3.39.36 \(\int \frac {-80 x-80 x^3+e^x (-16 x-16 x^2-16 x^3)-32 \log (x)-16 x^2 \log ^2(x)}{e^{2 x^2} (3125 x^6+3125 e^x x^6+1250 e^{2 x} x^6+250 e^{3 x} x^6+25 e^{4 x} x^6+e^{5 x} x^6)+e^{2 x^2} (3125 x^5+2500 e^x x^5+750 e^{2 x} x^5+100 e^{3 x} x^5+5 e^{4 x} x^5) \log ^2(x)+e^{2 x^2} (1250 x^4+750 e^x x^4+150 e^{2 x} x^4+10 e^{3 x} x^4) \log ^4(x)+e^{2 x^2} (250 x^3+100 e^x x^3+10 e^{2 x} x^3) \log ^6(x)+e^{2 x^2} (25 x^2+5 e^x x^2) \log ^8(x)+e^{2 x^2} x \log ^{10}(x)} \, dx\)

Optimal. Leaf size=24 \[ \frac {4 e^{-2 x^2}}{\left (5 x+e^x x+\log ^2(x)\right )^4} \]

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Rubi [F]  time = 5.85, 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 {-80 x-80 x^3+e^x \left (-16 x-16 x^2-16 x^3\right )-32 \log (x)-16 x^2 \log ^2(x)}{e^{2 x^2} \left (3125 x^6+3125 e^x x^6+1250 e^{2 x} x^6+250 e^{3 x} x^6+25 e^{4 x} x^6+e^{5 x} x^6\right )+e^{2 x^2} \left (3125 x^5+2500 e^x x^5+750 e^{2 x} x^5+100 e^{3 x} x^5+5 e^{4 x} x^5\right ) \log ^2(x)+e^{2 x^2} \left (1250 x^4+750 e^x x^4+150 e^{2 x} x^4+10 e^{3 x} x^4\right ) \log ^4(x)+e^{2 x^2} \left (250 x^3+100 e^x x^3+10 e^{2 x} x^3\right ) \log ^6(x)+e^{2 x^2} \left (25 x^2+5 e^x x^2\right ) \log ^8(x)+e^{2 x^2} x \log ^{10}(x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-80*x - 80*x^3 + E^x*(-16*x - 16*x^2 - 16*x^3) - 32*Log[x] - 16*x^2*Log[x]^2)/(E^(2*x^2)*(3125*x^6 + 3125
*E^x*x^6 + 1250*E^(2*x)*x^6 + 250*E^(3*x)*x^6 + 25*E^(4*x)*x^6 + E^(5*x)*x^6) + E^(2*x^2)*(3125*x^5 + 2500*E^x
*x^5 + 750*E^(2*x)*x^5 + 100*E^(3*x)*x^5 + 5*E^(4*x)*x^5)*Log[x]^2 + E^(2*x^2)*(1250*x^4 + 750*E^x*x^4 + 150*E
^(2*x)*x^4 + 10*E^(3*x)*x^4)*Log[x]^4 + E^(2*x^2)*(250*x^3 + 100*E^x*x^3 + 10*E^(2*x)*x^3)*Log[x]^6 + E^(2*x^2
)*(25*x^2 + 5*E^x*x^2)*Log[x]^8 + E^(2*x^2)*x*Log[x]^10),x]

[Out]

80*Defer[Int][x/(E^(2*x^2)*(5*x + E^x*x + Log[x]^2)^5), x] - 32*Defer[Int][Log[x]/(E^(2*x^2)*x*(5*x + E^x*x +
Log[x]^2)^5), x] + 16*Defer[Int][Log[x]^2/(E^(2*x^2)*(5*x + E^x*x + Log[x]^2)^5), x] + 16*Defer[Int][Log[x]^2/
(E^(2*x^2)*x*(5*x + E^x*x + Log[x]^2)^5), x] - 16*Defer[Int][1/(E^(2*x^2)*(5*x + E^x*x + Log[x]^2)^4), x] - 16
*Defer[Int][1/(E^(2*x^2)*x*(5*x + E^x*x + Log[x]^2)^4), x] - 16*Defer[Int][x/(E^(2*x^2)*(5*x + E^x*x + Log[x]^
2)^4), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {16 e^{-2 x^2} \left (-5 x \left (1+x^2\right )-e^x x \left (1+x+x^2\right )-2 \log (x)-x^2 \log ^2(x)\right )}{x \left (\left (5+e^x\right ) x+\log ^2(x)\right )^5} \, dx\\ &=16 \int \frac {e^{-2 x^2} \left (-5 x \left (1+x^2\right )-e^x x \left (1+x+x^2\right )-2 \log (x)-x^2 \log ^2(x)\right )}{x \left (\left (5+e^x\right ) x+\log ^2(x)\right )^5} \, dx\\ &=16 \int \left (-\frac {e^{-2 x^2} \left (1+x+x^2\right )}{x \left (5 x+e^x x+\log ^2(x)\right )^4}+\frac {e^{-2 x^2} \left (5 x^2-2 \log (x)+\log ^2(x)+x \log ^2(x)\right )}{x \left (5 x+e^x x+\log ^2(x)\right )^5}\right ) \, dx\\ &=-\left (16 \int \frac {e^{-2 x^2} \left (1+x+x^2\right )}{x \left (5 x+e^x x+\log ^2(x)\right )^4} \, dx\right )+16 \int \frac {e^{-2 x^2} \left (5 x^2-2 \log (x)+\log ^2(x)+x \log ^2(x)\right )}{x \left (5 x+e^x x+\log ^2(x)\right )^5} \, dx\\ &=16 \int \left (\frac {5 e^{-2 x^2} x}{\left (5 x+e^x x+\log ^2(x)\right )^5}-\frac {2 e^{-2 x^2} \log (x)}{x \left (5 x+e^x x+\log ^2(x)\right )^5}+\frac {e^{-2 x^2} \log ^2(x)}{\left (5 x+e^x x+\log ^2(x)\right )^5}+\frac {e^{-2 x^2} \log ^2(x)}{x \left (5 x+e^x x+\log ^2(x)\right )^5}\right ) \, dx-16 \int \left (\frac {e^{-2 x^2}}{\left (5 x+e^x x+\log ^2(x)\right )^4}+\frac {e^{-2 x^2}}{x \left (5 x+e^x x+\log ^2(x)\right )^4}+\frac {e^{-2 x^2} x}{\left (5 x+e^x x+\log ^2(x)\right )^4}\right ) \, dx\\ &=16 \int \frac {e^{-2 x^2} \log ^2(x)}{\left (5 x+e^x x+\log ^2(x)\right )^5} \, dx+16 \int \frac {e^{-2 x^2} \log ^2(x)}{x \left (5 x+e^x x+\log ^2(x)\right )^5} \, dx-16 \int \frac {e^{-2 x^2}}{\left (5 x+e^x x+\log ^2(x)\right )^4} \, dx-16 \int \frac {e^{-2 x^2}}{x \left (5 x+e^x x+\log ^2(x)\right )^4} \, dx-16 \int \frac {e^{-2 x^2} x}{\left (5 x+e^x x+\log ^2(x)\right )^4} \, dx-32 \int \frac {e^{-2 x^2} \log (x)}{x \left (5 x+e^x x+\log ^2(x)\right )^5} \, dx+80 \int \frac {e^{-2 x^2} x}{\left (5 x+e^x x+\log ^2(x)\right )^5} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 1.53, size = 24, normalized size = 1.00 \begin {gather*} \frac {4 e^{-2 x^2}}{\left (5 x+e^x x+\log ^2(x)\right )^4} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-80*x - 80*x^3 + E^x*(-16*x - 16*x^2 - 16*x^3) - 32*Log[x] - 16*x^2*Log[x]^2)/(E^(2*x^2)*(3125*x^6
+ 3125*E^x*x^6 + 1250*E^(2*x)*x^6 + 250*E^(3*x)*x^6 + 25*E^(4*x)*x^6 + E^(5*x)*x^6) + E^(2*x^2)*(3125*x^5 + 25
00*E^x*x^5 + 750*E^(2*x)*x^5 + 100*E^(3*x)*x^5 + 5*E^(4*x)*x^5)*Log[x]^2 + E^(2*x^2)*(1250*x^4 + 750*E^x*x^4 +
150*E^(2*x)*x^4 + 10*E^(3*x)*x^4)*Log[x]^4 + E^(2*x^2)*(250*x^3 + 100*E^x*x^3 + 10*E^(2*x)*x^3)*Log[x]^6 + E^
(2*x^2)*(25*x^2 + 5*E^x*x^2)*Log[x]^8 + E^(2*x^2)*x*Log[x]^10),x]

[Out]

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

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fricas [B]  time = 0.62, size = 157, normalized size = 6.54 \begin {gather*} \frac {4}{e^{\left (2 \, x^{2}\right )} \log \relax (x)^{8} + 4 \, {\left (x e^{x} + 5 \, x\right )} e^{\left (2 \, x^{2}\right )} \log \relax (x)^{6} + 6 \, {\left (x^{2} e^{\left (2 \, x\right )} + 10 \, x^{2} e^{x} + 25 \, x^{2}\right )} e^{\left (2 \, x^{2}\right )} \log \relax (x)^{4} + 4 \, {\left (x^{3} e^{\left (3 \, x\right )} + 15 \, x^{3} e^{\left (2 \, x\right )} + 75 \, x^{3} e^{x} + 125 \, x^{3}\right )} e^{\left (2 \, x^{2}\right )} \log \relax (x)^{2} + {\left (x^{4} e^{\left (4 \, x\right )} + 20 \, x^{4} e^{\left (3 \, x\right )} + 150 \, x^{4} e^{\left (2 \, x\right )} + 500 \, x^{4} e^{x} + 625 \, x^{4}\right )} e^{\left (2 \, x^{2}\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-16*x^2*log(x)^2-32*log(x)+(-16*x^3-16*x^2-16*x)*exp(x)-80*x^3-80*x)/(x*exp(x^2)^2*log(x)^10+(5*exp
(x)*x^2+25*x^2)*exp(x^2)^2*log(x)^8+(10*exp(x)^2*x^3+100*exp(x)*x^3+250*x^3)*exp(x^2)^2*log(x)^6+(10*x^4*exp(x
)^3+150*exp(x)^2*x^4+750*exp(x)*x^4+1250*x^4)*exp(x^2)^2*log(x)^4+(5*x^5*exp(x)^4+100*x^5*exp(x)^3+750*x^5*exp
(x)^2+2500*x^5*exp(x)+3125*x^5)*exp(x^2)^2*log(x)^2+(x^6*exp(x)^5+25*x^6*exp(x)^4+250*x^6*exp(x)^3+1250*x^6*ex
p(x)^2+3125*x^6*exp(x)+3125*x^6)*exp(x^2)^2),x, algorithm="fricas")

[Out]

4/(e^(2*x^2)*log(x)^8 + 4*(x*e^x + 5*x)*e^(2*x^2)*log(x)^6 + 6*(x^2*e^(2*x) + 10*x^2*e^x + 25*x^2)*e^(2*x^2)*l
og(x)^4 + 4*(x^3*e^(3*x) + 15*x^3*e^(2*x) + 75*x^3*e^x + 125*x^3)*e^(2*x^2)*log(x)^2 + (x^4*e^(4*x) + 20*x^4*e
^(3*x) + 150*x^4*e^(2*x) + 500*x^4*e^x + 625*x^4)*e^(2*x^2))

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giac [B]  time = 0.84, size = 239, normalized size = 9.96 \begin {gather*} \frac {4 \, e^{\left (2 \, x^{2}\right )}}{e^{\left (4 \, x^{2}\right )} \log \relax (x)^{8} + 20 \, x e^{\left (4 \, x^{2}\right )} \log \relax (x)^{6} + 4 \, x e^{\left (4 \, x^{2} + x\right )} \log \relax (x)^{6} + 150 \, x^{2} e^{\left (4 \, x^{2}\right )} \log \relax (x)^{4} + 6 \, x^{2} e^{\left (4 \, x^{2} + 2 \, x\right )} \log \relax (x)^{4} + 60 \, x^{2} e^{\left (4 \, x^{2} + x\right )} \log \relax (x)^{4} + 500 \, x^{3} e^{\left (4 \, x^{2}\right )} \log \relax (x)^{2} + 4 \, x^{3} e^{\left (4 \, x^{2} + 3 \, x\right )} \log \relax (x)^{2} + 60 \, x^{3} e^{\left (4 \, x^{2} + 2 \, x\right )} \log \relax (x)^{2} + 300 \, x^{3} e^{\left (4 \, x^{2} + x\right )} \log \relax (x)^{2} + 625 \, x^{4} e^{\left (4 \, x^{2}\right )} + x^{4} e^{\left (4 \, x^{2} + 4 \, x\right )} + 20 \, x^{4} e^{\left (4 \, x^{2} + 3 \, x\right )} + 150 \, x^{4} e^{\left (4 \, x^{2} + 2 \, x\right )} + 500 \, x^{4} e^{\left (4 \, x^{2} + x\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-16*x^2*log(x)^2-32*log(x)+(-16*x^3-16*x^2-16*x)*exp(x)-80*x^3-80*x)/(x*exp(x^2)^2*log(x)^10+(5*exp
(x)*x^2+25*x^2)*exp(x^2)^2*log(x)^8+(10*exp(x)^2*x^3+100*exp(x)*x^3+250*x^3)*exp(x^2)^2*log(x)^6+(10*x^4*exp(x
)^3+150*exp(x)^2*x^4+750*exp(x)*x^4+1250*x^4)*exp(x^2)^2*log(x)^4+(5*x^5*exp(x)^4+100*x^5*exp(x)^3+750*x^5*exp
(x)^2+2500*x^5*exp(x)+3125*x^5)*exp(x^2)^2*log(x)^2+(x^6*exp(x)^5+25*x^6*exp(x)^4+250*x^6*exp(x)^3+1250*x^6*ex
p(x)^2+3125*x^6*exp(x)+3125*x^6)*exp(x^2)^2),x, algorithm="giac")

[Out]

4*e^(2*x^2)/(e^(4*x^2)*log(x)^8 + 20*x*e^(4*x^2)*log(x)^6 + 4*x*e^(4*x^2 + x)*log(x)^6 + 150*x^2*e^(4*x^2)*log
(x)^4 + 6*x^2*e^(4*x^2 + 2*x)*log(x)^4 + 60*x^2*e^(4*x^2 + x)*log(x)^4 + 500*x^3*e^(4*x^2)*log(x)^2 + 4*x^3*e^
(4*x^2 + 3*x)*log(x)^2 + 60*x^3*e^(4*x^2 + 2*x)*log(x)^2 + 300*x^3*e^(4*x^2 + x)*log(x)^2 + 625*x^4*e^(4*x^2)
+ x^4*e^(4*x^2 + 4*x) + 20*x^4*e^(4*x^2 + 3*x) + 150*x^4*e^(4*x^2 + 2*x) + 500*x^4*e^(4*x^2 + x))

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maple [A]  time = 0.08, size = 23, normalized size = 0.96

method	result	size
risch	\(\frac {4 \,{\mathrm e}^{-2 x^{2}}}{\left (\ln \relax (x )^{2}+5 x +{\mathrm e}^{x} x \right )^{4}}\)	\(23\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((-16*x^2*ln(x)^2-32*ln(x)+(-16*x^3-16*x^2-16*x)*exp(x)-80*x^3-80*x)/(x*exp(x^2)^2*ln(x)^10+(5*exp(x)*x^2+2
5*x^2)*exp(x^2)^2*ln(x)^8+(10*exp(x)^2*x^3+100*exp(x)*x^3+250*x^3)*exp(x^2)^2*ln(x)^6+(10*x^4*exp(x)^3+150*exp
(x)^2*x^4+750*exp(x)*x^4+1250*x^4)*exp(x^2)^2*ln(x)^4+(5*x^5*exp(x)^4+100*x^5*exp(x)^3+750*x^5*exp(x)^2+2500*x
^5*exp(x)+3125*x^5)*exp(x^2)^2*ln(x)^2+(x^6*exp(x)^5+25*x^6*exp(x)^4+250*x^6*exp(x)^3+1250*x^6*exp(x)^2+3125*x
^6*exp(x)+3125*x^6)*exp(x^2)^2),x,method=_RETURNVERBOSE)

[Out]

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

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maxima [B]  time = 0.47, size = 136, normalized size = 5.67 \begin {gather*} \frac {4 \, e^{\left (-2 \, x^{2}\right )}}{\log \relax (x)^{8} + 20 \, x \log \relax (x)^{6} + 150 \, x^{2} \log \relax (x)^{4} + x^{4} e^{\left (4 \, x\right )} + 500 \, x^{3} \log \relax (x)^{2} + 625 \, x^{4} + 4 \, {\left (x^{3} \log \relax (x)^{2} + 5 \, x^{4}\right )} e^{\left (3 \, x\right )} + 6 \, {\left (x^{2} \log \relax (x)^{4} + 10 \, x^{3} \log \relax (x)^{2} + 25 \, x^{4}\right )} e^{\left (2 \, x\right )} + 4 \, {\left (x \log \relax (x)^{6} + 15 \, x^{2} \log \relax (x)^{4} + 75 \, x^{3} \log \relax (x)^{2} + 125 \, x^{4}\right )} e^{x}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-16*x^2*log(x)^2-32*log(x)+(-16*x^3-16*x^2-16*x)*exp(x)-80*x^3-80*x)/(x*exp(x^2)^2*log(x)^10+(5*exp
(x)*x^2+25*x^2)*exp(x^2)^2*log(x)^8+(10*exp(x)^2*x^3+100*exp(x)*x^3+250*x^3)*exp(x^2)^2*log(x)^6+(10*x^4*exp(x
)^3+150*exp(x)^2*x^4+750*exp(x)*x^4+1250*x^4)*exp(x^2)^2*log(x)^4+(5*x^5*exp(x)^4+100*x^5*exp(x)^3+750*x^5*exp
(x)^2+2500*x^5*exp(x)+3125*x^5)*exp(x^2)^2*log(x)^2+(x^6*exp(x)^5+25*x^6*exp(x)^4+250*x^6*exp(x)^3+1250*x^6*ex
p(x)^2+3125*x^6*exp(x)+3125*x^6)*exp(x^2)^2),x, algorithm="maxima")

[Out]

4*e^(-2*x^2)/(log(x)^8 + 20*x*log(x)^6 + 150*x^2*log(x)^4 + x^4*e^(4*x) + 500*x^3*log(x)^2 + 625*x^4 + 4*(x^3*
log(x)^2 + 5*x^4)*e^(3*x) + 6*(x^2*log(x)^4 + 10*x^3*log(x)^2 + 25*x^4)*e^(2*x) + 4*(x*log(x)^6 + 15*x^2*log(x
)^4 + 75*x^3*log(x)^2 + 125*x^4)*e^x)

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mupad [B]  time = 3.00, size = 148, normalized size = 6.17 \begin {gather*} \frac {4\,{\mathrm {e}}^{-2\,x^2}}{500\,x^4\,{\mathrm {e}}^x+20\,x\,{\ln \relax (x)}^6+{\ln \relax (x)}^8+150\,x^4\,{\mathrm {e}}^{2\,x}+20\,x^4\,{\mathrm {e}}^{3\,x}+x^4\,{\mathrm {e}}^{4\,x}+500\,x^3\,{\ln \relax (x)}^2+150\,x^2\,{\ln \relax (x)}^4+625\,x^4+300\,x^3\,{\mathrm {e}}^x\,{\ln \relax (x)}^2+60\,x^2\,{\mathrm {e}}^x\,{\ln \relax (x)}^4+60\,x^3\,{\mathrm {e}}^{2\,x}\,{\ln \relax (x)}^2+6\,x^2\,{\mathrm {e}}^{2\,x}\,{\ln \relax (x)}^4+4\,x^3\,{\mathrm {e}}^{3\,x}\,{\ln \relax (x)}^2+4\,x\,{\mathrm {e}}^x\,{\ln \relax (x)}^6} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(80*x + 32*log(x) + 16*x^2*log(x)^2 + 80*x^3 + exp(x)*(16*x + 16*x^2 + 16*x^3))/(exp(2*x^2)*(3125*x^6*exp
(x) + 1250*x^6*exp(2*x) + 250*x^6*exp(3*x) + 25*x^6*exp(4*x) + x^6*exp(5*x) + 3125*x^6) + exp(2*x^2)*log(x)^2*
(2500*x^5*exp(x) + 750*x^5*exp(2*x) + 100*x^5*exp(3*x) + 5*x^5*exp(4*x) + 3125*x^5) + exp(2*x^2)*log(x)^6*(100
*x^3*exp(x) + 10*x^3*exp(2*x) + 250*x^3) + x*exp(2*x^2)*log(x)^10 + exp(2*x^2)*log(x)^4*(750*x^4*exp(x) + 150*
x^4*exp(2*x) + 10*x^4*exp(3*x) + 1250*x^4) + exp(2*x^2)*log(x)^8*(5*x^2*exp(x) + 25*x^2)),x)

[Out]

(4*exp(-2*x^2))/(500*x^4*exp(x) + 20*x*log(x)^6 + log(x)^8 + 150*x^4*exp(2*x) + 20*x^4*exp(3*x) + x^4*exp(4*x)
+ 500*x^3*log(x)^2 + 150*x^2*log(x)^4 + 625*x^4 + 300*x^3*exp(x)*log(x)^2 + 60*x^2*exp(x)*log(x)^4 + 60*x^3*e
xp(2*x)*log(x)^2 + 6*x^2*exp(2*x)*log(x)^4 + 4*x^3*exp(3*x)*log(x)^2 + 4*x*exp(x)*log(x)^6)

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sympy [B]  time = 0.84, size = 168, normalized size = 7.00 \begin {gather*} \frac {4 e^{- 2 x^{2}}}{x^{4} e^{4 x} + 20 x^{4} e^{3 x} + 150 x^{4} e^{2 x} + 500 x^{4} e^{x} + 625 x^{4} + 4 x^{3} e^{3 x} \log {\relax (x )}^{2} + 60 x^{3} e^{2 x} \log {\relax (x )}^{2} + 300 x^{3} e^{x} \log {\relax (x )}^{2} + 500 x^{3} \log {\relax (x )}^{2} + 6 x^{2} e^{2 x} \log {\relax (x )}^{4} + 60 x^{2} e^{x} \log {\relax (x )}^{4} + 150 x^{2} \log {\relax (x )}^{4} + 4 x e^{x} \log {\relax (x )}^{6} + 20 x \log {\relax (x )}^{6} + \log {\relax (x )}^{8}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-16*x**2*ln(x)**2-32*ln(x)+(-16*x**3-16*x**2-16*x)*exp(x)-80*x**3-80*x)/(x*exp(x**2)**2*ln(x)**10+(
5*exp(x)*x**2+25*x**2)*exp(x**2)**2*ln(x)**8+(10*exp(x)**2*x**3+100*exp(x)*x**3+250*x**3)*exp(x**2)**2*ln(x)**
6+(10*x**4*exp(x)**3+150*exp(x)**2*x**4+750*exp(x)*x**4+1250*x**4)*exp(x**2)**2*ln(x)**4+(5*x**5*exp(x)**4+100
*x**5*exp(x)**3+750*x**5*exp(x)**2+2500*x**5*exp(x)+3125*x**5)*exp(x**2)**2*ln(x)**2+(x**6*exp(x)**5+25*x**6*e
xp(x)**4+250*x**6*exp(x)**3+1250*x**6*exp(x)**2+3125*x**6*exp(x)+3125*x**6)*exp(x**2)**2),x)

[Out]

4*exp(-2*x**2)/(x**4*exp(4*x) + 20*x**4*exp(3*x) + 150*x**4*exp(2*x) + 500*x**4*exp(x) + 625*x**4 + 4*x**3*exp
(3*x)*log(x)**2 + 60*x**3*exp(2*x)*log(x)**2 + 300*x**3*exp(x)*log(x)**2 + 500*x**3*log(x)**2 + 6*x**2*exp(2*x
)*log(x)**4 + 60*x**2*exp(x)*log(x)**4 + 150*x**2*log(x)**4 + 4*x*exp(x)*log(x)**6 + 20*x*log(x)**6 + log(x)**
8)

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