3.43.81 \(\int \frac {e^{\frac {-23+12 x+(-18-21 x+9 x^2+3 x^3) \log (3)+(-8+4 x+(-6-7 x+3 x^2+x^3) \log (3)) \log (x)}{-6+3 x+(-2+x) \log (x)}} (2-4 x+(180 x-108 x^2-27 x^3+18 x^4) \log (3)+(-x+(120 x-72 x^2-18 x^3+12 x^4) \log (3)) \log (x)+(20 x-12 x^2-3 x^3+2 x^4) \log (3) \log ^2(x))}{36 x-36 x^2+9 x^3+(24 x-24 x^2+6 x^3) \log (x)+(4 x-4 x^2+x^3) \log ^2(x)} \, dx\)

Optimal. Leaf size=30 \[ e^{4+\left (3+5 x+x^2\right ) \log (3)-\frac {1}{(2-x) (3+\log (x))}} \]

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Rubi [F]  time = 20.24, 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 {-23+12 x+\left (-18-21 x+9 x^2+3 x^3\right ) \log (3)+\left (-8+4 x+\left (-6-7 x+3 x^2+x^3\right ) \log (3)\right ) \log (x)}{-6+3 x+(-2+x) \log (x)}\right ) \left (2-4 x+\left (180 x-108 x^2-27 x^3+18 x^4\right ) \log (3)+\left (-x+\left (120 x-72 x^2-18 x^3+12 x^4\right ) \log (3)\right ) \log (x)+\left (20 x-12 x^2-3 x^3+2 x^4\right ) \log (3) \log ^2(x)\right )}{36 x-36 x^2+9 x^3+\left (24 x-24 x^2+6 x^3\right ) \log (x)+\left (4 x-4 x^2+x^3\right ) \log ^2(x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^((-23 + 12*x + (-18 - 21*x + 9*x^2 + 3*x^3)*Log[3] + (-8 + 4*x + (-6 - 7*x + 3*x^2 + x^3)*Log[3])*Log[x
])/(-6 + 3*x + (-2 + x)*Log[x]))*(2 - 4*x + (180*x - 108*x^2 - 27*x^3 + 18*x^4)*Log[3] + (-x + (120*x - 72*x^2
- 18*x^3 + 12*x^4)*Log[3])*Log[x] + (20*x - 12*x^2 - 3*x^3 + 2*x^4)*Log[3]*Log[x]^2))/(36*x - 36*x^2 + 9*x^3
+ (24*x - 24*x^2 + 6*x^3)*Log[x] + (4*x - 4*x^2 + x^3)*Log[x]^2),x]

[Out]

5*Log[3]*Defer[Int][E^((-23 + 12*x + (-18 - 21*x + 9*x^2 + 3*x^3)*Log[3] + (-8 + 4*x + (-6 - 7*x + 3*x^2 + x^3
)*Log[3])*Log[x])/((-2 + x)*(3 + Log[x]))), x] + 2*Log[3]*Defer[Int][E^((-23 + 12*x + (-18 - 21*x + 9*x^2 + 3*
x^3)*Log[3] + (-8 + 4*x + (-6 - 7*x + 3*x^2 + x^3)*Log[3])*Log[x])/((-2 + x)*(3 + Log[x])))*x, x] - Defer[Int]
[E^((-23 + 12*x + (-18 - 21*x + 9*x^2 + 3*x^3)*Log[3] + (-8 + 4*x + (-6 - 7*x + 3*x^2 + x^3)*Log[3])*Log[x])/(
(-2 + x)*(3 + Log[x])))/((-2 + x)*(3 + Log[x])^2), x]/2 + Defer[Int][E^((-23 + 12*x + (-18 - 21*x + 9*x^2 + 3*
x^3)*Log[3] + (-8 + 4*x + (-6 - 7*x + 3*x^2 + x^3)*Log[3])*Log[x])/((-2 + x)*(3 + Log[x])))/(x*(3 + Log[x])^2)
, x]/2 - Defer[Int][E^((-23 + 12*x + (-18 - 21*x + 9*x^2 + 3*x^3)*Log[3] + (-8 + 4*x + (-6 - 7*x + 3*x^2 + x^3
)*Log[3])*Log[x])/((-2 + x)*(3 + Log[x])))/((-2 + x)^2*(3 + Log[x])), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {\exp \left (\frac {-23+12 x+\left (-18-21 x+9 x^2+3 x^3\right ) \log (3)+\left (-8+4 x+\left (-6-7 x+3 x^2+x^3\right ) \log (3)\right ) \log (x)}{(-2+x) (3+\log (x))}\right ) \left (2-4 x+\left (180 x-108 x^2-27 x^3+18 x^4\right ) \log (3)+\left (-x+\left (120 x-72 x^2-18 x^3+12 x^4\right ) \log (3)\right ) \log (x)+\left (20 x-12 x^2-3 x^3+2 x^4\right ) \log (3) \log ^2(x)\right )}{(2-x)^2 x (3+\log (x))^2} \, dx\\ &=\int \left (\exp \left (\frac {-23+12 x+\left (-18-21 x+9 x^2+3 x^3\right ) \log (3)+\left (-8+4 x+\left (-6-7 x+3 x^2+x^3\right ) \log (3)\right ) \log (x)}{(-2+x) (3+\log (x))}\right ) (5+2 x) \log (3)-\frac {\exp \left (\frac {-23+12 x+\left (-18-21 x+9 x^2+3 x^3\right ) \log (3)+\left (-8+4 x+\left (-6-7 x+3 x^2+x^3\right ) \log (3)\right ) \log (x)}{(-2+x) (3+\log (x))}\right )}{(-2+x) x (3+\log (x))^2}-\frac {\exp \left (\frac {-23+12 x+\left (-18-21 x+9 x^2+3 x^3\right ) \log (3)+\left (-8+4 x+\left (-6-7 x+3 x^2+x^3\right ) \log (3)\right ) \log (x)}{(-2+x) (3+\log (x))}\right )}{(-2+x)^2 (3+\log (x))}\right ) \, dx\\ &=\log (3) \int \exp \left (\frac {-23+12 x+\left (-18-21 x+9 x^2+3 x^3\right ) \log (3)+\left (-8+4 x+\left (-6-7 x+3 x^2+x^3\right ) \log (3)\right ) \log (x)}{(-2+x) (3+\log (x))}\right ) (5+2 x) \, dx-\int \frac {\exp \left (\frac {-23+12 x+\left (-18-21 x+9 x^2+3 x^3\right ) \log (3)+\left (-8+4 x+\left (-6-7 x+3 x^2+x^3\right ) \log (3)\right ) \log (x)}{(-2+x) (3+\log (x))}\right )}{(-2+x) x (3+\log (x))^2} \, dx-\int \frac {\exp \left (\frac {-23+12 x+\left (-18-21 x+9 x^2+3 x^3\right ) \log (3)+\left (-8+4 x+\left (-6-7 x+3 x^2+x^3\right ) \log (3)\right ) \log (x)}{(-2+x) (3+\log (x))}\right )}{(-2+x)^2 (3+\log (x))} \, dx\\ &=\log (3) \int \left (5 \exp \left (\frac {-23+12 x+\left (-18-21 x+9 x^2+3 x^3\right ) \log (3)+\left (-8+4 x+\left (-6-7 x+3 x^2+x^3\right ) \log (3)\right ) \log (x)}{(-2+x) (3+\log (x))}\right )+2 \exp \left (\frac {-23+12 x+\left (-18-21 x+9 x^2+3 x^3\right ) \log (3)+\left (-8+4 x+\left (-6-7 x+3 x^2+x^3\right ) \log (3)\right ) \log (x)}{(-2+x) (3+\log (x))}\right ) x\right ) \, dx-\int \frac {\exp \left (\frac {-23+12 x+\left (-18-21 x+9 x^2+3 x^3\right ) \log (3)+\left (-8+4 x+\left (-6-7 x+3 x^2+x^3\right ) \log (3)\right ) \log (x)}{(-2+x) (3+\log (x))}\right )}{(-2+x)^2 (3+\log (x))} \, dx-\int \left (\frac {\exp \left (\frac {-23+12 x+\left (-18-21 x+9 x^2+3 x^3\right ) \log (3)+\left (-8+4 x+\left (-6-7 x+3 x^2+x^3\right ) \log (3)\right ) \log (x)}{(-2+x) (3+\log (x))}\right )}{2 (-2+x) (3+\log (x))^2}-\frac {\exp \left (\frac {-23+12 x+\left (-18-21 x+9 x^2+3 x^3\right ) \log (3)+\left (-8+4 x+\left (-6-7 x+3 x^2+x^3\right ) \log (3)\right ) \log (x)}{(-2+x) (3+\log (x))}\right )}{2 x (3+\log (x))^2}\right ) \, dx\\ &=-\left (\frac {1}{2} \int \frac {\exp \left (\frac {-23+12 x+\left (-18-21 x+9 x^2+3 x^3\right ) \log (3)+\left (-8+4 x+\left (-6-7 x+3 x^2+x^3\right ) \log (3)\right ) \log (x)}{(-2+x) (3+\log (x))}\right )}{(-2+x) (3+\log (x))^2} \, dx\right )+\frac {1}{2} \int \frac {\exp \left (\frac {-23+12 x+\left (-18-21 x+9 x^2+3 x^3\right ) \log (3)+\left (-8+4 x+\left (-6-7 x+3 x^2+x^3\right ) \log (3)\right ) \log (x)}{(-2+x) (3+\log (x))}\right )}{x (3+\log (x))^2} \, dx+(2 \log (3)) \int \exp \left (\frac {-23+12 x+\left (-18-21 x+9 x^2+3 x^3\right ) \log (3)+\left (-8+4 x+\left (-6-7 x+3 x^2+x^3\right ) \log (3)\right ) \log (x)}{(-2+x) (3+\log (x))}\right ) x \, dx+(5 \log (3)) \int \exp \left (\frac {-23+12 x+\left (-18-21 x+9 x^2+3 x^3\right ) \log (3)+\left (-8+4 x+\left (-6-7 x+3 x^2+x^3\right ) \log (3)\right ) \log (x)}{(-2+x) (3+\log (x))}\right ) \, dx-\int \frac {\exp \left (\frac {-23+12 x+\left (-18-21 x+9 x^2+3 x^3\right ) \log (3)+\left (-8+4 x+\left (-6-7 x+3 x^2+x^3\right ) \log (3)\right ) \log (x)}{(-2+x) (3+\log (x))}\right )}{(-2+x)^2 (3+\log (x))} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [F]  time = 5.37, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {e^{\frac {-23+12 x+\left (-18-21 x+9 x^2+3 x^3\right ) \log (3)+\left (-8+4 x+\left (-6-7 x+3 x^2+x^3\right ) \log (3)\right ) \log (x)}{-6+3 x+(-2+x) \log (x)}} \left (2-4 x+\left (180 x-108 x^2-27 x^3+18 x^4\right ) \log (3)+\left (-x+\left (120 x-72 x^2-18 x^3+12 x^4\right ) \log (3)\right ) \log (x)+\left (20 x-12 x^2-3 x^3+2 x^4\right ) \log (3) \log ^2(x)\right )}{36 x-36 x^2+9 x^3+\left (24 x-24 x^2+6 x^3\right ) \log (x)+\left (4 x-4 x^2+x^3\right ) \log ^2(x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[(E^((-23 + 12*x + (-18 - 21*x + 9*x^2 + 3*x^3)*Log[3] + (-8 + 4*x + (-6 - 7*x + 3*x^2 + x^3)*Log[3])
*Log[x])/(-6 + 3*x + (-2 + x)*Log[x]))*(2 - 4*x + (180*x - 108*x^2 - 27*x^3 + 18*x^4)*Log[3] + (-x + (120*x -
72*x^2 - 18*x^3 + 12*x^4)*Log[3])*Log[x] + (20*x - 12*x^2 - 3*x^3 + 2*x^4)*Log[3]*Log[x]^2))/(36*x - 36*x^2 +
9*x^3 + (24*x - 24*x^2 + 6*x^3)*Log[x] + (4*x - 4*x^2 + x^3)*Log[x]^2),x]

[Out]

Integrate[(E^((-23 + 12*x + (-18 - 21*x + 9*x^2 + 3*x^3)*Log[3] + (-8 + 4*x + (-6 - 7*x + 3*x^2 + x^3)*Log[3])
*Log[x])/(-6 + 3*x + (-2 + x)*Log[x]))*(2 - 4*x + (180*x - 108*x^2 - 27*x^3 + 18*x^4)*Log[3] + (-x + (120*x -
72*x^2 - 18*x^3 + 12*x^4)*Log[3])*Log[x] + (20*x - 12*x^2 - 3*x^3 + 2*x^4)*Log[3]*Log[x]^2))/(36*x - 36*x^2 +
9*x^3 + (24*x - 24*x^2 + 6*x^3)*Log[x] + (4*x - 4*x^2 + x^3)*Log[x]^2), x]

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fricas [B]  time = 0.69, size = 61, normalized size = 2.03 \begin {gather*} e^{\left (\frac {3 \, {\left (x^{3} + 3 \, x^{2} - 7 \, x - 6\right )} \log \relax (3) + {\left ({\left (x^{3} + 3 \, x^{2} - 7 \, x - 6\right )} \log \relax (3) + 4 \, x - 8\right )} \log \relax (x) + 12 \, x - 23}{{\left (x - 2\right )} \log \relax (x) + 3 \, x - 6}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*x^4-3*x^3-12*x^2+20*x)*log(3)*log(x)^2+((12*x^4-18*x^3-72*x^2+120*x)*log(3)-x)*log(x)+(18*x^4-27
*x^3-108*x^2+180*x)*log(3)-4*x+2)*exp((((x^3+3*x^2-7*x-6)*log(3)+4*x-8)*log(x)+(3*x^3+9*x^2-21*x-18)*log(3)+12
*x-23)/((x-2)*log(x)+3*x-6))/((x^3-4*x^2+4*x)*log(x)^2+(6*x^3-24*x^2+24*x)*log(x)+9*x^3-36*x^2+36*x),x, algori
thm="fricas")

[Out]

e^((3*(x^3 + 3*x^2 - 7*x - 6)*log(3) + ((x^3 + 3*x^2 - 7*x - 6)*log(3) + 4*x - 8)*log(x) + 12*x - 23)/((x - 2)
*log(x) + 3*x - 6))

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giac [B]  time = 1.46, size = 249, normalized size = 8.30 \begin {gather*} e^{\left (\frac {x^{3} \log \relax (3) \log \relax (x)}{x \log \relax (x) + 3 \, x - 2 \, \log \relax (x) - 6} + \frac {3 \, x^{3} \log \relax (3)}{x \log \relax (x) + 3 \, x - 2 \, \log \relax (x) - 6} + \frac {3 \, x^{2} \log \relax (3) \log \relax (x)}{x \log \relax (x) + 3 \, x - 2 \, \log \relax (x) - 6} + \frac {9 \, x^{2} \log \relax (3)}{x \log \relax (x) + 3 \, x - 2 \, \log \relax (x) - 6} - \frac {7 \, x \log \relax (3) \log \relax (x)}{x \log \relax (x) + 3 \, x - 2 \, \log \relax (x) - 6} - \frac {21 \, x \log \relax (3)}{x \log \relax (x) + 3 \, x - 2 \, \log \relax (x) - 6} + \frac {4 \, x \log \relax (x)}{x \log \relax (x) + 3 \, x - 2 \, \log \relax (x) - 6} - \frac {6 \, \log \relax (3) \log \relax (x)}{x \log \relax (x) + 3 \, x - 2 \, \log \relax (x) - 6} + \frac {12 \, x}{x \log \relax (x) + 3 \, x - 2 \, \log \relax (x) - 6} - \frac {18 \, \log \relax (3)}{x \log \relax (x) + 3 \, x - 2 \, \log \relax (x) - 6} - \frac {8 \, \log \relax (x)}{x \log \relax (x) + 3 \, x - 2 \, \log \relax (x) - 6} - \frac {23}{x \log \relax (x) + 3 \, x - 2 \, \log \relax (x) - 6}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*x^4-3*x^3-12*x^2+20*x)*log(3)*log(x)^2+((12*x^4-18*x^3-72*x^2+120*x)*log(3)-x)*log(x)+(18*x^4-27
*x^3-108*x^2+180*x)*log(3)-4*x+2)*exp((((x^3+3*x^2-7*x-6)*log(3)+4*x-8)*log(x)+(3*x^3+9*x^2-21*x-18)*log(3)+12
*x-23)/((x-2)*log(x)+3*x-6))/((x^3-4*x^2+4*x)*log(x)^2+(6*x^3-24*x^2+24*x)*log(x)+9*x^3-36*x^2+36*x),x, algori
thm="giac")

[Out]

e^(x^3*log(3)*log(x)/(x*log(x) + 3*x - 2*log(x) - 6) + 3*x^3*log(3)/(x*log(x) + 3*x - 2*log(x) - 6) + 3*x^2*lo
g(3)*log(x)/(x*log(x) + 3*x - 2*log(x) - 6) + 9*x^2*log(3)/(x*log(x) + 3*x - 2*log(x) - 6) - 7*x*log(3)*log(x)
/(x*log(x) + 3*x - 2*log(x) - 6) - 21*x*log(3)/(x*log(x) + 3*x - 2*log(x) - 6) + 4*x*log(x)/(x*log(x) + 3*x -
2*log(x) - 6) - 6*log(3)*log(x)/(x*log(x) + 3*x - 2*log(x) - 6) + 12*x/(x*log(x) + 3*x - 2*log(x) - 6) - 18*lo
g(3)/(x*log(x) + 3*x - 2*log(x) - 6) - 8*log(x)/(x*log(x) + 3*x - 2*log(x) - 6) - 23/(x*log(x) + 3*x - 2*log(x
) - 6))

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maple [B]  time = 0.05, size = 81, normalized size = 2.70

method	result	size
risch	\({\mathrm e}^{\frac {\ln \relax (x ) \ln \relax (3) x^{3}+3 x^{2} \ln \relax (3) \ln \relax (x )+3 x^{3} \ln \relax (3)-7 x \ln \relax (3) \ln \relax (x )+9 x^{2} \ln \relax (3)-6 \ln \relax (3) \ln \relax (x )+4 x \ln \relax (x )-21 x \ln \relax (3)-8 \ln \relax (x )-18 \ln \relax (3)+12 x -23}{\left (x -2\right ) \left (3+\ln \relax (x )\right )}}\)	\(81\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((2*x^4-3*x^3-12*x^2+20*x)*ln(3)*ln(x)^2+((12*x^4-18*x^3-72*x^2+120*x)*ln(3)-x)*ln(x)+(18*x^4-27*x^3-108*x
^2+180*x)*ln(3)-4*x+2)*exp((((x^3+3*x^2-7*x-6)*ln(3)+4*x-8)*ln(x)+(3*x^3+9*x^2-21*x-18)*ln(3)+12*x-23)/((x-2)*
ln(x)+3*x-6))/((x^3-4*x^2+4*x)*ln(x)^2+(6*x^3-24*x^2+24*x)*ln(x)+9*x^3-36*x^2+36*x),x,method=_RETURNVERBOSE)

[Out]

exp((ln(x)*ln(3)*x^3+3*x^2*ln(3)*ln(x)+3*x^3*ln(3)-7*x*ln(3)*ln(x)+9*x^2*ln(3)-6*ln(3)*ln(x)+4*x*ln(x)-21*x*ln
(3)-8*ln(x)-18*ln(3)+12*x-23)/(x-2)/(3+ln(x)))

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maxima [B]  time = 1.02, size = 106, normalized size = 3.53 \begin {gather*} e^{\left (\frac {x^{2} \log \relax (3) \log \relax (x)}{\log \relax (x) + 3} + \frac {3 \, x^{2} \log \relax (3)}{\log \relax (x) + 3} + \frac {5 \, x \log \relax (3) \log \relax (x)}{\log \relax (x) + 3} + \frac {15 \, x \log \relax (3)}{\log \relax (x) + 3} + \frac {3 \, \log \relax (3) \log \relax (x)}{\log \relax (x) + 3} + \frac {9 \, \log \relax (3)}{\log \relax (x) + 3} + \frac {4 \, \log \relax (x)}{\log \relax (x) + 3} + \frac {1}{{\left (x - 2\right )} \log \relax (x) + 3 \, x - 6} + \frac {12}{\log \relax (x) + 3}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*x^4-3*x^3-12*x^2+20*x)*log(3)*log(x)^2+((12*x^4-18*x^3-72*x^2+120*x)*log(3)-x)*log(x)+(18*x^4-27
*x^3-108*x^2+180*x)*log(3)-4*x+2)*exp((((x^3+3*x^2-7*x-6)*log(3)+4*x-8)*log(x)+(3*x^3+9*x^2-21*x-18)*log(3)+12
*x-23)/((x-2)*log(x)+3*x-6))/((x^3-4*x^2+4*x)*log(x)^2+(6*x^3-24*x^2+24*x)*log(x)+9*x^3-36*x^2+36*x),x, algori
thm="maxima")

[Out]

e^(x^2*log(3)*log(x)/(log(x) + 3) + 3*x^2*log(3)/(log(x) + 3) + 5*x*log(3)*log(x)/(log(x) + 3) + 15*x*log(3)/(
log(x) + 3) + 3*log(3)*log(x)/(log(x) + 3) + 9*log(3)/(log(x) + 3) + 4*log(x)/(log(x) + 3) + 1/((x - 2)*log(x)
+ 3*x - 6) + 12/(log(x) + 3))

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mupad [B]  time = 4.13, size = 81, normalized size = 2.70 \begin {gather*} {27}^{\frac {x^2+5\,x+3}{\ln \relax (x)+3}}\,x^{\frac {\ln \relax (3)\,x^2+5\,\ln \relax (3)\,x+3\,\ln \relax (3)+4}{\ln \relax (x)+3}}\,{\mathrm {e}}^{\frac {12\,x}{3\,x-2\,\ln \relax (x)+x\,\ln \relax (x)-6}-\frac {23}{3\,x-2\,\ln \relax (x)+x\,\ln \relax (x)-6}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(-(log(3)*(21*x - 9*x^2 - 3*x^3 + 18) - 12*x + log(x)*(log(3)*(7*x - 3*x^2 - x^3 + 6) - 4*x + 8) + 23)
/(3*x + log(x)*(x - 2) - 6))*(log(3)*(180*x - 108*x^2 - 27*x^3 + 18*x^4) - 4*x - log(x)*(x - log(3)*(120*x - 7
2*x^2 - 18*x^3 + 12*x^4)) + log(3)*log(x)^2*(20*x - 12*x^2 - 3*x^3 + 2*x^4) + 2))/(36*x - 36*x^2 + 9*x^3 + log
(x)*(24*x - 24*x^2 + 6*x^3) + log(x)^2*(4*x - 4*x^2 + x^3)),x)

[Out]

27^((5*x + x^2 + 3)/(log(x) + 3))*x^((3*log(3) + 5*x*log(3) + x^2*log(3) + 4)/(log(x) + 3))*exp((12*x)/(3*x -
2*log(x) + x*log(x) - 6) - 23/(3*x - 2*log(x) + x*log(x) - 6))

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sympy [B]  time = 1.48, size = 61, normalized size = 2.03 \begin {gather*} e^{\frac {12 x + \left (4 x + \left (x^{3} + 3 x^{2} - 7 x - 6\right ) \log {\relax (3 )} - 8\right ) \log {\relax (x )} + \left (3 x^{3} + 9 x^{2} - 21 x - 18\right ) \log {\relax (3 )} - 23}{3 x + \left (x - 2\right ) \log {\relax (x )} - 6}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*x**4-3*x**3-12*x**2+20*x)*ln(3)*ln(x)**2+((12*x**4-18*x**3-72*x**2+120*x)*ln(3)-x)*ln(x)+(18*x**
4-27*x**3-108*x**2+180*x)*ln(3)-4*x+2)*exp((((x**3+3*x**2-7*x-6)*ln(3)+4*x-8)*ln(x)+(3*x**3+9*x**2-21*x-18)*ln
(3)+12*x-23)/((x-2)*ln(x)+3*x-6))/((x**3-4*x**2+4*x)*ln(x)**2+(6*x**3-24*x**2+24*x)*ln(x)+9*x**3-36*x**2+36*x)
,x)

[Out]

exp((12*x + (4*x + (x**3 + 3*x**2 - 7*x - 6)*log(3) - 8)*log(x) + (3*x**3 + 9*x**2 - 21*x - 18)*log(3) - 23)/(
3*x + (x - 2)*log(x) - 6))

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