3.27.93 \(\int \frac {e^{\frac {-4 x-x^3}{40-3 x-11 x^2+2 x^3-5 x^4+x^5+(-5+x) \log (5)}} (-160-164 x^2+22 x^3-49 x^4+16 x^5-5 x^6+2 x^7+(20+15 x^2-2 x^3) \log (5))}{1600-240 x-871 x^2+226 x^3-291 x^4+66 x^5+108 x^6-42 x^7+29 x^8-10 x^9+x^{10}+(-400+110 x+104 x^2-42 x^3+54 x^4-20 x^5+2 x^6) \log (5)+(25-10 x+x^2) \log ^2(5)} \, dx\)

Optimal. Leaf size=32 \[ e^{\frac {x}{(5-x) \left (-2+x^2+\frac {-x+\log (5)}{4+x^2}\right )}} \]

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Rubi [F]  time = 10.69, 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 {-4 x-x^3}{40-3 x-11 x^2+2 x^3-5 x^4+x^5+(-5+x) \log (5)}\right ) \left (-160-164 x^2+22 x^3-49 x^4+16 x^5-5 x^6+2 x^7+\left (20+15 x^2-2 x^3\right ) \log (5)\right )}{1600-240 x-871 x^2+226 x^3-291 x^4+66 x^5+108 x^6-42 x^7+29 x^8-10 x^9+x^{10}+\left (-400+110 x+104 x^2-42 x^3+54 x^4-20 x^5+2 x^6\right ) \log (5)+\left (25-10 x+x^2\right ) \log ^2(5)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^((-4*x - x^3)/(40 - 3*x - 11*x^2 + 2*x^3 - 5*x^4 + x^5 + (-5 + x)*Log[5]))*(-160 - 164*x^2 + 22*x^3 - 4
9*x^4 + 16*x^5 - 5*x^6 + 2*x^7 + (20 + 15*x^2 - 2*x^3)*Log[5]))/(1600 - 240*x - 871*x^2 + 226*x^3 - 291*x^4 +
66*x^5 + 108*x^6 - 42*x^7 + 29*x^8 - 10*x^9 + x^10 + (-400 + 110*x + 104*x^2 - 42*x^3 + 54*x^4 - 20*x^5 + 2*x^
6)*Log[5] + (25 - 10*x + x^2)*Log[5]^2),x]

[Out]

(145*Defer[Int][1/(E^((x*(4 + x^2))/((-5 + x)*(-8 - x + 2*x^2 + x^4 + Log[5])))*(-5 + x)^2), x])/(662 + Log[5]
) - ((1811 - 20*Log[5])*(8 - Log[5])*Defer[Int][1/(E^((x*(4 + x^2))/((-5 + x)*(-8 - x + 2*x^2 + x^4 + Log[5]))
)*(-8 - x + 2*x^2 + x^4 + Log[5])^2), x])/(662 + Log[5]) - ((4179 - 415*Log[5] + 4*Log[5]^2)*Defer[Int][x/(E^(
(x*(4 + x^2))/((-5 + x)*(-8 - x + 2*x^2 + x^4 + Log[5])))*(-8 - x + 2*x^2 + x^4 + Log[5])^2), x])/(662 + Log[5
]) - ((3569 - 563*Log[5])*Defer[Int][x^2/(E^((x*(4 + x^2))/((-5 + x)*(-8 - x + 2*x^2 + x^4 + Log[5])))*(-8 - x
+ 2*x^2 + x^4 + Log[5])^2), x])/(662 + Log[5]) - ((1111 - 112*Log[5])*Defer[Int][x^3/(E^((x*(4 + x^2))/((-5 +
x)*(-8 - x + 2*x^2 + x^4 + Log[5])))*(-8 - x + 2*x^2 + x^4 + Log[5])^2), x])/(662 + Log[5]) - (5*(247 - Log[1
25])*Defer[Int][1/(E^((x*(4 + x^2))/((-5 + x)*(-8 - x + 2*x^2 + x^4 + Log[5])))*(-8 - x + 2*x^2 + x^4 + Log[5]
)), x])/(662 + Log[5]) - (2*(63 - Log[5])*Defer[Int][x/(E^((x*(4 + x^2))/((-5 + x)*(-8 - x + 2*x^2 + x^4 + Log
[5])))*(-8 - x + 2*x^2 + x^4 + Log[5])), x])/(662 + Log[5]) - (145*Defer[Int][x^2/(E^((x*(4 + x^2))/((-5 + x)*
(-8 - x + 2*x^2 + x^4 + Log[5])))*(-8 - x + 2*x^2 + x^4 + Log[5])), x])/(662 + Log[5])

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {\exp \left (-\frac {x \left (4+x^2\right )}{(-5+x) \left (-8-x+2 x^2+x^4+\log (5)\right )}\right ) \left (-49 x^4+16 x^5-5 x^6+2 x^7-2 x^3 (-11+\log (5))+20 (-8+\log (5))+x^2 (-164+15 \log (5))\right )}{(5-x)^2 \left (8+x-2 x^2-x^4-\log (5)\right )^2} \, dx\\ &=\int \left (\frac {145 \exp \left (-\frac {x \left (4+x^2\right )}{(-5+x) \left (-8-x+2 x^2+x^4+\log (5)\right )}\right )}{(-5+x)^2 (662+\log (5))}+\frac {\exp \left (-\frac {x \left (4+x^2\right )}{(-5+x) \left (-8-x+2 x^2+x^4+\log (5)\right )}\right ) \left (-14488-x^2 (3569-563 \log (5))-x^3 (1111-112 \log (5))+1971 \log (5)-20 \log ^2(5)-x \left (4179-415 \log (5)+4 \log ^2(5)\right )\right )}{\left (8+x-2 x^2-x^4-\log (5)\right )^2 (662+\log (5))}+\frac {\exp \left (-\frac {x \left (4+x^2\right )}{(-5+x) \left (-8-x+2 x^2+x^4+\log (5)\right )}\right ) \left (145 x^2+2 x (63-\log (5))+5 (247-\log (125))\right )}{\left (8+x-2 x^2-x^4-\log (5)\right ) (662+\log (5))}\right ) \, dx\\ &=\frac {\int \frac {\exp \left (-\frac {x \left (4+x^2\right )}{(-5+x) \left (-8-x+2 x^2+x^4+\log (5)\right )}\right ) \left (-14488-x^2 (3569-563 \log (5))-x^3 (1111-112 \log (5))+1971 \log (5)-20 \log ^2(5)-x \left (4179-415 \log (5)+4 \log ^2(5)\right )\right )}{\left (8+x-2 x^2-x^4-\log (5)\right )^2} \, dx}{662+\log (5)}+\frac {\int \frac {\exp \left (-\frac {x \left (4+x^2\right )}{(-5+x) \left (-8-x+2 x^2+x^4+\log (5)\right )}\right ) \left (145 x^2+2 x (63-\log (5))+5 (247-\log (125))\right )}{8+x-2 x^2-x^4-\log (5)} \, dx}{662+\log (5)}+\frac {145 \int \frac {\exp \left (-\frac {x \left (4+x^2\right )}{(-5+x) \left (-8-x+2 x^2+x^4+\log (5)\right )}\right )}{(-5+x)^2} \, dx}{662+\log (5)}\\ &=\frac {\int \left (\frac {\exp \left (-\frac {x \left (4+x^2\right )}{(-5+x) \left (-8-x+2 x^2+x^4+\log (5)\right )}\right ) x^3 (-1111+112 \log (5))}{\left (-8-x+2 x^2+x^4+\log (5)\right )^2}+\frac {\exp \left (-\frac {x \left (4+x^2\right )}{(-5+x) \left (-8-x+2 x^2+x^4+\log (5)\right )}\right ) x^2 (-3569+563 \log (5))}{\left (-8-x+2 x^2+x^4+\log (5)\right )^2}-\frac {\exp \left (-\frac {x \left (4+x^2\right )}{(-5+x) \left (-8-x+2 x^2+x^4+\log (5)\right )}\right ) x \left (4179-415 \log (5)+4 \log ^2(5)\right )}{\left (-8-x+2 x^2+x^4+\log (5)\right )^2}-\frac {14488 \exp \left (-\frac {x \left (4+x^2\right )}{(-5+x) \left (-8-x+2 x^2+x^4+\log (5)\right )}\right ) \left (1+\frac {\log (5) (-1971+20 \log (5))}{14488}\right )}{\left (-8-x+2 x^2+x^4+\log (5)\right )^2}\right ) \, dx}{662+\log (5)}+\frac {\int \left (-\frac {145 \exp \left (-\frac {x \left (4+x^2\right )}{(-5+x) \left (-8-x+2 x^2+x^4+\log (5)\right )}\right ) x^2}{-8-x+2 x^2+x^4+\log (5)}+\frac {2 \exp \left (-\frac {x \left (4+x^2\right )}{(-5+x) \left (-8-x+2 x^2+x^4+\log (5)\right )}\right ) x (-63+\log (5))}{-8-x+2 x^2+x^4+\log (5)}+\frac {5 \exp \left (-\frac {x \left (4+x^2\right )}{(-5+x) \left (-8-x+2 x^2+x^4+\log (5)\right )}\right ) (-247+\log (125))}{-8-x+2 x^2+x^4+\log (5)}\right ) \, dx}{662+\log (5)}+\frac {145 \int \frac {\exp \left (-\frac {x \left (4+x^2\right )}{(-5+x) \left (-8-x+2 x^2+x^4+\log (5)\right )}\right )}{(-5+x)^2} \, dx}{662+\log (5)}\\ &=\frac {145 \int \frac {\exp \left (-\frac {x \left (4+x^2\right )}{(-5+x) \left (-8-x+2 x^2+x^4+\log (5)\right )}\right )}{(-5+x)^2} \, dx}{662+\log (5)}-\frac {145 \int \frac {\exp \left (-\frac {x \left (4+x^2\right )}{(-5+x) \left (-8-x+2 x^2+x^4+\log (5)\right )}\right ) x^2}{-8-x+2 x^2+x^4+\log (5)} \, dx}{662+\log (5)}-\frac {(3569-563 \log (5)) \int \frac {\exp \left (-\frac {x \left (4+x^2\right )}{(-5+x) \left (-8-x+2 x^2+x^4+\log (5)\right )}\right ) x^2}{\left (-8-x+2 x^2+x^4+\log (5)\right )^2} \, dx}{662+\log (5)}-\frac {(1111-112 \log (5)) \int \frac {\exp \left (-\frac {x \left (4+x^2\right )}{(-5+x) \left (-8-x+2 x^2+x^4+\log (5)\right )}\right ) x^3}{\left (-8-x+2 x^2+x^4+\log (5)\right )^2} \, dx}{662+\log (5)}-\frac {((1811-20 \log (5)) (8-\log (5))) \int \frac {\exp \left (-\frac {x \left (4+x^2\right )}{(-5+x) \left (-8-x+2 x^2+x^4+\log (5)\right )}\right )}{\left (-8-x+2 x^2+x^4+\log (5)\right )^2} \, dx}{662+\log (5)}-\frac {(2 (63-\log (5))) \int \frac {\exp \left (-\frac {x \left (4+x^2\right )}{(-5+x) \left (-8-x+2 x^2+x^4+\log (5)\right )}\right ) x}{-8-x+2 x^2+x^4+\log (5)} \, dx}{662+\log (5)}-\frac {\left (4179-415 \log (5)+4 \log ^2(5)\right ) \int \frac {\exp \left (-\frac {x \left (4+x^2\right )}{(-5+x) \left (-8-x+2 x^2+x^4+\log (5)\right )}\right ) x}{\left (-8-x+2 x^2+x^4+\log (5)\right )^2} \, dx}{662+\log (5)}-\frac {(5 (247-\log (125))) \int \frac {\exp \left (-\frac {x \left (4+x^2\right )}{(-5+x) \left (-8-x+2 x^2+x^4+\log (5)\right )}\right )}{-8-x+2 x^2+x^4+\log (5)} \, dx}{662+\log (5)}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.09, size = 32, normalized size = 1.00 \begin {gather*} e^{-\frac {x \left (4+x^2\right )}{(-5+x) \left (-8-x+2 x^2+x^4+\log (5)\right )}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^((-4*x - x^3)/(40 - 3*x - 11*x^2 + 2*x^3 - 5*x^4 + x^5 + (-5 + x)*Log[5]))*(-160 - 164*x^2 + 22*x
^3 - 49*x^4 + 16*x^5 - 5*x^6 + 2*x^7 + (20 + 15*x^2 - 2*x^3)*Log[5]))/(1600 - 240*x - 871*x^2 + 226*x^3 - 291*
x^4 + 66*x^5 + 108*x^6 - 42*x^7 + 29*x^8 - 10*x^9 + x^10 + (-400 + 110*x + 104*x^2 - 42*x^3 + 54*x^4 - 20*x^5
+ 2*x^6)*Log[5] + (25 - 10*x + x^2)*Log[5]^2),x]

[Out]

E^(-((x*(4 + x^2))/((-5 + x)*(-8 - x + 2*x^2 + x^4 + Log[5]))))

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fricas [A]  time = 0.47, size = 41, normalized size = 1.28 \begin {gather*} e^{\left (-\frac {x^{3} + 4 \, x}{x^{5} - 5 \, x^{4} + 2 \, x^{3} - 11 \, x^{2} + {\left (x - 5\right )} \log \relax (5) - 3 \, x + 40}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-2*x^3+15*x^2+20)*log(5)+2*x^7-5*x^6+16*x^5-49*x^4+22*x^3-164*x^2-160)*exp((-x^3-4*x)/((x-5)*log(5
)+x^5-5*x^4+2*x^3-11*x^2-3*x+40))/((x^2-10*x+25)*log(5)^2+(2*x^6-20*x^5+54*x^4-42*x^3+104*x^2+110*x-400)*log(5
)+x^10-10*x^9+29*x^8-42*x^7+108*x^6+66*x^5-291*x^4+226*x^3-871*x^2-240*x+1600),x, algorithm="fricas")

[Out]

e^(-(x^3 + 4*x)/(x^5 - 5*x^4 + 2*x^3 - 11*x^2 + (x - 5)*log(5) - 3*x + 40))

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giac [B]  time = 0.29, size = 76, normalized size = 2.38 \begin {gather*} e^{\left (-\frac {x^{3}}{x^{5} - 5 \, x^{4} + 2 \, x^{3} - 11 \, x^{2} + x \log \relax (5) - 3 \, x - 5 \, \log \relax (5) + 40} - \frac {4 \, x}{x^{5} - 5 \, x^{4} + 2 \, x^{3} - 11 \, x^{2} + x \log \relax (5) - 3 \, x - 5 \, \log \relax (5) + 40}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-2*x^3+15*x^2+20)*log(5)+2*x^7-5*x^6+16*x^5-49*x^4+22*x^3-164*x^2-160)*exp((-x^3-4*x)/((x-5)*log(5
)+x^5-5*x^4+2*x^3-11*x^2-3*x+40))/((x^2-10*x+25)*log(5)^2+(2*x^6-20*x^5+54*x^4-42*x^3+104*x^2+110*x-400)*log(5
)+x^10-10*x^9+29*x^8-42*x^7+108*x^6+66*x^5-291*x^4+226*x^3-871*x^2-240*x+1600),x, algorithm="giac")

[Out]

e^(-x^3/(x^5 - 5*x^4 + 2*x^3 - 11*x^2 + x*log(5) - 3*x - 5*log(5) + 40) - 4*x/(x^5 - 5*x^4 + 2*x^3 - 11*x^2 +
x*log(5) - 3*x - 5*log(5) + 40))

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maple [A]  time = 0.45, size = 32, normalized size = 1.00

method	result	size
risch	\({\mathrm e}^{-\frac {x \left (x^{2}+4\right )}{\left (x -5\right ) \left (x^{4}+2 x^{2}+\ln \relax (5)-x -8\right )}}\)	\(32\)
gosper	\({\mathrm e}^{-\frac {x \left (x^{2}+4\right )}{x^{5}-5 x^{4}+2 x^{3}+x \ln \relax (5)-11 x^{2}-5 \ln \relax (5)-3 x +40}}\)	\(43\)
norman	\(\frac {x^{5} {\mathrm e}^{\frac {-x^{3}-4 x}{\left (x -5\right ) \ln \relax (5)+x^{5}-5 x^{4}+2 x^{3}-11 x^{2}-3 x +40}}+\left (-5 \ln \relax (5)+40\right ) {\mathrm e}^{\frac {-x^{3}-4 x}{\left (x -5\right ) \ln \relax (5)+x^{5}-5 x^{4}+2 x^{3}-11 x^{2}-3 x +40}}+\left (\ln \relax (5)-3\right ) x \,{\mathrm e}^{\frac {-x^{3}-4 x}{\left (x -5\right ) \ln \relax (5)+x^{5}-5 x^{4}+2 x^{3}-11 x^{2}-3 x +40}}-11 x^{2} {\mathrm e}^{\frac {-x^{3}-4 x}{\left (x -5\right ) \ln \relax (5)+x^{5}-5 x^{4}+2 x^{3}-11 x^{2}-3 x +40}}+2 x^{3} {\mathrm e}^{\frac {-x^{3}-4 x}{\left (x -5\right ) \ln \relax (5)+x^{5}-5 x^{4}+2 x^{3}-11 x^{2}-3 x +40}}-5 x^{4} {\mathrm e}^{\frac {-x^{3}-4 x}{\left (x -5\right ) \ln \relax (5)+x^{5}-5 x^{4}+2 x^{3}-11 x^{2}-3 x +40}}}{\left (x -5\right ) \left (x^{4}+2 x^{2}+\ln \relax (5)-x -8\right )}\)	\(309\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((-2*x^3+15*x^2+20)*ln(5)+2*x^7-5*x^6+16*x^5-49*x^4+22*x^3-164*x^2-160)*exp((-x^3-4*x)/((x-5)*ln(5)+x^5-5*
x^4+2*x^3-11*x^2-3*x+40))/((x^2-10*x+25)*ln(5)^2+(2*x^6-20*x^5+54*x^4-42*x^3+104*x^2+110*x-400)*ln(5)+x^10-10*
x^9+29*x^8-42*x^7+108*x^6+66*x^5-291*x^4+226*x^3-871*x^2-240*x+1600),x,method=_RETURNVERBOSE)

[Out]

exp(-x*(x^2+4)/(x-5)/(x^4+2*x^2+ln(5)-x-8))

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maxima [B]  time = 4.17, size = 301, normalized size = 9.41 \begin {gather*} e^{\left (\frac {145 \, x^{3}}{x^{4} {\left (\log \relax (5) + 662\right )} + 2 \, x^{2} {\left (\log \relax (5) + 662\right )} - x {\left (\log \relax (5) + 662\right )} + \log \relax (5)^{2} + 654 \, \log \relax (5) - 5296} - \frac {x^{2} \log \relax (5)}{x^{4} {\left (\log \relax (5) + 662\right )} + 2 \, x^{2} {\left (\log \relax (5) + 662\right )} - x {\left (\log \relax (5) + 662\right )} + \log \relax (5)^{2} + 654 \, \log \relax (5) - 5296} + \frac {63 \, x^{2}}{x^{4} {\left (\log \relax (5) + 662\right )} + 2 \, x^{2} {\left (\log \relax (5) + 662\right )} - x {\left (\log \relax (5) + 662\right )} + \log \relax (5)^{2} + 654 \, \log \relax (5) - 5296} - \frac {5 \, x \log \relax (5)}{x^{4} {\left (\log \relax (5) + 662\right )} + 2 \, x^{2} {\left (\log \relax (5) + 662\right )} - x {\left (\log \relax (5) + 662\right )} + \log \relax (5)^{2} + 654 \, \log \relax (5) - 5296} + \frac {605 \, x}{x^{4} {\left (\log \relax (5) + 662\right )} + 2 \, x^{2} {\left (\log \relax (5) + 662\right )} - x {\left (\log \relax (5) + 662\right )} + \log \relax (5)^{2} + 654 \, \log \relax (5) - 5296} - \frac {29 \, \log \relax (5)}{x^{4} {\left (\log \relax (5) + 662\right )} + 2 \, x^{2} {\left (\log \relax (5) + 662\right )} - x {\left (\log \relax (5) + 662\right )} + \log \relax (5)^{2} + 654 \, \log \relax (5) - 5296} + \frac {232}{x^{4} {\left (\log \relax (5) + 662\right )} + 2 \, x^{2} {\left (\log \relax (5) + 662\right )} - x {\left (\log \relax (5) + 662\right )} + \log \relax (5)^{2} + 654 \, \log \relax (5) - 5296} - \frac {145}{x {\left (\log \relax (5) + 662\right )} - 5 \, \log \relax (5) - 3310}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-2*x^3+15*x^2+20)*log(5)+2*x^7-5*x^6+16*x^5-49*x^4+22*x^3-164*x^2-160)*exp((-x^3-4*x)/((x-5)*log(5
)+x^5-5*x^4+2*x^3-11*x^2-3*x+40))/((x^2-10*x+25)*log(5)^2+(2*x^6-20*x^5+54*x^4-42*x^3+104*x^2+110*x-400)*log(5
)+x^10-10*x^9+29*x^8-42*x^7+108*x^6+66*x^5-291*x^4+226*x^3-871*x^2-240*x+1600),x, algorithm="maxima")

[Out]

e^(145*x^3/(x^4*(log(5) + 662) + 2*x^2*(log(5) + 662) - x*(log(5) + 662) + log(5)^2 + 654*log(5) - 5296) - x^2
*log(5)/(x^4*(log(5) + 662) + 2*x^2*(log(5) + 662) - x*(log(5) + 662) + log(5)^2 + 654*log(5) - 5296) + 63*x^2
/(x^4*(log(5) + 662) + 2*x^2*(log(5) + 662) - x*(log(5) + 662) + log(5)^2 + 654*log(5) - 5296) - 5*x*log(5)/(x
^4*(log(5) + 662) + 2*x^2*(log(5) + 662) - x*(log(5) + 662) + log(5)^2 + 654*log(5) - 5296) + 605*x/(x^4*(log(
5) + 662) + 2*x^2*(log(5) + 662) - x*(log(5) + 662) + log(5)^2 + 654*log(5) - 5296) - 29*log(5)/(x^4*(log(5) +
662) + 2*x^2*(log(5) + 662) - x*(log(5) + 662) + log(5)^2 + 654*log(5) - 5296) + 232/(x^4*(log(5) + 662) + 2*
x^2*(log(5) + 662) - x*(log(5) + 662) + log(5)^2 + 654*log(5) - 5296) - 145/(x*(log(5) + 662) - 5*log(5) - 331
0))

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mupad [B]  time = 178.82, size = 45, normalized size = 1.41 \begin {gather*} {\mathrm {e}}^{\frac {x^3+4\,x}{3\,x+5\,\ln \relax (5)-x\,\ln \relax (5)+11\,x^2-2\,x^3+5\,x^4-x^5-40}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(-(4*x + x^3)/(log(5)*(x - 5) - 3*x - 11*x^2 + 2*x^3 - 5*x^4 + x^5 + 40))*(log(5)*(15*x^2 - 2*x^3 + 20
) - 164*x^2 + 22*x^3 - 49*x^4 + 16*x^5 - 5*x^6 + 2*x^7 - 160))/(log(5)*(110*x + 104*x^2 - 42*x^3 + 54*x^4 - 20
*x^5 + 2*x^6 - 400) - 240*x + log(5)^2*(x^2 - 10*x + 25) - 871*x^2 + 226*x^3 - 291*x^4 + 66*x^5 + 108*x^6 - 42
*x^7 + 29*x^8 - 10*x^9 + x^10 + 1600),x)

[Out]

exp((4*x + x^3)/(3*x + 5*log(5) - x*log(5) + 11*x^2 - 2*x^3 + 5*x^4 - x^5 - 40))

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sympy [A]  time = 6.26, size = 39, normalized size = 1.22 \begin {gather*} e^{\frac {- x^{3} - 4 x}{x^{5} - 5 x^{4} + 2 x^{3} - 11 x^{2} - 3 x + \left (x - 5\right ) \log {\relax (5 )} + 40}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-2*x**3+15*x**2+20)*ln(5)+2*x**7-5*x**6+16*x**5-49*x**4+22*x**3-164*x**2-160)*exp((-x**3-4*x)/((x-
5)*ln(5)+x**5-5*x**4+2*x**3-11*x**2-3*x+40))/((x**2-10*x+25)*ln(5)**2+(2*x**6-20*x**5+54*x**4-42*x**3+104*x**2
+110*x-400)*ln(5)+x**10-10*x**9+29*x**8-42*x**7+108*x**6+66*x**5-291*x**4+226*x**3-871*x**2-240*x+1600),x)

[Out]

exp((-x**3 - 4*x)/(x**5 - 5*x**4 + 2*x**3 - 11*x**2 - 3*x + (x - 5)*log(5) + 40))

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