3.19.69 \(\int \frac {1-6 x+11 x^2-6 x^3+x^4+(18-54 x+18 x^2) \log (3)+81 \log ^2(3)+e^{e^x-x} ((-1+x-2 x^2+x^3) \log (3)+(-9+9 x) \log ^2(3)+e^x ((-x+3 x^2-x^3) \log (3)-9 x \log ^2(3)))}{1-6 x+11 x^2-6 x^3+x^4+(18-54 x+18 x^2) \log (3)+81 \log ^2(3)} \, dx\)

Optimal. Leaf size=33 \[ x+\frac {e^{e^x-x} x}{-9+\frac {-(1-x)^2+x}{\log (3)}} \]

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Rubi [F]  time = 4.05, 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 {1-6 x+11 x^2-6 x^3+x^4+\left (18-54 x+18 x^2\right ) \log (3)+81 \log ^2(3)+e^{e^x-x} \left (\left (-1+x-2 x^2+x^3\right ) \log (3)+(-9+9 x) \log ^2(3)+e^x \left (\left (-x+3 x^2-x^3\right ) \log (3)-9 x \log ^2(3)\right )\right )}{1-6 x+11 x^2-6 x^3+x^4+\left (18-54 x+18 x^2\right ) \log (3)+81 \log ^2(3)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(1 - 6*x + 11*x^2 - 6*x^3 + x^4 + (18 - 54*x + 18*x^2)*Log[3] + 81*Log[3]^2 + E^(E^x - x)*((-1 + x - 2*x^2
+ x^3)*Log[3] + (-9 + 9*x)*Log[3]^2 + E^x*((-x + 3*x^2 - x^3)*Log[3] - 9*x*Log[3]^2)))/(1 - 6*x + 11*x^2 - 6*
x^3 + x^4 + (18 - 54*x + 18*x^2)*Log[3] + 81*Log[3]^2),x]

[Out]

x - Log[3]*(1 - (3*I)/Sqrt[-5 + 36*Log[3]])*Defer[Int][E^E^x/(-3 + 2*x - I*Sqrt[-5 + 36*Log[3]]), x] + Log[3]*
(1 - (5*I)/Sqrt[-5 + 36*Log[3]])*Defer[Int][E^(E^x - x)/(-3 + 2*x - I*Sqrt[-5 + 36*Log[3]]), x] - (8*Log[3]*(1
+ 9*Log[3])*Defer[Int][E^(E^x - x)/(3 - 2*x + I*Sqrt[-5 + 36*Log[3]])^2, x])/(5 - 36*Log[3]) + (6*Log[3]*(3 +
I*Sqrt[-5 + 36*Log[3]])*Defer[Int][E^(E^x - x)/(3 - 2*x + I*Sqrt[-5 + 36*Log[3]])^2, x])/(5 - 36*Log[3]) + ((
18*I)*Log[3]*Defer[Int][E^(E^x - x)/(3 - 2*x + I*Sqrt[-5 + 36*Log[3]]), x])/(-5 + 36*Log[3])^(3/2) - ((8*I)*Lo
g[3]*(1 + 9*Log[3])*Defer[Int][E^(E^x - x)/(3 - 2*x + I*Sqrt[-5 + 36*Log[3]]), x])/(-5 + 36*Log[3])^(3/2) - (8
*Log[3]*(1 + 9*Log[3])*Defer[Int][E^(E^x - x)/(-3 + 2*x + I*Sqrt[-5 + 36*Log[3]])^2, x])/(5 - 36*Log[3]) + (6*
Log[3]*(3 - I*Sqrt[-5 + 36*Log[3]])*Defer[Int][E^(E^x - x)/(-3 + 2*x + I*Sqrt[-5 + 36*Log[3]])^2, x])/(5 - 36*
Log[3]) - Log[3]*(1 + (3*I)/Sqrt[-5 + 36*Log[3]])*Defer[Int][E^E^x/(-3 + 2*x + I*Sqrt[-5 + 36*Log[3]]), x] + (
(18*I)*Log[3]*Defer[Int][E^(E^x - x)/(-3 + 2*x + I*Sqrt[-5 + 36*Log[3]]), x])/(-5 + 36*Log[3])^(3/2) - ((8*I)*
Log[3]*(1 + 9*Log[3])*Defer[Int][E^(E^x - x)/(-3 + 2*x + I*Sqrt[-5 + 36*Log[3]]), x])/(-5 + 36*Log[3])^(3/2) +
Log[3]*(1 + (5*I)/Sqrt[-5 + 36*Log[3]])*Defer[Int][E^(E^x - x)/(-3 + 2*x + I*Sqrt[-5 + 36*Log[3]]), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (1-\frac {e^{e^x} x \log (3)}{1-3 x+x^2+9 \log (3)}+\frac {e^{e^x-x} \log (3) \left (-1-2 x^2+x^3-9 \log (3)+x (1+9 \log (3))\right )}{\left (1-3 x+x^2+9 \log (3)\right )^2}\right ) \, dx\\ &=x-\log (3) \int \frac {e^{e^x} x}{1-3 x+x^2+9 \log (3)} \, dx+\log (3) \int \frac {e^{e^x-x} \left (-1-2 x^2+x^3-9 \log (3)+x (1+9 \log (3))\right )}{\left (1-3 x+x^2+9 \log (3)\right )^2} \, dx\\ &=x+\log (3) \int \left (\frac {e^{e^x-x} (-2+3 x-18 \log (3))}{\left (1-3 x+x^2+9 \log (3)\right )^2}+\frac {e^{e^x-x} (1+x)}{1-3 x+x^2+9 \log (3)}\right ) \, dx-\log (3) \int \left (\frac {e^{e^x} \left (1-\frac {3 i}{\sqrt {-5+36 \log (3)}}\right )}{-3+2 x-i \sqrt {-5+36 \log (3)}}+\frac {e^{e^x} \left (1+\frac {3 i}{\sqrt {-5+36 \log (3)}}\right )}{-3+2 x+i \sqrt {-5+36 \log (3)}}\right ) \, dx\\ &=x+\log (3) \int \frac {e^{e^x-x} (-2+3 x-18 \log (3))}{\left (1-3 x+x^2+9 \log (3)\right )^2} \, dx+\log (3) \int \frac {e^{e^x-x} (1+x)}{1-3 x+x^2+9 \log (3)} \, dx-\left (\log (3) \left (1-\frac {3 i}{\sqrt {-5+36 \log (3)}}\right )\right ) \int \frac {e^{e^x}}{-3+2 x-i \sqrt {-5+36 \log (3)}} \, dx-\left (\log (3) \left (1+\frac {3 i}{\sqrt {-5+36 \log (3)}}\right )\right ) \int \frac {e^{e^x}}{-3+2 x+i \sqrt {-5+36 \log (3)}} \, dx\\ &=x+\log (3) \int \left (\frac {3 e^{e^x-x} x}{\left (1-3 x+x^2+9 \log (3)\right )^2}-\frac {2 e^{e^x-x} (1+9 \log (3))}{\left (1-3 x+x^2+9 \log (3)\right )^2}\right ) \, dx+\log (3) \int \left (\frac {e^{e^x-x} \left (1-\frac {5 i}{\sqrt {-5+36 \log (3)}}\right )}{-3+2 x-i \sqrt {-5+36 \log (3)}}+\frac {e^{e^x-x} \left (1+\frac {5 i}{\sqrt {-5+36 \log (3)}}\right )}{-3+2 x+i \sqrt {-5+36 \log (3)}}\right ) \, dx-\left (\log (3) \left (1-\frac {3 i}{\sqrt {-5+36 \log (3)}}\right )\right ) \int \frac {e^{e^x}}{-3+2 x-i \sqrt {-5+36 \log (3)}} \, dx-\left (\log (3) \left (1+\frac {3 i}{\sqrt {-5+36 \log (3)}}\right )\right ) \int \frac {e^{e^x}}{-3+2 x+i \sqrt {-5+36 \log (3)}} \, dx\\ &=x+(3 \log (3)) \int \frac {e^{e^x-x} x}{\left (1-3 x+x^2+9 \log (3)\right )^2} \, dx-(2 \log (3) (1+9 \log (3))) \int \frac {e^{e^x-x}}{\left (1-3 x+x^2+9 \log (3)\right )^2} \, dx-\left (\log (3) \left (1-\frac {3 i}{\sqrt {-5+36 \log (3)}}\right )\right ) \int \frac {e^{e^x}}{-3+2 x-i \sqrt {-5+36 \log (3)}} \, dx-\left (\log (3) \left (1+\frac {3 i}{\sqrt {-5+36 \log (3)}}\right )\right ) \int \frac {e^{e^x}}{-3+2 x+i \sqrt {-5+36 \log (3)}} \, dx+\left (\log (3) \left (1-\frac {5 i}{\sqrt {-5+36 \log (3)}}\right )\right ) \int \frac {e^{e^x-x}}{-3+2 x-i \sqrt {-5+36 \log (3)}} \, dx+\left (\log (3) \left (1+\frac {5 i}{\sqrt {-5+36 \log (3)}}\right )\right ) \int \frac {e^{e^x-x}}{-3+2 x+i \sqrt {-5+36 \log (3)}} \, dx\\ &=x+(3 \log (3)) \int \left (-\frac {2 e^{e^x-x} \left (3+i \sqrt {-5+36 \log (3)}\right )}{(-5+36 \log (3)) \left (3-2 x+i \sqrt {-5+36 \log (3)}\right )^2}+\frac {6 i e^{e^x-x}}{(-5+36 \log (3))^{3/2} \left (3-2 x+i \sqrt {-5+36 \log (3)}\right )}-\frac {2 e^{e^x-x} \left (3-i \sqrt {-5+36 \log (3)}\right )}{(-5+36 \log (3)) \left (-3+2 x+i \sqrt {-5+36 \log (3)}\right )^2}+\frac {6 i e^{e^x-x}}{(-5+36 \log (3))^{3/2} \left (-3+2 x+i \sqrt {-5+36 \log (3)}\right )}\right ) \, dx-(2 \log (3) (1+9 \log (3))) \int \left (-\frac {4 e^{e^x-x}}{(-5+36 \log (3)) \left (3-2 x+i \sqrt {-5+36 \log (3)}\right )^2}+\frac {4 i e^{e^x-x}}{(-5+36 \log (3))^{3/2} \left (3-2 x+i \sqrt {-5+36 \log (3)}\right )}-\frac {4 e^{e^x-x}}{(-5+36 \log (3)) \left (-3+2 x+i \sqrt {-5+36 \log (3)}\right )^2}+\frac {4 i e^{e^x-x}}{(-5+36 \log (3))^{3/2} \left (-3+2 x+i \sqrt {-5+36 \log (3)}\right )}\right ) \, dx-\left (\log (3) \left (1-\frac {3 i}{\sqrt {-5+36 \log (3)}}\right )\right ) \int \frac {e^{e^x}}{-3+2 x-i \sqrt {-5+36 \log (3)}} \, dx-\left (\log (3) \left (1+\frac {3 i}{\sqrt {-5+36 \log (3)}}\right )\right ) \int \frac {e^{e^x}}{-3+2 x+i \sqrt {-5+36 \log (3)}} \, dx+\left (\log (3) \left (1-\frac {5 i}{\sqrt {-5+36 \log (3)}}\right )\right ) \int \frac {e^{e^x-x}}{-3+2 x-i \sqrt {-5+36 \log (3)}} \, dx+\left (\log (3) \left (1+\frac {5 i}{\sqrt {-5+36 \log (3)}}\right )\right ) \int \frac {e^{e^x-x}}{-3+2 x+i \sqrt {-5+36 \log (3)}} \, dx\\ &=x-\frac {(8 \log (3) (1+9 \log (3))) \int \frac {e^{e^x-x}}{\left (3-2 x+i \sqrt {-5+36 \log (3)}\right )^2} \, dx}{5-36 \log (3)}-\frac {(8 \log (3) (1+9 \log (3))) \int \frac {e^{e^x-x}}{\left (-3+2 x+i \sqrt {-5+36 \log (3)}\right )^2} \, dx}{5-36 \log (3)}+\frac {(18 i \log (3)) \int \frac {e^{e^x-x}}{3-2 x+i \sqrt {-5+36 \log (3)}} \, dx}{(-5+36 \log (3))^{3/2}}+\frac {(18 i \log (3)) \int \frac {e^{e^x-x}}{-3+2 x+i \sqrt {-5+36 \log (3)}} \, dx}{(-5+36 \log (3))^{3/2}}-\frac {(8 i \log (3) (1+9 \log (3))) \int \frac {e^{e^x-x}}{3-2 x+i \sqrt {-5+36 \log (3)}} \, dx}{(-5+36 \log (3))^{3/2}}-\frac {(8 i \log (3) (1+9 \log (3))) \int \frac {e^{e^x-x}}{-3+2 x+i \sqrt {-5+36 \log (3)}} \, dx}{(-5+36 \log (3))^{3/2}}-\left (\log (3) \left (1-\frac {3 i}{\sqrt {-5+36 \log (3)}}\right )\right ) \int \frac {e^{e^x}}{-3+2 x-i \sqrt {-5+36 \log (3)}} \, dx-\left (\log (3) \left (1+\frac {3 i}{\sqrt {-5+36 \log (3)}}\right )\right ) \int \frac {e^{e^x}}{-3+2 x+i \sqrt {-5+36 \log (3)}} \, dx+\left (\log (3) \left (1-\frac {5 i}{\sqrt {-5+36 \log (3)}}\right )\right ) \int \frac {e^{e^x-x}}{-3+2 x-i \sqrt {-5+36 \log (3)}} \, dx+\left (\log (3) \left (1+\frac {5 i}{\sqrt {-5+36 \log (3)}}\right )\right ) \int \frac {e^{e^x-x}}{-3+2 x+i \sqrt {-5+36 \log (3)}} \, dx+\frac {\left (6 \log (3) \left (3-i \sqrt {-5+36 \log (3)}\right )\right ) \int \frac {e^{e^x-x}}{\left (-3+2 x+i \sqrt {-5+36 \log (3)}\right )^2} \, dx}{5-36 \log (3)}+\frac {\left (6 \log (3) \left (3+i \sqrt {-5+36 \log (3)}\right )\right ) \int \frac {e^{e^x-x}}{\left (3-2 x+i \sqrt {-5+36 \log (3)}\right )^2} \, dx}{5-36 \log (3)}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.27, size = 30, normalized size = 0.91 \begin {gather*} x-\frac {e^{e^x-x} x \log (3)}{1-3 x+x^2+9 \log (3)} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(1 - 6*x + 11*x^2 - 6*x^3 + x^4 + (18 - 54*x + 18*x^2)*Log[3] + 81*Log[3]^2 + E^(E^x - x)*((-1 + x -
2*x^2 + x^3)*Log[3] + (-9 + 9*x)*Log[3]^2 + E^x*((-x + 3*x^2 - x^3)*Log[3] - 9*x*Log[3]^2)))/(1 - 6*x + 11*x^
2 - 6*x^3 + x^4 + (18 - 54*x + 18*x^2)*Log[3] + 81*Log[3]^2),x]

[Out]

x - (E^(E^x - x)*x*Log[3])/(1 - 3*x + x^2 + 9*Log[3])

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fricas [A]  time = 0.69, size = 42, normalized size = 1.27 \begin {gather*} \frac {x^{3} - x e^{\left (-x + e^{x}\right )} \log \relax (3) - 3 \, x^{2} + 9 \, x \log \relax (3) + x}{x^{2} - 3 \, x + 9 \, \log \relax (3) + 1} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-9*x*log(3)^2+(-x^3+3*x^2-x)*log(3))*exp(x)+(9*x-9)*log(3)^2+(x^3-2*x^2+x-1)*log(3))*exp(exp(x)-x
)+81*log(3)^2+(18*x^2-54*x+18)*log(3)+x^4-6*x^3+11*x^2-6*x+1)/(81*log(3)^2+(18*x^2-54*x+18)*log(3)+x^4-6*x^3+1
1*x^2-6*x+1),x, algorithm="fricas")

[Out]

(x^3 - x*e^(-x + e^x)*log(3) - 3*x^2 + 9*x*log(3) + x)/(x^2 - 3*x + 9*log(3) + 1)

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {x^{4} - 6 \, x^{3} + 11 \, x^{2} + {\left (9 \, {\left (x - 1\right )} \log \relax (3)^{2} - {\left (9 \, x \log \relax (3)^{2} + {\left (x^{3} - 3 \, x^{2} + x\right )} \log \relax (3)\right )} e^{x} + {\left (x^{3} - 2 \, x^{2} + x - 1\right )} \log \relax (3)\right )} e^{\left (-x + e^{x}\right )} + 18 \, {\left (x^{2} - 3 \, x + 1\right )} \log \relax (3) + 81 \, \log \relax (3)^{2} - 6 \, x + 1}{x^{4} - 6 \, x^{3} + 11 \, x^{2} + 18 \, {\left (x^{2} - 3 \, x + 1\right )} \log \relax (3) + 81 \, \log \relax (3)^{2} - 6 \, x + 1}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-9*x*log(3)^2+(-x^3+3*x^2-x)*log(3))*exp(x)+(9*x-9)*log(3)^2+(x^3-2*x^2+x-1)*log(3))*exp(exp(x)-x
)+81*log(3)^2+(18*x^2-54*x+18)*log(3)+x^4-6*x^3+11*x^2-6*x+1)/(81*log(3)^2+(18*x^2-54*x+18)*log(3)+x^4-6*x^3+1
1*x^2-6*x+1),x, algorithm="giac")

[Out]

integrate((x^4 - 6*x^3 + 11*x^2 + (9*(x - 1)*log(3)^2 - (9*x*log(3)^2 + (x^3 - 3*x^2 + x)*log(3))*e^x + (x^3 -
2*x^2 + x - 1)*log(3))*e^(-x + e^x) + 18*(x^2 - 3*x + 1)*log(3) + 81*log(3)^2 - 6*x + 1)/(x^4 - 6*x^3 + 11*x^
2 + 18*(x^2 - 3*x + 1)*log(3) + 81*log(3)^2 - 6*x + 1), x)

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maple [A]  time = 0.31, size = 29, normalized size = 0.88

method	result	size
risch	\(x -\frac {\ln \relax (3) x \,{\mathrm e}^{{\mathrm e}^{x}-x}}{x^{2}+9 \ln \relax (3)-3 x +1}\)	\(29\)
norman	\(\frac {x^{3}+\left (9 \ln \relax (3)-8\right ) x -\ln \relax (3) {\mathrm e}^{{\mathrm e}^{x}-x} x +27 \ln \relax (3)+3}{x^{2}+9 \ln \relax (3)-3 x +1}\)	\(45\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((-9*x*ln(3)^2+(-x^3+3*x^2-x)*ln(3))*exp(x)+(9*x-9)*ln(3)^2+(x^3-2*x^2+x-1)*ln(3))*exp(exp(x)-x)+81*ln(3)
^2+(18*x^2-54*x+18)*ln(3)+x^4-6*x^3+11*x^2-6*x+1)/(81*ln(3)^2+(18*x^2-54*x+18)*ln(3)+x^4-6*x^3+11*x^2-6*x+1),x
,method=_RETURNVERBOSE)

[Out]

x-ln(3)*x/(x^2+9*ln(3)-3*x+1)*exp(exp(x)-x)

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maxima [B]  time = 0.62, size = 698, normalized size = 21.15 result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-9*x*log(3)^2+(-x^3+3*x^2-x)*log(3))*exp(x)+(9*x-9)*log(3)^2+(x^3-2*x^2+x-1)*log(3))*exp(exp(x)-x
)+81*log(3)^2+(18*x^2-54*x+18)*log(3)+x^4-6*x^3+11*x^2-6*x+1)/(81*log(3)^2+(18*x^2-54*x+18)*log(3)+x^4-6*x^3+1
1*x^2-6*x+1),x, algorithm="maxima")

[Out]

81*((2*x - 3)/(x^2*(36*log(3) - 5) - 3*x*(36*log(3) - 5) + 324*log(3)^2 - 9*log(3) - 5) + 4*arctan((2*x - 3)/s
qrt(36*log(3) - 5))/(36*log(3) - 5)^(3/2))*log(3)^2 + 18*(4*(9*log(3) + 1)*arctan((2*x - 3)/sqrt(36*log(3) - 5
))/(36*log(3) - 5)^(3/2) - (x*(18*log(3) - 7) + 27*log(3) + 3)/(x^2*(36*log(3) - 5) - 3*x*(36*log(3) - 5) + 32
4*log(3)^2 - 9*log(3) - 5))*log(3) - 54*((3*x - 18*log(3) - 2)/(x^2*(36*log(3) - 5) - 3*x*(36*log(3) - 5) + 32
4*log(3)^2 - 9*log(3) - 5) + 6*arctan((2*x - 3)/sqrt(36*log(3) - 5))/(36*log(3) - 5)^(3/2))*log(3) + 18*((2*x
- 3)/(x^2*(36*log(3) - 5) - 3*x*(36*log(3) - 5) + 324*log(3)^2 - 9*log(3) - 5) + 4*arctan((2*x - 3)/sqrt(36*lo
g(3) - 5))/(36*log(3) - 5)^(3/2))*log(3) - x*e^(-x + e^x)*log(3)/(x^2 - 3*x + 9*log(3) + 1) + x - 6*(162*log(3
)^2 - 126*log(3) + 11)*arctan((2*x - 3)/sqrt(36*log(3) - 5))/(36*log(3) - 5)^(3/2) - 54*(18*log(3) - 1)*arctan
((2*x - 3)/sqrt(36*log(3) - 5))/(36*log(3) - 5)^(3/2) + 44*(9*log(3) + 1)*arctan((2*x - 3)/sqrt(36*log(3) - 5)
)/(36*log(3) - 5)^(3/2) + ((162*log(3)^2 - 288*log(3) + 47)*x + 729*log(3)^2 - 81*log(3) - 18)/(x^2*(36*log(3)
- 5) - 3*x*(36*log(3) - 5) + 324*log(3)^2 - 9*log(3) - 5) - 11*(x*(18*log(3) - 7) + 27*log(3) + 3)/(x^2*(36*l
og(3) - 5) - 3*x*(36*log(3) - 5) + 324*log(3)^2 - 9*log(3) - 5) + 6*(9*x*(9*log(3) - 2) - 162*log(3)^2 + 45*lo
g(3) + 7)/(x^2*(36*log(3) - 5) - 3*x*(36*log(3) - 5) + 324*log(3)^2 - 9*log(3) - 5) - 6*(3*x - 18*log(3) - 2)/
(x^2*(36*log(3) - 5) - 3*x*(36*log(3) - 5) + 324*log(3)^2 - 9*log(3) - 5) + (2*x - 3)/(x^2*(36*log(3) - 5) - 3
*x*(36*log(3) - 5) + 324*log(3)^2 - 9*log(3) - 5) - 32*arctan((2*x - 3)/sqrt(36*log(3) - 5))/(36*log(3) - 5)^(
3/2)

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mupad [B]  time = 1.72, size = 28, normalized size = 0.85 \begin {gather*} x-\frac {x\,{\mathrm {e}}^{{\mathrm {e}}^x-x}\,\ln \relax (3)}{x^2-3\,x+9\,\ln \relax (3)+1} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((log(3)*(18*x^2 - 54*x + 18) - 6*x + exp(exp(x) - x)*(log(3)^2*(9*x - 9) + log(3)*(x - 2*x^2 + x^3 - 1) -
exp(x)*(9*x*log(3)^2 + log(3)*(x - 3*x^2 + x^3))) + 81*log(3)^2 + 11*x^2 - 6*x^3 + x^4 + 1)/(log(3)*(18*x^2 -
54*x + 18) - 6*x + 81*log(3)^2 + 11*x^2 - 6*x^3 + x^4 + 1),x)

[Out]

x - (x*exp(exp(x) - x)*log(3))/(9*log(3) - 3*x + x^2 + 1)

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sympy [A]  time = 0.26, size = 26, normalized size = 0.79 \begin {gather*} x - \frac {x e^{- x + e^{x}} \log {\relax (3 )}}{x^{2} - 3 x + 1 + 9 \log {\relax (3 )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-9*x*ln(3)**2+(-x**3+3*x**2-x)*ln(3))*exp(x)+(9*x-9)*ln(3)**2+(x**3-2*x**2+x-1)*ln(3))*exp(exp(x)
-x)+81*ln(3)**2+(18*x**2-54*x+18)*ln(3)+x**4-6*x**3+11*x**2-6*x+1)/(81*ln(3)**2+(18*x**2-54*x+18)*ln(3)+x**4-6
*x**3+11*x**2-6*x+1),x)

[Out]

x - x*exp(-x + exp(x))*log(3)/(x**2 - 3*x + 1 + 9*log(3))

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