3.80.75 \(\int (4 x^7-9 x^8+(-12 x^5+28 x^6) \log (3)+(12 x^3-30 x^4) \log ^2(3)+(-4 x+12 x^2) \log ^3(3)-\log ^4(3)+e^x (-8 x^7-x^8+(24 x^5+4 x^6) \log (3)+(-24 x^3-6 x^4) \log ^2(3)+(8 x+4 x^2) \log ^3(3)-\log ^4(3))) \, dx\)

Optimal. Leaf size=23 \[ \left (\frac {1}{2}-e^x-x\right ) \left (-x^2+\log (3)\right )^4 \]

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Rubi [B]  time = 0.51, antiderivative size = 121, normalized size of antiderivative = 5.26, number of steps used = 57, number of rules used = 3, integrand size = 126, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.024, Rules used = {2196, 2176, 2194} \begin {gather*} -x^9-e^x x^8+\frac {x^8}{2}+4 x^7 \log (3)+4 e^x x^6 \log (3)-2 x^6 \log (3)-6 x^5 \log ^2(3)-6 e^x x^4 \log ^2(3)+3 x^4 \log ^2(3)+4 x^3 \log ^3(3)+4 e^x x^2 \log ^3(3)-2 x^2 \log ^3(3)-x \log ^4(3)-e^x \log ^4(3) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[4*x^7 - 9*x^8 + (-12*x^5 + 28*x^6)*Log[3] + (12*x^3 - 30*x^4)*Log[3]^2 + (-4*x + 12*x^2)*Log[3]^3 - Log[3]
^4 + E^x*(-8*x^7 - x^8 + (24*x^5 + 4*x^6)*Log[3] + (-24*x^3 - 6*x^4)*Log[3]^2 + (8*x + 4*x^2)*Log[3]^3 - Log[3
]^4),x]

[Out]

x^8/2 - E^x*x^8 - x^9 - 2*x^6*Log[3] + 4*E^x*x^6*Log[3] + 4*x^7*Log[3] + 3*x^4*Log[3]^2 - 6*E^x*x^4*Log[3]^2 -
6*x^5*Log[3]^2 - 2*x^2*Log[3]^3 + 4*E^x*x^2*Log[3]^3 + 4*x^3*Log[3]^3 - E^x*Log[3]^4 - x*Log[3]^4

Rule 2176

Int[((b_.)*(F_)^((g_.)*((e_.) + (f_.)*(x_))))^(n_.)*((c_.) + (d_.)*(x_))^(m_.), x_Symbol] :> Simp[((c + d*x)^m
*(b*F^(g*(e + f*x)))^n)/(f*g*n*Log[F]), x] - Dist[(d*m)/(f*g*n*Log[F]), Int[(c + d*x)^(m - 1)*(b*F^(g*(e + f*x
)))^n, x], x] /; FreeQ[{F, b, c, d, e, f, g, n}, x] && GtQ[m, 0] && IntegerQ[2*m] &&  !$UseGamma === True

Rule 2194

Int[((F_)^((c_.)*((a_.) + (b_.)*(x_))))^(n_.), x_Symbol] :> Simp[(F^(c*(a + b*x)))^n/(b*c*n*Log[F]), x] /; Fre
eQ[{F, a, b, c, n}, x]

Rule 2196

Int[(F_)^((c_.)*(v_))*(u_), x_Symbol] :> Int[ExpandIntegrand[F^(c*ExpandToSum[v, x]), u, x], x] /; FreeQ[{F, c
}, x] && PolynomialQ[u, x] && LinearQ[v, x] &&  !$UseGamma === True

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {x^8}{2}-x^9-x \log ^4(3)+\log (3) \int \left (-12 x^5+28 x^6\right ) \, dx+\log ^2(3) \int \left (12 x^3-30 x^4\right ) \, dx+\log ^3(3) \int \left (-4 x+12 x^2\right ) \, dx+\int e^x \left (-8 x^7-x^8+\left (24 x^5+4 x^6\right ) \log (3)+\left (-24 x^3-6 x^4\right ) \log ^2(3)+\left (8 x+4 x^2\right ) \log ^3(3)-\log ^4(3)\right ) \, dx\\ &=\frac {x^8}{2}-x^9-2 x^6 \log (3)+4 x^7 \log (3)+3 x^4 \log ^2(3)-6 x^5 \log ^2(3)-2 x^2 \log ^3(3)+4 x^3 \log ^3(3)-x \log ^4(3)+\int \left (-8 e^x x^7-e^x x^8+4 e^x x^5 (6+x) \log (3)-6 e^x x^3 (4+x) \log ^2(3)+4 e^x x (2+x) \log ^3(3)-e^x \log ^4(3)\right ) \, dx\\ &=\frac {x^8}{2}-x^9-2 x^6 \log (3)+4 x^7 \log (3)+3 x^4 \log ^2(3)-6 x^5 \log ^2(3)-2 x^2 \log ^3(3)+4 x^3 \log ^3(3)-x \log ^4(3)-8 \int e^x x^7 \, dx+(4 \log (3)) \int e^x x^5 (6+x) \, dx-\left (6 \log ^2(3)\right ) \int e^x x^3 (4+x) \, dx+\left (4 \log ^3(3)\right ) \int e^x x (2+x) \, dx-\log ^4(3) \int e^x \, dx-\int e^x x^8 \, dx\\ &=-8 e^x x^7+\frac {x^8}{2}-e^x x^8-x^9-2 x^6 \log (3)+4 x^7 \log (3)+3 x^4 \log ^2(3)-6 x^5 \log ^2(3)-2 x^2 \log ^3(3)+4 x^3 \log ^3(3)-e^x \log ^4(3)-x \log ^4(3)+8 \int e^x x^7 \, dx+56 \int e^x x^6 \, dx+(4 \log (3)) \int \left (6 e^x x^5+e^x x^6\right ) \, dx-\left (6 \log ^2(3)\right ) \int \left (4 e^x x^3+e^x x^4\right ) \, dx+\left (4 \log ^3(3)\right ) \int \left (2 e^x x+e^x x^2\right ) \, dx\\ &=56 e^x x^6+\frac {x^8}{2}-e^x x^8-x^9-2 x^6 \log (3)+4 x^7 \log (3)+3 x^4 \log ^2(3)-6 x^5 \log ^2(3)-2 x^2 \log ^3(3)+4 x^3 \log ^3(3)-e^x \log ^4(3)-x \log ^4(3)-56 \int e^x x^6 \, dx-336 \int e^x x^5 \, dx+(4 \log (3)) \int e^x x^6 \, dx+(24 \log (3)) \int e^x x^5 \, dx-\left (6 \log ^2(3)\right ) \int e^x x^4 \, dx-\left (24 \log ^2(3)\right ) \int e^x x^3 \, dx+\left (4 \log ^3(3)\right ) \int e^x x^2 \, dx+\left (8 \log ^3(3)\right ) \int e^x x \, dx\\ &=-336 e^x x^5+\frac {x^8}{2}-e^x x^8-x^9+24 e^x x^5 \log (3)-2 x^6 \log (3)+4 e^x x^6 \log (3)+4 x^7 \log (3)-24 e^x x^3 \log ^2(3)+3 x^4 \log ^2(3)-6 e^x x^4 \log ^2(3)-6 x^5 \log ^2(3)+8 e^x x \log ^3(3)-2 x^2 \log ^3(3)+4 e^x x^2 \log ^3(3)+4 x^3 \log ^3(3)-e^x \log ^4(3)-x \log ^4(3)+336 \int e^x x^5 \, dx+1680 \int e^x x^4 \, dx-(24 \log (3)) \int e^x x^5 \, dx-(120 \log (3)) \int e^x x^4 \, dx+\left (24 \log ^2(3)\right ) \int e^x x^3 \, dx+\left (72 \log ^2(3)\right ) \int e^x x^2 \, dx-\left (8 \log ^3(3)\right ) \int e^x \, dx-\left (8 \log ^3(3)\right ) \int e^x x \, dx\\ &=1680 e^x x^4+\frac {x^8}{2}-e^x x^8-x^9-120 e^x x^4 \log (3)-2 x^6 \log (3)+4 e^x x^6 \log (3)+4 x^7 \log (3)+72 e^x x^2 \log ^2(3)+3 x^4 \log ^2(3)-6 e^x x^4 \log ^2(3)-6 x^5 \log ^2(3)-8 e^x \log ^3(3)-2 x^2 \log ^3(3)+4 e^x x^2 \log ^3(3)+4 x^3 \log ^3(3)-e^x \log ^4(3)-x \log ^4(3)-1680 \int e^x x^4 \, dx-6720 \int e^x x^3 \, dx+(120 \log (3)) \int e^x x^4 \, dx+(480 \log (3)) \int e^x x^3 \, dx-\left (72 \log ^2(3)\right ) \int e^x x^2 \, dx-\left (144 \log ^2(3)\right ) \int e^x x \, dx+\left (8 \log ^3(3)\right ) \int e^x \, dx\\ &=-6720 e^x x^3+\frac {x^8}{2}-e^x x^8-x^9+480 e^x x^3 \log (3)-2 x^6 \log (3)+4 e^x x^6 \log (3)+4 x^7 \log (3)-144 e^x x \log ^2(3)+3 x^4 \log ^2(3)-6 e^x x^4 \log ^2(3)-6 x^5 \log ^2(3)-2 x^2 \log ^3(3)+4 e^x x^2 \log ^3(3)+4 x^3 \log ^3(3)-e^x \log ^4(3)-x \log ^4(3)+6720 \int e^x x^3 \, dx+20160 \int e^x x^2 \, dx-(480 \log (3)) \int e^x x^3 \, dx-(1440 \log (3)) \int e^x x^2 \, dx+\left (144 \log ^2(3)\right ) \int e^x \, dx+\left (144 \log ^2(3)\right ) \int e^x x \, dx\\ &=20160 e^x x^2+\frac {x^8}{2}-e^x x^8-x^9-1440 e^x x^2 \log (3)-2 x^6 \log (3)+4 e^x x^6 \log (3)+4 x^7 \log (3)+144 e^x \log ^2(3)+3 x^4 \log ^2(3)-6 e^x x^4 \log ^2(3)-6 x^5 \log ^2(3)-2 x^2 \log ^3(3)+4 e^x x^2 \log ^3(3)+4 x^3 \log ^3(3)-e^x \log ^4(3)-x \log ^4(3)-20160 \int e^x x^2 \, dx-40320 \int e^x x \, dx+(1440 \log (3)) \int e^x x^2 \, dx+(2880 \log (3)) \int e^x x \, dx-\left (144 \log ^2(3)\right ) \int e^x \, dx\\ &=-40320 e^x x+\frac {x^8}{2}-e^x x^8-x^9+2880 e^x x \log (3)-2 x^6 \log (3)+4 e^x x^6 \log (3)+4 x^7 \log (3)+3 x^4 \log ^2(3)-6 e^x x^4 \log ^2(3)-6 x^5 \log ^2(3)-2 x^2 \log ^3(3)+4 e^x x^2 \log ^3(3)+4 x^3 \log ^3(3)-e^x \log ^4(3)-x \log ^4(3)+40320 \int e^x \, dx+40320 \int e^x x \, dx-(2880 \log (3)) \int e^x \, dx-(2880 \log (3)) \int e^x x \, dx\\ &=40320 e^x+\frac {x^8}{2}-e^x x^8-x^9-2880 e^x \log (3)-2 x^6 \log (3)+4 e^x x^6 \log (3)+4 x^7 \log (3)+3 x^4 \log ^2(3)-6 e^x x^4 \log ^2(3)-6 x^5 \log ^2(3)-2 x^2 \log ^3(3)+4 e^x x^2 \log ^3(3)+4 x^3 \log ^3(3)-e^x \log ^4(3)-x \log ^4(3)-40320 \int e^x \, dx+(2880 \log (3)) \int e^x \, dx\\ &=\frac {x^8}{2}-e^x x^8-x^9-2 x^6 \log (3)+4 e^x x^6 \log (3)+4 x^7 \log (3)+3 x^4 \log ^2(3)-6 e^x x^4 \log ^2(3)-6 x^5 \log ^2(3)-2 x^2 \log ^3(3)+4 e^x x^2 \log ^3(3)+4 x^3 \log ^3(3)-e^x \log ^4(3)-x \log ^4(3)\\ \end {aligned} \end {gather*}

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Mathematica [B]  time = 0.16, size = 85, normalized size = 3.70 \begin {gather*} \frac {x^8}{2}-x^9-e^x \left (x^2-\log (3)\right )^4-2 x^6 \log (3)+4 x^7 \log (3)+3 x^4 \log ^2(3)-6 x^5 \log ^2(3)-2 x^2 \log ^3(3)+4 x^3 \log ^3(3)-x \log ^4(3) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[4*x^7 - 9*x^8 + (-12*x^5 + 28*x^6)*Log[3] + (12*x^3 - 30*x^4)*Log[3]^2 + (-4*x + 12*x^2)*Log[3]^3 -
Log[3]^4 + E^x*(-8*x^7 - x^8 + (24*x^5 + 4*x^6)*Log[3] + (-24*x^3 - 6*x^4)*Log[3]^2 + (8*x + 4*x^2)*Log[3]^3 -
Log[3]^4),x]

[Out]

x^8/2 - x^9 - E^x*(x^2 - Log[3])^4 - 2*x^6*Log[3] + 4*x^7*Log[3] + 3*x^4*Log[3]^2 - 6*x^5*Log[3]^2 - 2*x^2*Log
[3]^3 + 4*x^3*Log[3]^3 - x*Log[3]^4

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fricas [B]  time = 0.62, size = 104, normalized size = 4.52 \begin {gather*} -x^{9} + \frac {1}{2} \, x^{8} - x \log \relax (3)^{4} + 2 \, {\left (2 \, x^{3} - x^{2}\right )} \log \relax (3)^{3} - 3 \, {\left (2 \, x^{5} - x^{4}\right )} \log \relax (3)^{2} - {\left (x^{8} - 4 \, x^{6} \log \relax (3) + 6 \, x^{4} \log \relax (3)^{2} - 4 \, x^{2} \log \relax (3)^{3} + \log \relax (3)^{4}\right )} e^{x} + 2 \, {\left (2 \, x^{7} - x^{6}\right )} \log \relax (3) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-log(3)^4+(4*x^2+8*x)*log(3)^3+(-6*x^4-24*x^3)*log(3)^2+(4*x^6+24*x^5)*log(3)-x^8-8*x^7)*exp(x)-log
(3)^4+(12*x^2-4*x)*log(3)^3+(-30*x^4+12*x^3)*log(3)^2+(28*x^6-12*x^5)*log(3)-9*x^8+4*x^7,x, algorithm="fricas"
)

[Out]

-x^9 + 1/2*x^8 - x*log(3)^4 + 2*(2*x^3 - x^2)*log(3)^3 - 3*(2*x^5 - x^4)*log(3)^2 - (x^8 - 4*x^6*log(3) + 6*x^
4*log(3)^2 - 4*x^2*log(3)^3 + log(3)^4)*e^x + 2*(2*x^7 - x^6)*log(3)

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giac [B]  time = 0.15, size = 104, normalized size = 4.52 \begin {gather*} -x^{9} + \frac {1}{2} \, x^{8} - x \log \relax (3)^{4} + 2 \, {\left (2 \, x^{3} - x^{2}\right )} \log \relax (3)^{3} - 3 \, {\left (2 \, x^{5} - x^{4}\right )} \log \relax (3)^{2} - {\left (x^{8} - 4 \, x^{6} \log \relax (3) + 6 \, x^{4} \log \relax (3)^{2} - 4 \, x^{2} \log \relax (3)^{3} + \log \relax (3)^{4}\right )} e^{x} + 2 \, {\left (2 \, x^{7} - x^{6}\right )} \log \relax (3) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-log(3)^4+(4*x^2+8*x)*log(3)^3+(-6*x^4-24*x^3)*log(3)^2+(4*x^6+24*x^5)*log(3)-x^8-8*x^7)*exp(x)-log
(3)^4+(12*x^2-4*x)*log(3)^3+(-30*x^4+12*x^3)*log(3)^2+(28*x^6-12*x^5)*log(3)-9*x^8+4*x^7,x, algorithm="giac")

[Out]

-x^9 + 1/2*x^8 - x*log(3)^4 + 2*(2*x^3 - x^2)*log(3)^3 - 3*(2*x^5 - x^4)*log(3)^2 - (x^8 - 4*x^6*log(3) + 6*x^
4*log(3)^2 - 4*x^2*log(3)^3 + log(3)^4)*e^x + 2*(2*x^7 - x^6)*log(3)

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maple [B]  time = 0.07, size = 109, normalized size = 4.74

method	result	size
risch	\(\left (-x^{8}+4 x^{6} \ln \relax (3)-6 x^{4} \ln \relax (3)^{2}+4 \ln \relax (3)^{3} x^{2}-\ln \relax (3)^{4}\right ) {\mathrm e}^{x}-x \ln \relax (3)^{4}+4 x^{3} \ln \relax (3)^{3}-2 \ln \relax (3)^{3} x^{2}-6 x^{5} \ln \relax (3)^{2}+3 x^{4} \ln \relax (3)^{2}+4 \ln \relax (3) x^{7}-2 x^{6} \ln \relax (3)-x^{9}+\frac {x^{8}}{2}\)	\(109\)
default	\(-x^{8} {\mathrm e}^{x}-{\mathrm e}^{x} \ln \relax (3)^{4}-6 \,{\mathrm e}^{x} x^{4} \ln \relax (3)^{2}+4 \,{\mathrm e}^{x} \ln \relax (3) x^{6}+4 \,{\mathrm e}^{x} \ln \relax (3)^{3} x^{2}+4 x^{3} \ln \relax (3)^{3}-2 \ln \relax (3)^{3} x^{2}-6 x^{5} \ln \relax (3)^{2}+3 x^{4} \ln \relax (3)^{2}+4 \ln \relax (3) x^{7}-2 x^{6} \ln \relax (3)+\frac {x^{8}}{2}-x^{9}-x \ln \relax (3)^{4}\)	\(115\)
norman	\(-x^{8} {\mathrm e}^{x}-{\mathrm e}^{x} \ln \relax (3)^{4}-6 \,{\mathrm e}^{x} x^{4} \ln \relax (3)^{2}+4 \,{\mathrm e}^{x} \ln \relax (3) x^{6}+4 \,{\mathrm e}^{x} \ln \relax (3)^{3} x^{2}+4 x^{3} \ln \relax (3)^{3}-2 \ln \relax (3)^{3} x^{2}-6 x^{5} \ln \relax (3)^{2}+3 x^{4} \ln \relax (3)^{2}+4 \ln \relax (3) x^{7}-2 x^{6} \ln \relax (3)+\frac {x^{8}}{2}-x^{9}-x \ln \relax (3)^{4}\)	\(115\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((-ln(3)^4+(4*x^2+8*x)*ln(3)^3+(-6*x^4-24*x^3)*ln(3)^2+(4*x^6+24*x^5)*ln(3)-x^8-8*x^7)*exp(x)-ln(3)^4+(12*x
^2-4*x)*ln(3)^3+(-30*x^4+12*x^3)*ln(3)^2+(28*x^6-12*x^5)*ln(3)-9*x^8+4*x^7,x,method=_RETURNVERBOSE)

[Out]

(-x^8+4*x^6*ln(3)-6*x^4*ln(3)^2+4*ln(3)^3*x^2-ln(3)^4)*exp(x)-x*ln(3)^4+4*x^3*ln(3)^3-2*ln(3)^3*x^2-6*x^5*ln(3
)^2+3*x^4*ln(3)^2+4*ln(3)*x^7-2*x^6*ln(3)-x^9+1/2*x^8

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maxima [B]  time = 0.45, size = 104, normalized size = 4.52 \begin {gather*} -x^{9} + \frac {1}{2} \, x^{8} - x \log \relax (3)^{4} + 2 \, {\left (2 \, x^{3} - x^{2}\right )} \log \relax (3)^{3} - 3 \, {\left (2 \, x^{5} - x^{4}\right )} \log \relax (3)^{2} - {\left (x^{8} - 4 \, x^{6} \log \relax (3) + 6 \, x^{4} \log \relax (3)^{2} - 4 \, x^{2} \log \relax (3)^{3} + \log \relax (3)^{4}\right )} e^{x} + 2 \, {\left (2 \, x^{7} - x^{6}\right )} \log \relax (3) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-log(3)^4+(4*x^2+8*x)*log(3)^3+(-6*x^4-24*x^3)*log(3)^2+(4*x^6+24*x^5)*log(3)-x^8-8*x^7)*exp(x)-log
(3)^4+(12*x^2-4*x)*log(3)^3+(-30*x^4+12*x^3)*log(3)^2+(28*x^6-12*x^5)*log(3)-9*x^8+4*x^7,x, algorithm="maxima"
)

[Out]

-x^9 + 1/2*x^8 - x*log(3)^4 + 2*(2*x^3 - x^2)*log(3)^3 - 3*(2*x^5 - x^4)*log(3)^2 - (x^8 - 4*x^6*log(3) + 6*x^
4*log(3)^2 - 4*x^2*log(3)^3 + log(3)^4)*e^x + 2*(2*x^7 - x^6)*log(3)

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mupad [B]  time = 0.36, size = 114, normalized size = 4.96 \begin {gather*} 4\,x^3\,{\ln \relax (3)}^3-2\,x^2\,{\ln \relax (3)}^3+3\,x^4\,{\ln \relax (3)}^2-6\,x^5\,{\ln \relax (3)}^2-{\mathrm {e}}^x\,{\ln \relax (3)}^4-x^8\,{\mathrm {e}}^x-x\,{\ln \relax (3)}^4-2\,x^6\,\ln \relax (3)+4\,x^7\,\ln \relax (3)+\frac {x^8}{2}-x^9+4\,x^6\,{\mathrm {e}}^x\,\ln \relax (3)+4\,x^2\,{\mathrm {e}}^x\,{\ln \relax (3)}^3-6\,x^4\,{\mathrm {e}}^x\,{\ln \relax (3)}^2 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(4*x^7 - log(3)*(12*x^5 - 28*x^6) - exp(x)*(log(3)^4 - log(3)*(24*x^5 + 4*x^6) - log(3)^3*(8*x + 4*x^2) + 8
*x^7 + x^8 + log(3)^2*(24*x^3 + 6*x^4)) - log(3)^4 - log(3)^3*(4*x - 12*x^2) - 9*x^8 + log(3)^2*(12*x^3 - 30*x
^4),x)

[Out]

4*x^3*log(3)^3 - 2*x^2*log(3)^3 + 3*x^4*log(3)^2 - 6*x^5*log(3)^2 - exp(x)*log(3)^4 - x^8*exp(x) - x*log(3)^4
- 2*x^6*log(3) + 4*x^7*log(3) + x^8/2 - x^9 + 4*x^6*exp(x)*log(3) + 4*x^2*exp(x)*log(3)^3 - 6*x^4*exp(x)*log(3
)^2

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sympy [B]  time = 0.18, size = 112, normalized size = 4.87 \begin {gather*} - x^{9} + \frac {x^{8}}{2} + 4 x^{7} \log {\relax (3 )} - 2 x^{6} \log {\relax (3 )} - 6 x^{5} \log {\relax (3 )}^{2} + 3 x^{4} \log {\relax (3 )}^{2} + 4 x^{3} \log {\relax (3 )}^{3} - 2 x^{2} \log {\relax (3 )}^{3} - x \log {\relax (3 )}^{4} + \left (- x^{8} + 4 x^{6} \log {\relax (3 )} - 6 x^{4} \log {\relax (3 )}^{2} + 4 x^{2} \log {\relax (3 )}^{3} - \log {\relax (3 )}^{4}\right ) e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-ln(3)**4+(4*x**2+8*x)*ln(3)**3+(-6*x**4-24*x**3)*ln(3)**2+(4*x**6+24*x**5)*ln(3)-x**8-8*x**7)*exp(
x)-ln(3)**4+(12*x**2-4*x)*ln(3)**3+(-30*x**4+12*x**3)*ln(3)**2+(28*x**6-12*x**5)*ln(3)-9*x**8+4*x**7,x)

[Out]

-x**9 + x**8/2 + 4*x**7*log(3) - 2*x**6*log(3) - 6*x**5*log(3)**2 + 3*x**4*log(3)**2 + 4*x**3*log(3)**3 - 2*x*
*2*log(3)**3 - x*log(3)**4 + (-x**8 + 4*x**6*log(3) - 6*x**4*log(3)**2 + 4*x**2*log(3)**3 - log(3)**4)*exp(x)

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