Integrand size = 206, antiderivative size = 26 \[ \int \frac {12 x-24 x^2+8 x^3+3 x^4+e^6 \left (7-12 x+3 x^2+2 x^3\right )+\left (26 x-22 x^2-6 x^3+e^6 \left (14-10 x-4 x^2\right )\right ) \log (3)+\left (14 x+3 x^2+e^6 (7+2 x)\right ) \log ^2(3)}{-2+4 x+4 x^2-12 x^3+5 x^4+x^5+e^6 \left (7 x-13 x^2+5 x^3+x^4\right )+\left (-4+4 x+13 x^2-12 x^3-2 x^4+e^6 \left (14 x-12 x^2-2 x^3\right )\right ) \log (3)+\left (-2+7 x^2+x^3+e^6 \left (7 x+x^2\right )\right ) \log ^2(3)} \, dx=\log \left (-2+x \left ((7+x) \left (e^6+x\right )+\frac {x}{-1+x-\log (3)}\right )\right ) \] Output:
ln(x*((exp(3)^2+x)*(7+x)+x/(x-ln(3)-1))-2)
Result contains higher order function than in optimal. Order 9 vs. order 3 in optimal.
Time = 0.59 (sec) , antiderivative size = 1010, normalized size of antiderivative = 38.85 \[ \int \frac {12 x-24 x^2+8 x^3+3 x^4+e^6 \left (7-12 x+3 x^2+2 x^3\right )+\left (26 x-22 x^2-6 x^3+e^6 \left (14-10 x-4 x^2\right )\right ) \log (3)+\left (14 x+3 x^2+e^6 (7+2 x)\right ) \log ^2(3)}{-2+4 x+4 x^2-12 x^3+5 x^4+x^5+e^6 \left (7 x-13 x^2+5 x^3+x^4\right )+\left (-4+4 x+13 x^2-12 x^3-2 x^4+e^6 \left (14 x-12 x^2-2 x^3\right )\right ) \log (3)+\left (-2+7 x^2+x^3+e^6 \left (7 x+x^2\right )\right ) \log ^2(3)} \, dx =\text {Too large to display} \] Input:
Integrate[(12*x - 24*x^2 + 8*x^3 + 3*x^4 + E^6*(7 - 12*x + 3*x^2 + 2*x^3) + (26*x - 22*x^2 - 6*x^3 + E^6*(14 - 10*x - 4*x^2))*Log[3] + (14*x + 3*x^2 + E^6*(7 + 2*x))*Log[3]^2)/(-2 + 4*x + 4*x^2 - 12*x^3 + 5*x^4 + x^5 + E^6 *(7*x - 13*x^2 + 5*x^3 + x^4) + (-4 + 4*x + 13*x^2 - 12*x^3 - 2*x^4 + E^6* (14*x - 12*x^2 - 2*x^3))*Log[3] + (-2 + 7*x^2 + x^3 + E^6*(7*x + x^2))*Log [3]^2),x]
Output:
-Log[-1 + x - Log[3]] + RootSum[1 + Log[3]^2 + Log[9] + 8*#1 + 8*E^6*#1 + 19*Log[3]*#1 + 9*E^6*Log[3]*#1 + 10*Log[3]^2*#1 + E^6*Log[3]^2*#1 + Log[3] ^3*#1 + 18*#1^2 + 9*E^6*#1^2 + 20*Log[3]*#1^2 + 3*Log[3]^2*#1^2 + E^6*Log[ 9]*#1^2 + 10*#1^3 + E^6*#1^3 + Log[27]*#1^3 + #1^4 & , (8*Log[-1 + x - Log [3] - #1] + 8*E^6*Log[-1 + x - Log[3] - #1] + 35*Log[3]*Log[-1 + x - Log[3 ] - #1] + 25*E^6*Log[3]*Log[-1 + x - Log[3] - #1] + 56*Log[3]^2*Log[-1 + x - Log[3] - #1] + 27*E^6*Log[3]^2*Log[-1 + x - Log[3] - #1] + 40*Log[3]^3* Log[-1 + x - Log[3] - #1] + 11*E^6*Log[3]^3*Log[-1 + x - Log[3] - #1] + 12 *Log[3]^4*Log[-1 + x - Log[3] - #1] + E^6*Log[3]^4*Log[-1 + x - Log[3] - # 1] + Log[3]^5*Log[-1 + x - Log[3] - #1] + 36*Log[-1 + x - Log[3] - #1]*#1 + 18*E^6*Log[-1 + x - Log[3] - #1]*#1 + 76*Log[3]*Log[-1 + x - Log[3] - #1 ]*#1 + 22*E^6*Log[3]*Log[-1 + x - Log[3] - #1]*#1 + 82*Log[3]^2*Log[-1 + x - Log[3] - #1]*#1 + 22*E^6*Log[3]^2*Log[-1 + x - Log[3] - #1]*#1 + 46*Log [3]^3*Log[-1 + x - Log[3] - #1]*#1 + 4*E^6*Log[3]^3*Log[-1 + x - Log[3] - #1]*#1 + 6*Log[3]^4*Log[-1 + x - Log[3] - #1]*#1 + 18*Log[9]*Log[-1 + x - Log[3] - #1]*#1 + 9*E^6*Log[9]*Log[-1 + x - Log[3] - #1]*#1 + 20*Log[3]*Lo g[9]*Log[-1 + x - Log[3] - #1]*#1 + 3*Log[3]^2*Log[9]*Log[-1 + x - Log[3] - #1]*#1 + E^6*Log[9]^2*Log[-1 + x - Log[3] - #1]*#1 + 30*Log[-1 + x - Log [3] - #1]*#1^2 + 3*E^6*Log[-1 + x - Log[3] - #1]*#1^2 + 29*Log[3]*Log[-1 + x - Log[3] - #1]*#1^2 + 36*Log[3]^2*Log[-1 + x - Log[3] - #1]*#1^2 + 3...
Leaf count is larger than twice the leaf count of optimal. \(68\) vs. \(2(26)=52\).
Time = 0.61 (sec) , antiderivative size = 68, normalized size of antiderivative = 2.62, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.010, Rules used = {2462, 2009}
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
| \(\displaystyle \int \frac {3 x^4+8 x^3-24 x^2+\left (3 x^2+14 x+e^6 (2 x+7)\right ) \log ^2(3)+e^6 \left (2 x^3+3 x^2-12 x+7\right )+\left (-6 x^3-22 x^2+e^6 \left (-4 x^2-10 x+14\right )+26 x\right ) \log (3)+12 x}{x^5+5 x^4-12 x^3+4 x^2+\left (x^3+7 x^2+e^6 \left (x^2+7 x\right )-2\right ) \log ^2(3)+e^6 \left (x^4+5 x^3-13 x^2+7 x\right )+\left (-2 x^4-12 x^3+13 x^2+e^6 \left (-2 x^3-12 x^2+14 x\right )+4 x-4\right ) \log (3)+4 x-2} \, dx\) |
| \(\Big \downarrow \) 2462 |
| \(\displaystyle \int \left (\frac {4 x^3+3 x^2 \left (6+e^6-\log (3)\right )-2 x \left (6-e^6 (6-\log (3))+7 \log (3)\right )-2-7 e^6 (1+\log (3))}{x^4+x^3 \left (6+e^6-\log (3)\right )-x^2 \left (6-e^6 (6-\log (3))+7 \log (3)\right )-x \left (2+7 e^6 (1+\log (3))\right )+2+\log (9)}+\frac {1}{-x+1+\log (3)}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle \log \left (x^4+x^3 \left (6+e^6-\log (3)\right )-x^2 \left (6-e^6 (6-\log (3))+7 \log (3)\right )-x \left (2+7 e^6 (1+\log (3))\right )+2+\log (9)\right )-\log (-x+1+\log (3))\) |
Input:
Int[(12*x - 24*x^2 + 8*x^3 + 3*x^4 + E^6*(7 - 12*x + 3*x^2 + 2*x^3) + (26* x - 22*x^2 - 6*x^3 + E^6*(14 - 10*x - 4*x^2))*Log[3] + (14*x + 3*x^2 + E^6 *(7 + 2*x))*Log[3]^2)/(-2 + 4*x + 4*x^2 - 12*x^3 + 5*x^4 + x^5 + E^6*(7*x - 13*x^2 + 5*x^3 + x^4) + (-4 + 4*x + 13*x^2 - 12*x^3 - 2*x^4 + E^6*(14*x - 12*x^2 - 2*x^3))*Log[3] + (-2 + 7*x^2 + x^3 + E^6*(7*x + x^2))*Log[3]^2) ,x]
Output:
-Log[1 - x + Log[3]] + Log[2 + x^4 + x^3*(6 + E^6 - Log[3]) - x^2*(6 - E^6 *(6 - Log[3]) + 7*Log[3]) - x*(2 + 7*E^6*(1 + Log[3])) + Log[9]]
Int[(u_.)*(Px_)^(p_), x_Symbol] :> With[{Qx = Factor[Px]}, Int[ExpandIntegr and[u*Qx^p, x], x] /; !SumQ[NonfreeFactors[Qx, x]]] /; PolyQ[Px, x] && GtQ [Expon[Px, x], 2] && !BinomialQ[Px, x] && !TrinomialQ[Px, x] && ILtQ[p, 0 ] && RationalFunctionQ[u, x]
Leaf count of result is larger than twice the leaf count of optimal. \(67\) vs. \(2(27)=54\).
Time = 0.98 (sec) , antiderivative size = 68, normalized size of antiderivative = 2.62
| method | result | size |
| risch | \(-\ln \left (1+\ln \left (3\right )-x \right )+\ln \left (x^{4}+\left (-\ln \left (3\right )+{\mathrm e}^{6}+6\right ) x^{3}+\left (-{\mathrm e}^{6} \ln \left (3\right )-7 \ln \left (3\right )+6 \,{\mathrm e}^{6}-6\right ) x^{2}+\left (-7 \,{\mathrm e}^{6} \ln \left (3\right )-7 \,{\mathrm e}^{6}-2\right ) x +2 \ln \left (3\right )+2\right )\) | \(68\) |
| default | \(-\ln \left (x -\ln \left (3\right )-1\right )+\ln \left (-{\mathrm e}^{6} \ln \left (3\right ) x^{2}+{\mathrm e}^{6} x^{3}-x^{3} \ln \left (3\right )+x^{4}-7 \,{\mathrm e}^{6} \ln \left (3\right ) x +6 x^{2} {\mathrm e}^{6}-7 x^{2} \ln \left (3\right )+6 x^{3}-7 x \,{\mathrm e}^{6}-6 x^{2}+2 \ln \left (3\right )-2 x +2\right )\) | \(83\) |
| parallelrisch | \(-\ln \left (x -\ln \left (3\right )-1\right )+\ln \left (-{\mathrm e}^{6} \ln \left (3\right ) x^{2}+{\mathrm e}^{6} x^{3}-x^{3} \ln \left (3\right )+x^{4}-7 \,{\mathrm e}^{6} \ln \left (3\right ) x +6 x^{2} {\mathrm e}^{6}-7 x^{2} \ln \left (3\right )+6 x^{3}-7 x \,{\mathrm e}^{6}-6 x^{2}+2 \ln \left (3\right )-2 x +2\right )\) | \(93\) |
| norman | \(-\ln \left (1+\ln \left (3\right )-x \right )+\ln \left ({\mathrm e}^{6} \ln \left (3\right ) x^{2}-{\mathrm e}^{6} x^{3}+x^{3} \ln \left (3\right )-x^{4}+7 \,{\mathrm e}^{6} \ln \left (3\right ) x -6 x^{2} {\mathrm e}^{6}+7 x^{2} \ln \left (3\right )-6 x^{3}+7 x \,{\mathrm e}^{6}+6 x^{2}-2 \ln \left (3\right )+2 x -2\right )\) | \(94\) |
Input:
int((((2*x+7)*exp(3)^2+3*x^2+14*x)*ln(3)^2+((-4*x^2-10*x+14)*exp(3)^2-6*x^ 3-22*x^2+26*x)*ln(3)+(2*x^3+3*x^2-12*x+7)*exp(3)^2+3*x^4+8*x^3-24*x^2+12*x )/(((x^2+7*x)*exp(3)^2+x^3+7*x^2-2)*ln(3)^2+((-2*x^3-12*x^2+14*x)*exp(3)^2 -2*x^4-12*x^3+13*x^2+4*x-4)*ln(3)+(x^4+5*x^3-13*x^2+7*x)*exp(3)^2+x^5+5*x^ 4-12*x^3+4*x^2+4*x-2),x,method=_RETURNVERBOSE)
Output:
-ln(1+ln(3)-x)+ln(x^4+(-ln(3)+exp(6)+6)*x^3+(-exp(6)*ln(3)-7*ln(3)+6*exp(6 )-6)*x^2+(-7*exp(6)*ln(3)-7*exp(6)-2)*x+2*ln(3)+2)
Leaf count of result is larger than twice the leaf count of optimal. 69 vs. \(2 (25) = 50\).
Time = 0.11 (sec) , antiderivative size = 69, normalized size of antiderivative = 2.65 \[ \int \frac {12 x-24 x^2+8 x^3+3 x^4+e^6 \left (7-12 x+3 x^2+2 x^3\right )+\left (26 x-22 x^2-6 x^3+e^6 \left (14-10 x-4 x^2\right )\right ) \log (3)+\left (14 x+3 x^2+e^6 (7+2 x)\right ) \log ^2(3)}{-2+4 x+4 x^2-12 x^3+5 x^4+x^5+e^6 \left (7 x-13 x^2+5 x^3+x^4\right )+\left (-4+4 x+13 x^2-12 x^3-2 x^4+e^6 \left (14 x-12 x^2-2 x^3\right )\right ) \log (3)+\left (-2+7 x^2+x^3+e^6 \left (7 x+x^2\right )\right ) \log ^2(3)} \, dx=\log \left (x^{4} + 6 \, x^{3} - 6 \, x^{2} + {\left (x^{3} + 6 \, x^{2} - 7 \, x\right )} e^{6} - {\left (x^{3} + 7 \, x^{2} + {\left (x^{2} + 7 \, x\right )} e^{6} - 2\right )} \log \left (3\right ) - 2 \, x + 2\right ) - \log \left (x - \log \left (3\right ) - 1\right ) \] Input:
integrate((((2*x+7)*exp(3)^2+3*x^2+14*x)*log(3)^2+((-4*x^2-10*x+14)*exp(3) ^2-6*x^3-22*x^2+26*x)*log(3)+(2*x^3+3*x^2-12*x+7)*exp(3)^2+3*x^4+8*x^3-24* x^2+12*x)/(((x^2+7*x)*exp(3)^2+x^3+7*x^2-2)*log(3)^2+((-2*x^3-12*x^2+14*x) *exp(3)^2-2*x^4-12*x^3+13*x^2+4*x-4)*log(3)+(x^4+5*x^3-13*x^2+7*x)*exp(3)^ 2+x^5+5*x^4-12*x^3+4*x^2+4*x-2),x, algorithm="fricas")
Output:
log(x^4 + 6*x^3 - 6*x^2 + (x^3 + 6*x^2 - 7*x)*e^6 - (x^3 + 7*x^2 + (x^2 + 7*x)*e^6 - 2)*log(3) - 2*x + 2) - log(x - log(3) - 1)
Timed out. \[ \int \frac {12 x-24 x^2+8 x^3+3 x^4+e^6 \left (7-12 x+3 x^2+2 x^3\right )+\left (26 x-22 x^2-6 x^3+e^6 \left (14-10 x-4 x^2\right )\right ) \log (3)+\left (14 x+3 x^2+e^6 (7+2 x)\right ) \log ^2(3)}{-2+4 x+4 x^2-12 x^3+5 x^4+x^5+e^6 \left (7 x-13 x^2+5 x^3+x^4\right )+\left (-4+4 x+13 x^2-12 x^3-2 x^4+e^6 \left (14 x-12 x^2-2 x^3\right )\right ) \log (3)+\left (-2+7 x^2+x^3+e^6 \left (7 x+x^2\right )\right ) \log ^2(3)} \, dx=\text {Timed out} \] Input:
integrate((((2*x+7)*exp(3)**2+3*x**2+14*x)*ln(3)**2+((-4*x**2-10*x+14)*exp (3)**2-6*x**3-22*x**2+26*x)*ln(3)+(2*x**3+3*x**2-12*x+7)*exp(3)**2+3*x**4+ 8*x**3-24*x**2+12*x)/(((x**2+7*x)*exp(3)**2+x**3+7*x**2-2)*ln(3)**2+((-2*x **3-12*x**2+14*x)*exp(3)**2-2*x**4-12*x**3+13*x**2+4*x-4)*ln(3)+(x**4+5*x* *3-13*x**2+7*x)*exp(3)**2+x**5+5*x**4-12*x**3+4*x**2+4*x-2),x)
Output:
Timed out
Leaf count of result is larger than twice the leaf count of optimal. 66 vs. \(2 (25) = 50\).
Time = 0.03 (sec) , antiderivative size = 66, normalized size of antiderivative = 2.54 \[ \int \frac {12 x-24 x^2+8 x^3+3 x^4+e^6 \left (7-12 x+3 x^2+2 x^3\right )+\left (26 x-22 x^2-6 x^3+e^6 \left (14-10 x-4 x^2\right )\right ) \log (3)+\left (14 x+3 x^2+e^6 (7+2 x)\right ) \log ^2(3)}{-2+4 x+4 x^2-12 x^3+5 x^4+x^5+e^6 \left (7 x-13 x^2+5 x^3+x^4\right )+\left (-4+4 x+13 x^2-12 x^3-2 x^4+e^6 \left (14 x-12 x^2-2 x^3\right )\right ) \log (3)+\left (-2+7 x^2+x^3+e^6 \left (7 x+x^2\right )\right ) \log ^2(3)} \, dx=\log \left (x^{4} + x^{3} {\left (e^{6} - \log \left (3\right ) + 6\right )} - {\left ({\left (e^{6} + 7\right )} \log \left (3\right ) - 6 \, e^{6} + 6\right )} x^{2} - {\left (7 \, e^{6} \log \left (3\right ) + 7 \, e^{6} + 2\right )} x + 2 \, \log \left (3\right ) + 2\right ) - \log \left (x - \log \left (3\right ) - 1\right ) \] Input:
integrate((((2*x+7)*exp(3)^2+3*x^2+14*x)*log(3)^2+((-4*x^2-10*x+14)*exp(3) ^2-6*x^3-22*x^2+26*x)*log(3)+(2*x^3+3*x^2-12*x+7)*exp(3)^2+3*x^4+8*x^3-24* x^2+12*x)/(((x^2+7*x)*exp(3)^2+x^3+7*x^2-2)*log(3)^2+((-2*x^3-12*x^2+14*x) *exp(3)^2-2*x^4-12*x^3+13*x^2+4*x-4)*log(3)+(x^4+5*x^3-13*x^2+7*x)*exp(3)^ 2+x^5+5*x^4-12*x^3+4*x^2+4*x-2),x, algorithm="maxima")
Output:
log(x^4 + x^3*(e^6 - log(3) + 6) - ((e^6 + 7)*log(3) - 6*e^6 + 6)*x^2 - (7 *e^6*log(3) + 7*e^6 + 2)*x + 2*log(3) + 2) - log(x - log(3) - 1)
Timed out. \[ \int \frac {12 x-24 x^2+8 x^3+3 x^4+e^6 \left (7-12 x+3 x^2+2 x^3\right )+\left (26 x-22 x^2-6 x^3+e^6 \left (14-10 x-4 x^2\right )\right ) \log (3)+\left (14 x+3 x^2+e^6 (7+2 x)\right ) \log ^2(3)}{-2+4 x+4 x^2-12 x^3+5 x^4+x^5+e^6 \left (7 x-13 x^2+5 x^3+x^4\right )+\left (-4+4 x+13 x^2-12 x^3-2 x^4+e^6 \left (14 x-12 x^2-2 x^3\right )\right ) \log (3)+\left (-2+7 x^2+x^3+e^6 \left (7 x+x^2\right )\right ) \log ^2(3)} \, dx=\text {Timed out} \] Input:
integrate((((2*x+7)*exp(3)^2+3*x^2+14*x)*log(3)^2+((-4*x^2-10*x+14)*exp(3) ^2-6*x^3-22*x^2+26*x)*log(3)+(2*x^3+3*x^2-12*x+7)*exp(3)^2+3*x^4+8*x^3-24* x^2+12*x)/(((x^2+7*x)*exp(3)^2+x^3+7*x^2-2)*log(3)^2+((-2*x^3-12*x^2+14*x) *exp(3)^2-2*x^4-12*x^3+13*x^2+4*x-4)*log(3)+(x^4+5*x^3-13*x^2+7*x)*exp(3)^ 2+x^5+5*x^4-12*x^3+4*x^2+4*x-2),x, algorithm="giac")
Output:
Timed out
Timed out. \[ \int \frac {12 x-24 x^2+8 x^3+3 x^4+e^6 \left (7-12 x+3 x^2+2 x^3\right )+\left (26 x-22 x^2-6 x^3+e^6 \left (14-10 x-4 x^2\right )\right ) \log (3)+\left (14 x+3 x^2+e^6 (7+2 x)\right ) \log ^2(3)}{-2+4 x+4 x^2-12 x^3+5 x^4+x^5+e^6 \left (7 x-13 x^2+5 x^3+x^4\right )+\left (-4+4 x+13 x^2-12 x^3-2 x^4+e^6 \left (14 x-12 x^2-2 x^3\right )\right ) \log (3)+\left (-2+7 x^2+x^3+e^6 \left (7 x+x^2\right )\right ) \log ^2(3)} \, dx=\text {Hanged} \] Input:
int((12*x + exp(6)*(3*x^2 - 12*x + 2*x^3 + 7) + log(3)^2*(14*x + 3*x^2 + e xp(6)*(2*x + 7)) - log(3)*(exp(6)*(10*x + 4*x^2 - 14) - 26*x + 22*x^2 + 6* x^3) - 24*x^2 + 8*x^3 + 3*x^4)/(4*x - log(3)*(exp(6)*(12*x^2 - 14*x + 2*x^ 3) - 4*x - 13*x^2 + 12*x^3 + 2*x^4 + 4) + exp(6)*(7*x - 13*x^2 + 5*x^3 + x ^4) + log(3)^2*(exp(6)*(7*x + x^2) + 7*x^2 + x^3 - 2) + 4*x^2 - 12*x^3 + 5 *x^4 + x^5 - 2),x)
Output:
\text{Hanged}
Time = 0.18 (sec) , antiderivative size = 88, normalized size of antiderivative = 3.38 \[ \int \frac {12 x-24 x^2+8 x^3+3 x^4+e^6 \left (7-12 x+3 x^2+2 x^3\right )+\left (26 x-22 x^2-6 x^3+e^6 \left (14-10 x-4 x^2\right )\right ) \log (3)+\left (14 x+3 x^2+e^6 (7+2 x)\right ) \log ^2(3)}{-2+4 x+4 x^2-12 x^3+5 x^4+x^5+e^6 \left (7 x-13 x^2+5 x^3+x^4\right )+\left (-4+4 x+13 x^2-12 x^3-2 x^4+e^6 \left (14 x-12 x^2-2 x^3\right )\right ) \log (3)+\left (-2+7 x^2+x^3+e^6 \left (7 x+x^2\right )\right ) \log ^2(3)} \, dx=-\mathrm {log}\left (\mathrm {log}\left (3\right )-x +1\right )+\mathrm {log}\left (\mathrm {log}\left (3\right ) e^{6} x^{2}+7 \,\mathrm {log}\left (3\right ) e^{6} x +\mathrm {log}\left (3\right ) x^{3}+7 \,\mathrm {log}\left (3\right ) x^{2}-2 \,\mathrm {log}\left (3\right )-e^{6} x^{3}-6 e^{6} x^{2}+7 e^{6} x -x^{4}-6 x^{3}+6 x^{2}+2 x -2\right ) \] Input:
int((((2*x+7)*exp(3)^2+3*x^2+14*x)*log(3)^2+((-4*x^2-10*x+14)*exp(3)^2-6*x ^3-22*x^2+26*x)*log(3)+(2*x^3+3*x^2-12*x+7)*exp(3)^2+3*x^4+8*x^3-24*x^2+12 *x)/(((x^2+7*x)*exp(3)^2+x^3+7*x^2-2)*log(3)^2+((-2*x^3-12*x^2+14*x)*exp(3 )^2-2*x^4-12*x^3+13*x^2+4*x-4)*log(3)+(x^4+5*x^3-13*x^2+7*x)*exp(3)^2+x^5+ 5*x^4-12*x^3+4*x^2+4*x-2),x)
Output:
- log(log(3) - x + 1) + log(log(3)*e**6*x**2 + 7*log(3)*e**6*x + log(3)*x **3 + 7*log(3)*x**2 - 2*log(3) - e**6*x**3 - 6*e**6*x**2 + 7*e**6*x - x**4 - 6*x**3 + 6*x**2 + 2*x - 2)