)))*(1014*E*x^2 - 54*E^2*x^3
+ E^(50/x)*(-209952*E*x^2 + 13122*E^2*x^3) + E^(20/x)*(18252000 - 4860*E^2*x^3 + E*(378000*x - 15390*x^2)) + E
^(10/x)*(2197000 + 810*E^2*x^3 + E*(-117000*x - 3510*x^2)) + E^(30/x)*(50544000 + 14580*E^2*x^3 + E*(891000*x
+ 54270*x^2)) + E^(40/x)*(46656000 - 21870*E^2*x^3 + E*(-2916000*x + 58320*x^2))))/(-27*x^2 + 405*E^(10/x)*x^2
- 2430*E^(20/x)*x^2 + 7290*E^(30/x)*x^2 - 10935*E^(40/x)*x^2 + 6561*E^(50/x)*x^2),x]

[Out]

E^((169 + 936*E^(10/x) + 1296*E^(20/x) - 9*E*x + 54*E^(1 + 10/x)*x - 81*E^(1 + 20/x)*x)^2/(81*(1 - 3*E^(10/x))
^4))

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fricas [B]  time = 0.69, size = 140, normalized size = 4.67 \begin {gather*} e^{\left (\frac {81 \, x^{2} e^{2} - 3042 \, x e + 6561 \, {\left (x^{2} e^{2} - 32 \, x e + 256\right )} e^{\frac {40}{x}} - 2916 \, {\left (3 \, x^{2} e^{2} + 4 \, x e - 832\right )} e^{\frac {30}{x}} + 162 \, {\left (27 \, x^{2} e^{2} + 311 \, x e + 8112\right )} e^{\frac {20}{x}} - 36 \, {\left (27 \, x^{2} e^{2} - 39 \, x e - 8788\right )} e^{\frac {10}{x}} + 28561}{81 \, {\left (81 \, e^{\frac {40}{x}} - 108 \, e^{\frac {30}{x}} + 54 \, e^{\frac {20}{x}} - 12 \, e^{\frac {10}{x}} + 1\right )}}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((13122*x^3*exp(1)^2-209952*x^2*exp(1))*exp(5/x)^10+(-21870*x^3*exp(1)^2+(58320*x^2-2916000*x)*exp(1
)[phone])*exp(5/x)^8+(14580*x^3*exp(1)^2+(54270*x^2+891000*x)*exp(1)[phone])*exp(5/x)^6+(-4860*x^3*exp(1)^
2+(-15390*x^2+378000*x)*exp(1)[phone])*exp(5/x)^4+(810*x^3*exp(1)^2+(-3510*x^2-117000*x)*exp(1)+2197000)*exp
(5/x)^2-54*x^3*exp(1)^2+1014*x^2*exp(1))*exp(((6561*x^2*exp(1)^2-209952*x*exp(1)+1679616)*exp(5/x)^8+(-8748*x^
2*exp(1)^2-11664*x*exp(1)+2426112)*exp(5/x)^6+(4374*x^2*exp(1)^2+50382*x*exp(1)+1314144)*exp(5/x)^4+(-972*x^2*
exp(1)^2+1404*x*exp(1)+316368)*exp(5/x)^2+81*x^2*exp(1)^2-3042*x*exp(1)+28561)/(6561*exp(5/x)^8-8748*exp(5/x)^
6+4374*exp(5/x)^4-972*exp(5/x)^2+81))/(6561*x^2*exp(5/x)^10-10935*x^2*exp(5/x)^8+7290*x^2*exp(5/x)^6-2430*x^2*
exp(5/x)^4+405*x^2*exp(5/x)^2-27*x^2),x, algorithm="fricas")

[Out]

e^(1/81*(81*x^2*e^2 - 3042*x*e + 6561*(x^2*e^2 - 32*x*e + 256)*e^(40/x) - 2916*(3*x^2*e^2 + 4*x*e - 832)*e^(30
/x) + 162*(27*x^2*e^2 + 311*x*e + 8112)*e^(20/x) - 36*(27*x^2*e^2 - 39*x*e - 8788)*e^(10/x) + 28561)/(81*e^(40
/x) - 108*e^(30/x) + 54*e^(20/x) - 12*e^(10/x) + 1))

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int -\frac {2 \, {\left (27 \, x^{3} e^{2} - 507 \, x^{2} e - 6561 \, {\left (x^{3} e^{2} - 16 \, x^{2} e\right )} e^{\frac {50}{x}} + 3645 \, {\left (3 \, x^{3} e^{2} - 8 \, {\left (x^{2} - 50 \, x\right )} e - 6400\right )} e^{\frac {40}{x}} - 405 \, {\left (18 \, x^{3} e^{2} + {\left (67 \, x^{2} + 1100 \, x\right )} e + 62400\right )} e^{\frac {30}{x}} + 135 \, {\left (18 \, x^{3} e^{2} + {\left (57 \, x^{2} - 1400 \, x\right )} e - 67600\right )} e^{\frac {20}{x}} - 5 \, {\left (81 \, x^{3} e^{2} - 117 \, {\left (3 \, x^{2} + 100 \, x\right )} e + 219700\right )} e^{\frac {10}{x}}\right )} e^{\left (\frac {81 \, x^{2} e^{2} - 3042 \, x e + 6561 \, {\left (x^{2} e^{2} - 32 \, x e + 256\right )} e^{\frac {40}{x}} - 2916 \, {\left (3 \, x^{2} e^{2} + 4 \, x e - 832\right )} e^{\frac {30}{x}} + 162 \, {\left (27 \, x^{2} e^{2} + 311 \, x e + 8112\right )} e^{\frac {20}{x}} - 36 \, {\left (27 \, x^{2} e^{2} - 39 \, x e - 8788\right )} e^{\frac {10}{x}} + 28561}{81 \, {\left (81 \, e^{\frac {40}{x}} - 108 \, e^{\frac {30}{x}} + 54 \, e^{\frac {20}{x}} - 12 \, e^{\frac {10}{x}} + 1\right )}}\right )}}{27 \, {\left (243 \, x^{2} e^{\frac {50}{x}} - 405 \, x^{2} e^{\frac {40}{x}} + 270 \, x^{2} e^{\frac {30}{x}} - 90 \, x^{2} e^{\frac {20}{x}} + 15 \, x^{2} e^{\frac {10}{x}} - x^{2}\right )}}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((13122*x^3*exp(1)^2-209952*x^2*exp(1))*exp(5/x)^10+(-21870*x^3*exp(1)^2+(58320*x^2-2916000*x)*exp(1
)[phone])*exp(5/x)^8+(14580*x^3*exp(1)^2+(54270*x^2+891000*x)*exp(1)[phone])*exp(5/x)^6+(-4860*x^3*exp(1)^
2+(-15390*x^2+378000*x)*exp(1)[phone])*exp(5/x)^4+(810*x^3*exp(1)^2+(-3510*x^2-117000*x)*exp(1)+2197000)*exp
(5/x)^2-54*x^3*exp(1)^2+1014*x^2*exp(1))*exp(((6561*x^2*exp(1)^2-209952*x*exp(1)+1679616)*exp(5/x)^8+(-8748*x^
2*exp(1)^2-11664*x*exp(1)+2426112)*exp(5/x)^6+(4374*x^2*exp(1)^2+50382*x*exp(1)+1314144)*exp(5/x)^4+(-972*x^2*
exp(1)^2+1404*x*exp(1)+316368)*exp(5/x)^2+81*x^2*exp(1)^2-3042*x*exp(1)+28561)/(6561*exp(5/x)^8-8748*exp(5/x)^
6+4374*exp(5/x)^4-972*exp(5/x)^2+81))/(6561*x^2*exp(5/x)^10-10935*x^2*exp(5/x)^8+7290*x^2*exp(5/x)^6-2430*x^2*
exp(5/x)^4+405*x^2*exp(5/x)^2-27*x^2),x, algorithm="giac")

[Out]

integrate(-2/27*(27*x^3*e^2 - 507*x^2*e - 6561*(x^3*e^2 - 16*x^2*e)*e^(50/x) + 3645*(3*x^3*e^2 - 8*(x^2 - 50*x
)*e - 6400)*e^(40/x) - 405*(18*x^3*e^2 + (67*x^2 + 1100*x)*e + 62400)*e^(30/x) + 135*(18*x^3*e^2 + (57*x^2 - 1
400*x)*e - 67600)*e^(20/x) - 5*(81*x^3*e^2 - 117*(3*x^2 + 100*x)*e + 219700)*e^(10/x))*e^(1/81*(81*x^2*e^2 - 3
042*x*e + 6561*(x^2*e^2 - 32*x*e + 256)*e^(40/x) - 2916*(3*x^2*e^2 + 4*x*e - 832)*e^(30/x) + 162*(27*x^2*e^2 +
311*x*e + 8112)*e^(20/x) - 36*(27*x^2*e^2 - 39*x*e - 8788)*e^(10/x) + 28561)/(81*e^(40/x) - 108*e^(30/x) + 54
*e^(20/x) - 12*e^(10/x) + 1))/(243*x^2*e^(50/x) - 405*x^2*e^(40/x) + 270*x^2*e^(30/x) - 90*x^2*e^(20/x) + 15*x
^2*e^(10/x) - x^2), x)

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maple [B]  time = 3.39, size = 186, normalized size = 6.20

method	result	size
risch	\({\mathrm e}^{\frac {-6561 x^{2} {\mathrm e}^{\frac {40+2 x}{x}}+8748 x^{2} {\mathrm e}^{\frac {2 x +30}{x}}-4374 x^{2} {\mathrm e}^{\frac {2 x +20}{x}}+972 x^{2} {\mathrm e}^{\frac {2 x +10}{x}}-81 x^{2} {\mathrm e}^{2}+209952 x \,{\mathrm e}^{\frac {40+x}{x}}+11664 x \,{\mathrm e}^{\frac {30+x}{x}}-50382 x \,{\mathrm e}^{\frac {20+x}{x}}-1404 x \,{\mathrm e}^{\frac {x +10}{x}}+3042 x \,{\mathrm e}-1679616 \,{\mathrm e}^{\frac {40}{x}}-2426112 \,{\mathrm e}^{\frac {30}{x}}-1314144 \,{\mathrm e}^{\frac {20}{x}}-316368 \,{\mathrm e}^{\frac {10}{x}}-28561}{-6561 \,{\mathrm e}^{\frac {40}{x}}+8748 \,{\mathrm e}^{\frac {30}{x}}-4374 \,{\mathrm e}^{\frac {20}{x}}+972 \,{\mathrm e}^{\frac {10}{x}}-81}}\)	\(186\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((13122*x^3*exp(1)^2-209952*x^2*exp(1))*exp(5/x)^10+(-21870*x^3*exp(1)^2+(58320*x^2-2916000*x)*exp(1)+4665
6000)*exp(5/x)^8+(14580*x^3*exp(1)^2+(54270*x^2+891000*x)*exp(1)[phone])*exp(5/x)^6+(-4860*x^3*exp(1)^2+(-15
390*x^2+378000*x)*exp(1)[phone])*exp(5/x)^4+(810*x^3*exp(1)^2+(-3510*x^2-117000*x)*exp(1)+2197000)*exp(5/x)^
2-54*x^3*exp(1)^2+1014*x^2*exp(1))*exp(((6561*x^2*exp(1)^2-209952*x*exp(1)+1679616)*exp(5/x)^8+(-8748*x^2*exp(
1)^2-11664*x*exp(1)+2426112)*exp(5/x)^6+(4374*x^2*exp(1)^2+50382*x*exp(1)+1314144)*exp(5/x)^4+(-972*x^2*exp(1)
^2+1404*x*exp(1)+316368)*exp(5/x)^2+81*x^2*exp(1)^2-3042*x*exp(1)+28561)/(6561*exp(5/x)^8-8748*exp(5/x)^6+4374
*exp(5/x)^4-972*exp(5/x)^2+81))/(6561*x^2*exp(5/x)^10-10935*x^2*exp(5/x)^8+7290*x^2*exp(5/x)^6-2430*x^2*exp(5/
x)^4+405*x^2*exp(5/x)^2-27*x^2),x,method=_RETURNVERBOSE)

[Out]

exp(1/81*(-6561*x^2*exp(2*(20+x)/x)+8748*x^2*exp(2*(x+15)/x)-4374*x^2*exp(2*(x+10)/x)+972*x^2*exp(2/x*(5+x))-8
1*x^2*exp(2)+209952*x*exp((40+x)/x)+11664*x*exp((30+x)/x)-50382*x*exp((20+x)/x)-1404*x*exp((x+10)/x)+3042*x*ex
p(1)-1679616*exp(40/x)-2426112*exp(30/x)-1314144*exp(20/x)-316368*exp(10/x)-28561)/(-81*exp(40/x)+108*exp(30/x
)-54*exp(20/x)+12*exp(10/x)-1))

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maxima [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(((13122*x^3*exp(1)^2-209952*x^2*exp(1))*exp(5/x)^10+(-21870*x^3*exp(1)^2+(58320*x^2-2916000*x)*exp(1
)[phone])*exp(5/x)^8+(14580*x^3*exp(1)^2+(54270*x^2+891000*x)*exp(1)[phone])*exp(5/x)^6+(-4860*x^3*exp(1)^
2+(-15390*x^2+378000*x)*exp(1)[phone])*exp(5/x)^4+(810*x^3*exp(1)^2+(-3510*x^2-117000*x)*exp(1)+2197000)*exp
(5/x)^2-54*x^3*exp(1)^2+1014*x^2*exp(1))*exp(((6561*x^2*exp(1)^2-209952*x*exp(1)+1679616)*exp(5/x)^8+(-8748*x^
2*exp(1)^2-11664*x*exp(1)+2426112)*exp(5/x)^6+(4374*x^2*exp(1)^2+50382*x*exp(1)+1314144)*exp(5/x)^4+(-972*x^2*
exp(1)^2+1404*x*exp(1)+316368)*exp(5/x)^2+81*x^2*exp(1)^2-3042*x*exp(1)+28561)/(6561*exp(5/x)^8-8748*exp(5/x)^
6+4374*exp(5/x)^4-972*exp(5/x)^2+81))/(6561*x^2*exp(5/x)^10-10935*x^2*exp(5/x)^8+7290*x^2*exp(5/x)^6-2430*x^2*
exp(5/x)^4+405*x^2*exp(5/x)^2-27*x^2),x, algorithm="maxima")

[Out]

Timed out

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mupad [B]  time = 9.22, size = 697, normalized size = 23.23 \begin {gather*} {\mathrm {e}}^{\frac {16224\,{\mathrm {e}}^{20/x}}{54\,{\mathrm {e}}^{20/x}-12\,{\mathrm {e}}^{10/x}-108\,{\mathrm {e}}^{30/x}+81\,{\mathrm {e}}^{40/x}+1}}\,{\mathrm {e}}^{\frac {20736\,{\mathrm {e}}^{40/x}}{54\,{\mathrm {e}}^{20/x}-12\,{\mathrm {e}}^{10/x}-108\,{\mathrm {e}}^{30/x}+81\,{\mathrm {e}}^{40/x}+1}}\,{\mathrm {e}}^{\frac {29952\,{\mathrm {e}}^{30/x}}{54\,{\mathrm {e}}^{20/x}-12\,{\mathrm {e}}^{10/x}-108\,{\mathrm {e}}^{30/x}+81\,{\mathrm {e}}^{40/x}+1}}\,{\mathrm {e}}^{\frac {35152\,{\mathrm {e}}^{10/x}}{486\,{\mathrm {e}}^{20/x}-108\,{\mathrm {e}}^{10/x}-972\,{\mathrm {e}}^{30/x}+729\,{\mathrm {e}}^{40/x}+9}}\,{\mathrm {e}}^{-\frac {12\,x^2\,{\mathrm {e}}^2\,{\mathrm {e}}^{10/x}}{54\,{\mathrm {e}}^{20/x}-12\,{\mathrm {e}}^{10/x}-108\,{\mathrm {e}}^{30/x}+81\,{\mathrm {e}}^{40/x}+1}}\,{\mathrm {e}}^{\frac {54\,x^2\,{\mathrm {e}}^2\,{\mathrm {e}}^{20/x}}{54\,{\mathrm {e}}^{20/x}-12\,{\mathrm {e}}^{10/x}-108\,{\mathrm {e}}^{30/x}+81\,{\mathrm {e}}^{40/x}+1}}\,{\mathrm {e}}^{\frac {81\,x^2\,{\mathrm {e}}^2\,{\mathrm {e}}^{40/x}}{54\,{\mathrm {e}}^{20/x}-12\,{\mathrm {e}}^{10/x}-108\,{\mathrm {e}}^{30/x}+81\,{\mathrm {e}}^{40/x}+1}}\,{\mathrm {e}}^{-\frac {108\,x^2\,{\mathrm {e}}^2\,{\mathrm {e}}^{30/x}}{54\,{\mathrm {e}}^{20/x}-12\,{\mathrm {e}}^{10/x}-108\,{\mathrm {e}}^{30/x}+81\,{\mathrm {e}}^{40/x}+1}}\,{\mathrm {e}}^{-\frac {338\,x\,\mathrm {e}}{486\,{\mathrm {e}}^{20/x}-108\,{\mathrm {e}}^{10/x}-972\,{\mathrm {e}}^{30/x}+729\,{\mathrm {e}}^{40/x}+9}}\,{\mathrm {e}}^{\frac {28561}{4374\,{\mathrm {e}}^{20/x}-972\,{\mathrm {e}}^{10/x}-8748\,{\mathrm {e}}^{30/x}+6561\,{\mathrm {e}}^{40/x}+81}}\,{\mathrm {e}}^{\frac {x^2\,{\mathrm {e}}^2}{54\,{\mathrm {e}}^{20/x}-12\,{\mathrm {e}}^{10/x}-108\,{\mathrm {e}}^{30/x}+81\,{\mathrm {e}}^{40/x}+1}}\,{\mathrm {e}}^{-\frac {144\,x\,\mathrm {e}\,{\mathrm {e}}^{30/x}}{54\,{\mathrm {e}}^{20/x}-12\,{\mathrm {e}}^{10/x}-108\,{\mathrm {e}}^{30/x}+81\,{\mathrm {e}}^{40/x}+1}}\,{\mathrm {e}}^{\frac {52\,x\,\mathrm {e}\,{\mathrm {e}}^{10/x}}{162\,{\mathrm {e}}^{20/x}-36\,{\mathrm {e}}^{10/x}-324\,{\mathrm {e}}^{30/x}+243\,{\mathrm {e}}^{40/x}+3}}\,{\mathrm {e}}^{\frac {622\,x\,\mathrm {e}\,{\mathrm {e}}^{20/x}}{54\,{\mathrm {e}}^{20/x}-12\,{\mathrm {e}}^{10/x}-108\,{\mathrm {e}}^{30/x}+81\,{\mathrm {e}}^{40/x}+1}}\,{\mathrm {e}}^{-\frac {2592\,x\,\mathrm {e}\,{\mathrm {e}}^{40/x}}{54\,{\mathrm {e}}^{20/x}-12\,{\mathrm {e}}^{10/x}-108\,{\mathrm {e}}^{30/x}+81\,{\mathrm {e}}^{40/x}+1}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp((exp(10/x)*(1404*x*exp(1) - 972*x^2*exp(2) + 316368) + exp(20/x)*(50382*x*exp(1) + 4374*x^2*exp(2) +
1314144) + exp(40/x)*(6561*x^2*exp(2) - 209952*x*exp(1) + 1679616) - exp(30/x)*(11664*x*exp(1) + 8748*x^2*exp(
2) - 2426112) - 3042*x*exp(1) + 81*x^2*exp(2) + 28561)/(4374*exp(20/x) - 972*exp(10/x) - 8748*exp(30/x) + 6561
*exp(40/x) + 81))*(exp(10/x)*(810*x^3*exp(2) - exp(1)*(117000*x + 3510*x^2) + 2197000) + exp(20/x)*(exp(1)*(37
8000*x - 15390*x^2) - 4860*x^3*exp(2) + 18252000) - exp(40/x)*(exp(1)*(2916000*x - 58320*x^2) + 21870*x^3*exp(
2) - 46656000) + exp(30/x)*(exp(1)*(891000*x + 54270*x^2) + 14580*x^3*exp(2) + 50544000) - exp(50/x)*(209952*x
^2*exp(1) - 13122*x^3*exp(2)) + 1014*x^2*exp(1) - 54*x^3*exp(2)))/(405*x^2*exp(10/x) - 2430*x^2*exp(20/x) + 72
90*x^2*exp(30/x) - 10935*x^2*exp(40/x) + 6561*x^2*exp(50/x) - 27*x^2),x)

[Out]

exp((16224*exp(20/x))/(54*exp(20/x) - 12*exp(10/x) - 108*exp(30/x) + 81*exp(40/x) + 1))*exp((20736*exp(40/x))/
(54*exp(20/x) - 12*exp(10/x) - 108*exp(30/x) + 81*exp(40/x) + 1))*exp((29952*exp(30/x))/(54*exp(20/x) - 12*exp
(10/x) - 108*exp(30/x) + 81*exp(40/x) + 1))*exp((35152*exp(10/x))/(486*exp(20/x) - 108*exp(10/x) - 972*exp(30/
x) + 729*exp(40/x) + 9))*exp(-(12*x^2*exp(2)*exp(10/x))/(54*exp(20/x) - 12*exp(10/x) - 108*exp(30/x) + 81*exp(
40/x) + 1))*exp((54*x^2*exp(2)*exp(20/x))/(54*exp(20/x) - 12*exp(10/x) - 108*exp(30/x) + 81*exp(40/x) + 1))*ex
p((81*x^2*exp(2)*exp(40/x))/(54*exp(20/x) - 12*exp(10/x) - 108*exp(30/x) + 81*exp(40/x) + 1))*exp(-(108*x^2*ex
p(2)*exp(30/x))/(54*exp(20/x) - 12*exp(10/x) - 108*exp(30/x) + 81*exp(40/x) + 1))*exp(-(338*x*exp(1))/(486*exp
(20/x) - 108*exp(10/x) - 972*exp(30/x) + 729*exp(40/x) + 9))*exp(28561/(4374*exp(20/x) - 972*exp(10/x) - 8748*
exp(30/x) + 6561*exp(40/x) + 81))*exp((x^2*exp(2))/(54*exp(20/x) - 12*exp(10/x) - 108*exp(30/x) + 81*exp(40/x)
+ 1))*exp(-(144*x*exp(1)*exp(30/x))/(54*exp(20/x) - 12*exp(10/x) - 108*exp(30/x) + 81*exp(40/x) + 1))*exp((52
*x*exp(1)*exp(10/x))/(162*exp(20/x) - 36*exp(10/x) - 324*exp(30/x) + 243*exp(40/x) + 3))*exp((622*x*exp(1)*exp
(20/x))/(54*exp(20/x) - 12*exp(10/x) - 108*exp(30/x) + 81*exp(40/x) + 1))*exp(-(2592*x*exp(1)*exp(40/x))/(54*e
xp(20/x) - 12*exp(10/x) - 108*exp(30/x) + 81*exp(40/x) + 1))

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sympy [B]  time = 3.64, size = 134, normalized size = 4.47 \begin {gather*} e^{\frac {81 x^{2} e^{2} - 3042 e x + \left (- 8748 x^{2} e^{2} - 11664 e x + 2426112\right ) e^{\frac {30}{x}} + \left (- 972 x^{2} e^{2} + 1404 e x + 316368\right ) e^{\frac {10}{x}} + \left (4374 x^{2} e^{2} + 50382 e x + 1314144\right ) e^{\frac {20}{x}} + \left (6561 x^{2} e^{2} - 209952 e x + 1679616\right ) e^{\frac {40}{x}} + 28561}{6561 e^{\frac {40}{x}} - 8748 e^{\frac {30}{x}} + 4374 e^{\frac {20}{x}} - 972 e^{\frac {10}{x}} + 81}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((13122*x**3*exp(1)**2-209952*x**2*exp(1))*exp(5/x)**10+(-21870*x**3*exp(1)**2+(58320*x**2-2916000*x
)*exp(1)[phone])*exp(5/x)**8+(14580*x**3*exp(1)**2+(54270*x**2+891000*x)*exp(1)[phone])*exp(5/x)**6+(-4860
*x**3*exp(1)**2+(-15390*x**2+378000*x)*exp(1)[phone])*exp(5/x)**4+(810*x**3*exp(1)**2+(-3510*x**2-117000*x)*
exp(1)+2197000)*exp(5/x)**2-54*x**3*exp(1)**2+1014*x**2*exp(1))*exp(((6561*x**2*exp(1)**2-209952*x*exp(1)+1679
616)*exp(5/x)**8+(-8748*x**2*exp(1)**2-11664*x*exp(1)+2426112)*exp(5/x)**6+(4374*x**2*exp(1)**2+50382*x*exp(1)
+1314144)*exp(5/x)**4+(-972*x**2*exp(1)**2+1404*x*exp(1)+316368)*exp(5/x)**2+81*x**2*exp(1)**2-3042*x*exp(1)+2
8561)/(6561*exp(5/x)**8-8748*exp(5/x)**6+4374*exp(5/x)**4-972*exp(5/x)**2+81))/(6561*x**2*exp(5/x)**10-10935*x
**2*exp(5/x)**8+7290*x**2*exp(5/x)**6-2430*x**2*exp(5/x)**4+405*x**2*exp(5/x)**2-27*x**2),x)

[Out]

exp((81*x**2*exp(2) - 3042*E*x + (-8748*x**2*exp(2) - 11664*E*x + 2426112)*exp(30/x) + (-972*x**2*exp(2) + 140
4*E*x + 316368)*exp(10/x) + (4374*x**2*exp(2) + 50382*E*x + 1314144)*exp(20/x) + (6561*x**2*exp(2) - 209952*E*
x + 1679616)*exp(40/x) + 28561)/(6561*exp(40/x) - 8748*exp(30/x) + 4374*exp(20/x) - 972*exp(10/x) + 81))

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