Integrand size = 251, antiderivative size = 35 \[ \int \frac {\left (-144 x+72 x^2-9 x^3\right ) \log (3)+\left (-24 x^2+6 x^3\right ) \log (3) \log (x)-x^3 \log (3) \log ^2(x)+e^{e^{\frac {\left (12 x-3 x^2\right ) \log (3)+\left (6-2 x+x^2 \log (3)\right ) \log (x)}{(12-3 x) \log (3)+x \log (3) \log (x)}}+\frac {\left (12 x-3 x^2\right ) \log (3)+\left (6-2 x+x^2 \log (3)\right ) \log (x)}{(12-3 x) \log (3)+x \log (3) \log (x)}} \left (72-42 x+6 x^2+\left (144 x-72 x^2+9 x^3\right ) \log (3)+\left (-6 x+\left (24 x^2-6 x^3\right ) \log (3)\right ) \log (x)+\left (-6 x+x^3 \log (3)\right ) \log ^2(x)\right )}{\left (144 x-72 x^2+9 x^3\right ) \log (3)+\left (24 x^2-6 x^3\right ) \log (3) \log (x)+x^3 \log (3) \log ^2(x)} \, dx=5+e^{e^{x+\frac {2 (-3+x)}{\log (3) \left (-x+\frac {3 (-4+x)}{\log (x)}\right )}}}-x \]
Time = 1.10 (sec) , antiderivative size = 57, normalized size of antiderivative = 1.63 \[ \int \frac {\left (-144 x+72 x^2-9 x^3\right ) \log (3)+\left (-24 x^2+6 x^3\right ) \log (3) \log (x)-x^3 \log (3) \log ^2(x)+e^{e^{\frac {\left (12 x-3 x^2\right ) \log (3)+\left (6-2 x+x^2 \log (3)\right ) \log (x)}{(12-3 x) \log (3)+x \log (3) \log (x)}}+\frac {\left (12 x-3 x^2\right ) \log (3)+\left (6-2 x+x^2 \log (3)\right ) \log (x)}{(12-3 x) \log (3)+x \log (3) \log (x)}} \left (72-42 x+6 x^2+\left (144 x-72 x^2+9 x^3\right ) \log (3)+\left (-6 x+\left (24 x^2-6 x^3\right ) \log (3)\right ) \log (x)+\left (-6 x+x^3 \log (3)\right ) \log ^2(x)\right )}{\left (144 x-72 x^2+9 x^3\right ) \log (3)+\left (24 x^2-6 x^3\right ) \log (3) \log (x)+x^3 \log (3) \log ^2(x)} \, dx=\frac {e^{e^{\frac {-3 (-4+x) x \log (3)+\left (6-2 x+x^2 \log (3)\right ) \log (x)}{\log (3) (12-3 x+x \log (x))}}} \log (3)-x \log (3)}{\log (3)} \]
Integrate[((-144*x + 72*x^2 - 9*x^3)*Log[3] + (-24*x^2 + 6*x^3)*Log[3]*Log [x] - x^3*Log[3]*Log[x]^2 + E^(E^(((12*x - 3*x^2)*Log[3] + (6 - 2*x + x^2* Log[3])*Log[x])/((12 - 3*x)*Log[3] + x*Log[3]*Log[x])) + ((12*x - 3*x^2)*L og[3] + (6 - 2*x + x^2*Log[3])*Log[x])/((12 - 3*x)*Log[3] + x*Log[3]*Log[x ]))*(72 - 42*x + 6*x^2 + (144*x - 72*x^2 + 9*x^3)*Log[3] + (-6*x + (24*x^2 - 6*x^3)*Log[3])*Log[x] + (-6*x + x^3*Log[3])*Log[x]^2))/((144*x - 72*x^2 + 9*x^3)*Log[3] + (24*x^2 - 6*x^3)*Log[3]*Log[x] + x^3*Log[3]*Log[x]^2),x ]
(E^E^((-3*(-4 + x)*x*Log[3] + (6 - 2*x + x^2*Log[3])*Log[x])/(Log[3]*(12 - 3*x + x*Log[x])))*Log[3] - x*Log[3])/Log[3]
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.
| \(\displaystyle \int \frac {\left (\left (x^3 \log (3)-6 x\right ) \log ^2(x)+6 x^2+\left (\left (24 x^2-6 x^3\right ) \log (3)-6 x\right ) \log (x)+\left (9 x^3-72 x^2+144 x\right ) \log (3)-42 x+72\right ) \exp \left (\exp \left (\frac {\left (12 x-3 x^2\right ) \log (3)+\left (x^2 \log (3)-2 x+6\right ) \log (x)}{(12-3 x) \log (3)+x \log (3) \log (x)}\right )+\frac {\left (12 x-3 x^2\right ) \log (3)+\left (x^2 \log (3)-2 x+6\right ) \log (x)}{(12-3 x) \log (3)+x \log (3) \log (x)}\right )+x^3 (-\log (3)) \log ^2(x)+\left (6 x^3-24 x^2\right ) \log (3) \log (x)+\left (-9 x^3+72 x^2-144 x\right ) \log (3)}{x^3 \log (3) \log ^2(x)+\left (24 x^2-6 x^3\right ) \log (3) \log (x)+\left (9 x^3-72 x^2+144 x\right ) \log (3)} \, dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {\left (\left (x^3 \log (3)-6 x\right ) \log ^2(x)+6 x^2+\left (\left (24 x^2-6 x^3\right ) \log (3)-6 x\right ) \log (x)+\left (9 x^3-72 x^2+144 x\right ) \log (3)-42 x+72\right ) \exp \left (\exp \left (\frac {\left (12 x-3 x^2\right ) \log (3)+\left (x^2 \log (3)-2 x+6\right ) \log (x)}{(12-3 x) \log (3)+x \log (3) \log (x)}\right )+\frac {\left (12 x-3 x^2\right ) \log (3)+\left (x^2 \log (3)-2 x+6\right ) \log (x)}{(12-3 x) \log (3)+x \log (3) \log (x)}\right )+x^3 (-\log (3)) \log ^2(x)+\left (6 x^3-24 x^2\right ) \log (3) \log (x)+\left (-9 x^3+72 x^2-144 x\right ) \log (3)}{x \log (3) (-3 x+x \log (x)+12)^2}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {\int -\frac {\log (3) \log ^2(x) x^3+6 \left (4 x^2-x^3\right ) \log (3) \log (x)-\exp \left (3^{\frac {12 x-3 x^2}{\log (3) (12-3 x)+x \log (3) \log (x)}} x^{\frac {\log (3) x^2-2 x+6}{3 \log (3) (4-x)+x \log (3) \log (x)}}+\frac {3 \log (3) \left (4 x-x^2\right )+\left (\log (3) x^2-2 x+6\right ) \log (x)}{3 \log (3) (4-x)+x \log (3) \log (x)}\right ) \left (6 x^2-42 x-\left (6 x-x^3 \log (3)\right ) \log ^2(x)-6 \left (x-\left (4 x^2-x^3\right ) \log (3)\right ) \log (x)+9 \left (x^3-8 x^2+16 x\right ) \log (3)+72\right )+9 \left (x^3-8 x^2+16 x\right ) \log (3)}{x (\log (x) x-3 x+12)^2}dx}{\log (3)}\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle -\frac {\int \frac {\log (3) \log ^2(x) x^3+6 \left (4 x^2-x^3\right ) \log (3) \log (x)-\exp \left (3^{\frac {3 \left (4 x-x^2\right )}{3 \log (3) (4-x)+x \log (3) \log (x)}} x^{\frac {\log (3) x^2-2 x+6}{3 \log (3) (4-x)+x \log (3) \log (x)}}+\frac {3 \log (3) \left (4 x-x^2\right )+\left (\log (3) x^2-2 x+6\right ) \log (x)}{3 \log (3) (4-x)+x \log (3) \log (x)}\right ) \left (6 x^2-42 x-\left (6 x-x^3 \log (3)\right ) \log ^2(x)-6 \left (x-\left (4 x^2-x^3\right ) \log (3)\right ) \log (x)+9 \left (x^3-8 x^2+16 x\right ) \log (3)+72\right )+9 \left (x^3-8 x^2+16 x\right ) \log (3)}{x (\log (x) x-3 x+12)^2}dx}{\log (3)}\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -\frac {\int \left (\frac {3^{-\frac {3 (x-4) x}{\log (3) (\log (x) x-3 x+12)}} \exp \left (3^{-\frac {3 (x-4) x}{\log (3) (\log (x) x-3 x+12)}} x^{\frac {\log (3) x^2-2 x+6}{\log (3) (\log (x) x-3 x+12)}}\right ) \left (-\log (3) \log ^2(x) x^3+6 \log (3) \log (x) x^3-3 \log (27) x^3-24 \log (3) \log (x) x^2-6 (1-12 \log (3)) x^2+6 \log ^2(x) x+6 \log (x) x+42 \left (1-\frac {24 \log (3)}{7}\right ) x-72\right ) x^{\frac {\log (3) x^2-\log (3) \log (x) x-2 \left (1-\frac {\log (27)}{2}\right ) x+6 (1-\log (9))}{\log (3) (\log (x) x-3 x+12)}}}{(\log (x) x-3 x+12)^2}+\log (3)\right )dx}{\log (3)}\) |
| \(\Big \downarrow \) 7299 |
| \(\displaystyle -\frac {\int \left (\frac {3^{-\frac {3 (x-4) x}{\log (3) (\log (x) x-3 x+12)}} \exp \left (3^{-\frac {3 (x-4) x}{\log (3) (\log (x) x-3 x+12)}} x^{\frac {\log (3) x^2-2 x+6}{\log (3) (\log (x) x-3 x+12)}}\right ) \left (-\log (3) \log ^2(x) x^3+6 \log (3) \log (x) x^3-3 \log (27) x^3-24 \log (3) \log (x) x^2-6 (1-12 \log (3)) x^2+6 \log ^2(x) x+6 \log (x) x+42 \left (1-\frac {24 \log (3)}{7}\right ) x-72\right ) x^{\frac {\log (3) x^2-\log (3) \log (x) x-2 \left (1-\frac {\log (27)}{2}\right ) x+6 (1-\log (9))}{\log (3) (\log (x) x-3 x+12)}}}{(\log (x) x-3 x+12)^2}+\log (3)\right )dx}{\log (3)}\) |
Int[((-144*x + 72*x^2 - 9*x^3)*Log[3] + (-24*x^2 + 6*x^3)*Log[3]*Log[x] - x^3*Log[3]*Log[x]^2 + E^(E^(((12*x - 3*x^2)*Log[3] + (6 - 2*x + x^2*Log[3] )*Log[x])/((12 - 3*x)*Log[3] + x*Log[3]*Log[x])) + ((12*x - 3*x^2)*Log[3] + (6 - 2*x + x^2*Log[3])*Log[x])/((12 - 3*x)*Log[3] + x*Log[3]*Log[x]))*(7 2 - 42*x + 6*x^2 + (144*x - 72*x^2 + 9*x^3)*Log[3] + (-6*x + (24*x^2 - 6*x ^3)*Log[3])*Log[x] + (-6*x + x^3*Log[3])*Log[x]^2))/((144*x - 72*x^2 + 9*x ^3)*Log[3] + (24*x^2 - 6*x^3)*Log[3]*Log[x] + x^3*Log[3]*Log[x]^2),x]
3.27.32.3.1 Defintions of rubi rules used
Int[(a_)*(Fx_), x_Symbol] :> Simp[a Int[Fx, x], x] /; FreeQ[a, x] && !Ma tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
Time = 277.96 (sec) , antiderivative size = 53, normalized size of antiderivative = 1.51
| method | result | size |
| risch | \(-x +{\mathrm e}^{{\mathrm e}^{\frac {x^{2} \ln \left (3\right ) \ln \left (x \right )-3 x^{2} \ln \left (3\right )-2 x \ln \left (x \right )+12 x \ln \left (3\right )+6 \ln \left (x \right )}{\ln \left (3\right ) \left (x \ln \left (x \right )-3 x +12\right )}}}\) | \(53\) |
| parallelrisch | \(\frac {-x \ln \left (3\right )+\ln \left (3\right ) {\mathrm e}^{{\mathrm e}^{\frac {\left (x^{2} \ln \left (3\right )+6-2 x \right ) \ln \left (x \right )+\left (-3 x^{2}+12 x \right ) \ln \left (3\right )}{\ln \left (3\right ) \left (x \ln \left (x \right )-3 x +12\right )}}}}{\ln \left (3\right )}\) | \(60\) |
int((((x^3*ln(3)-6*x)*ln(x)^2+((-6*x^3+24*x^2)*ln(3)-6*x)*ln(x)+(9*x^3-72* x^2+144*x)*ln(3)+6*x^2-42*x+72)*exp(((x^2*ln(3)+6-2*x)*ln(x)+(-3*x^2+12*x) *ln(3))/(x*ln(3)*ln(x)+(-3*x+12)*ln(3)))*exp(exp(((x^2*ln(3)+6-2*x)*ln(x)+ (-3*x^2+12*x)*ln(3))/(x*ln(3)*ln(x)+(-3*x+12)*ln(3))))-x^3*ln(3)*ln(x)^2+( 6*x^3-24*x^2)*ln(3)*ln(x)+(-9*x^3+72*x^2-144*x)*ln(3))/(x^3*ln(3)*ln(x)^2+ (-6*x^3+24*x^2)*ln(3)*ln(x)+(9*x^3-72*x^2+144*x)*ln(3)),x,method=_RETURNVE RBOSE)
-x+exp(exp((x^2*ln(3)*ln(x)-3*x^2*ln(3)-2*x*ln(x)+12*x*ln(3)+6*ln(x))/ln(3 )/(x*ln(x)-3*x+12)))
Leaf count of result is larger than twice the leaf count of optimal. 203 vs. \(2 (31) = 62\).
Time = 0.26 (sec) , antiderivative size = 203, normalized size of antiderivative = 5.80 \[ \int \frac {\left (-144 x+72 x^2-9 x^3\right ) \log (3)+\left (-24 x^2+6 x^3\right ) \log (3) \log (x)-x^3 \log (3) \log ^2(x)+e^{e^{\frac {\left (12 x-3 x^2\right ) \log (3)+\left (6-2 x+x^2 \log (3)\right ) \log (x)}{(12-3 x) \log (3)+x \log (3) \log (x)}}+\frac {\left (12 x-3 x^2\right ) \log (3)+\left (6-2 x+x^2 \log (3)\right ) \log (x)}{(12-3 x) \log (3)+x \log (3) \log (x)}} \left (72-42 x+6 x^2+\left (144 x-72 x^2+9 x^3\right ) \log (3)+\left (-6 x+\left (24 x^2-6 x^3\right ) \log (3)\right ) \log (x)+\left (-6 x+x^3 \log (3)\right ) \log ^2(x)\right )}{\left (144 x-72 x^2+9 x^3\right ) \log (3)+\left (24 x^2-6 x^3\right ) \log (3) \log (x)+x^3 \log (3) \log ^2(x)} \, dx=-{\left (x e^{\left (-\frac {3 \, {\left (x^{2} - 4 \, x\right )} \log \left (3\right ) - {\left (x^{2} \log \left (3\right ) - 2 \, x + 6\right )} \log \left (x\right )}{x \log \left (3\right ) \log \left (x\right ) - 3 \, {\left (x - 4\right )} \log \left (3\right )}\right )} - e^{\left (\frac {{\left (x \log \left (3\right ) \log \left (x\right ) - 3 \, {\left (x - 4\right )} \log \left (3\right )\right )} e^{\left (-\frac {3 \, {\left (x^{2} - 4 \, x\right )} \log \left (3\right ) - {\left (x^{2} \log \left (3\right ) - 2 \, x + 6\right )} \log \left (x\right )}{x \log \left (3\right ) \log \left (x\right ) - 3 \, {\left (x - 4\right )} \log \left (3\right )}\right )} - 3 \, {\left (x^{2} - 4 \, x\right )} \log \left (3\right ) + {\left (x^{2} \log \left (3\right ) - 2 \, x + 6\right )} \log \left (x\right )}{x \log \left (3\right ) \log \left (x\right ) - 3 \, {\left (x - 4\right )} \log \left (3\right )}\right )}\right )} e^{\left (\frac {3 \, {\left (x^{2} - 4 \, x\right )} \log \left (3\right ) - {\left (x^{2} \log \left (3\right ) - 2 \, x + 6\right )} \log \left (x\right )}{x \log \left (3\right ) \log \left (x\right ) - 3 \, {\left (x - 4\right )} \log \left (3\right )}\right )} \]
integrate((((x^3*log(3)-6*x)*log(x)^2+((-6*x^3+24*x^2)*log(3)-6*x)*log(x)+ (9*x^3-72*x^2+144*x)*log(3)+6*x^2-42*x+72)*exp(((x^2*log(3)+6-2*x)*log(x)+ (-3*x^2+12*x)*log(3))/(x*log(3)*log(x)+(-3*x+12)*log(3)))*exp(exp(((x^2*lo g(3)+6-2*x)*log(x)+(-3*x^2+12*x)*log(3))/(x*log(3)*log(x)+(-3*x+12)*log(3) )))-x^3*log(3)*log(x)^2+(6*x^3-24*x^2)*log(3)*log(x)+(-9*x^3+72*x^2-144*x) *log(3))/(x^3*log(3)*log(x)^2+(-6*x^3+24*x^2)*log(3)*log(x)+(9*x^3-72*x^2+ 144*x)*log(3)),x, algorithm=\
-(x*e^(-(3*(x^2 - 4*x)*log(3) - (x^2*log(3) - 2*x + 6)*log(x))/(x*log(3)*l og(x) - 3*(x - 4)*log(3))) - e^(((x*log(3)*log(x) - 3*(x - 4)*log(3))*e^(- (3*(x^2 - 4*x)*log(3) - (x^2*log(3) - 2*x + 6)*log(x))/(x*log(3)*log(x) - 3*(x - 4)*log(3))) - 3*(x^2 - 4*x)*log(3) + (x^2*log(3) - 2*x + 6)*log(x)) /(x*log(3)*log(x) - 3*(x - 4)*log(3))))*e^((3*(x^2 - 4*x)*log(3) - (x^2*lo g(3) - 2*x + 6)*log(x))/(x*log(3)*log(x) - 3*(x - 4)*log(3)))
Time = 3.21 (sec) , antiderivative size = 48, normalized size of antiderivative = 1.37 \[ \int \frac {\left (-144 x+72 x^2-9 x^3\right ) \log (3)+\left (-24 x^2+6 x^3\right ) \log (3) \log (x)-x^3 \log (3) \log ^2(x)+e^{e^{\frac {\left (12 x-3 x^2\right ) \log (3)+\left (6-2 x+x^2 \log (3)\right ) \log (x)}{(12-3 x) \log (3)+x \log (3) \log (x)}}+\frac {\left (12 x-3 x^2\right ) \log (3)+\left (6-2 x+x^2 \log (3)\right ) \log (x)}{(12-3 x) \log (3)+x \log (3) \log (x)}} \left (72-42 x+6 x^2+\left (144 x-72 x^2+9 x^3\right ) \log (3)+\left (-6 x+\left (24 x^2-6 x^3\right ) \log (3)\right ) \log (x)+\left (-6 x+x^3 \log (3)\right ) \log ^2(x)\right )}{\left (144 x-72 x^2+9 x^3\right ) \log (3)+\left (24 x^2-6 x^3\right ) \log (3) \log (x)+x^3 \log (3) \log ^2(x)} \, dx=- x + e^{e^{\frac {\left (- 3 x^{2} + 12 x\right ) \log {\left (3 \right )} + \left (x^{2} \log {\left (3 \right )} - 2 x + 6\right ) \log {\left (x \right )}}{x \log {\left (3 \right )} \log {\left (x \right )} + \left (12 - 3 x\right ) \log {\left (3 \right )}}}} \]
integrate((((x**3*ln(3)-6*x)*ln(x)**2+((-6*x**3+24*x**2)*ln(3)-6*x)*ln(x)+ (9*x**3-72*x**2+144*x)*ln(3)+6*x**2-42*x+72)*exp(((x**2*ln(3)+6-2*x)*ln(x) +(-3*x**2+12*x)*ln(3))/(x*ln(3)*ln(x)+(-3*x+12)*ln(3)))*exp(exp(((x**2*ln( 3)+6-2*x)*ln(x)+(-3*x**2+12*x)*ln(3))/(x*ln(3)*ln(x)+(-3*x+12)*ln(3))))-x* *3*ln(3)*ln(x)**2+(6*x**3-24*x**2)*ln(3)*ln(x)+(-9*x**3+72*x**2-144*x)*ln( 3))/(x**3*ln(3)*ln(x)**2+(-6*x**3+24*x**2)*ln(3)*ln(x)+(9*x**3-72*x**2+144 *x)*ln(3)),x)
-x + exp(exp(((-3*x**2 + 12*x)*log(3) + (x**2*log(3) - 2*x + 6)*log(x))/(x *log(3)*log(x) + (12 - 3*x)*log(3))))
Leaf count of result is larger than twice the leaf count of optimal. 264 vs. \(2 (31) = 62\).
Time = 0.55 (sec) , antiderivative size = 264, normalized size of antiderivative = 7.54 \[ \int \frac {\left (-144 x+72 x^2-9 x^3\right ) \log (3)+\left (-24 x^2+6 x^3\right ) \log (3) \log (x)-x^3 \log (3) \log ^2(x)+e^{e^{\frac {\left (12 x-3 x^2\right ) \log (3)+\left (6-2 x+x^2 \log (3)\right ) \log (x)}{(12-3 x) \log (3)+x \log (3) \log (x)}}+\frac {\left (12 x-3 x^2\right ) \log (3)+\left (6-2 x+x^2 \log (3)\right ) \log (x)}{(12-3 x) \log (3)+x \log (3) \log (x)}} \left (72-42 x+6 x^2+\left (144 x-72 x^2+9 x^3\right ) \log (3)+\left (-6 x+\left (24 x^2-6 x^3\right ) \log (3)\right ) \log (x)+\left (-6 x+x^3 \log (3)\right ) \log ^2(x)\right )}{\left (144 x-72 x^2+9 x^3\right ) \log (3)+\left (24 x^2-6 x^3\right ) \log (3) \log (x)+x^3 \log (3) \log ^2(x)} \, dx=-x + e^{\left (e^{\left (\frac {x \log \left (x\right )^{2}}{\log \left (x\right )^{2} - 6 \, \log \left (x\right ) + 9} - \frac {6 \, x \log \left (x\right )}{\log \left (x\right )^{2} - 6 \, \log \left (x\right ) + 9} + \frac {9 \, x}{\log \left (x\right )^{2} - 6 \, \log \left (x\right ) + 9} + \frac {24 \, \log \left (x\right )}{x \log \left (3\right ) \log \left (x\right )^{2} + 9 \, x \log \left (3\right ) - 6 \, {\left (x \log \left (3\right ) - 2 \, \log \left (3\right )\right )} \log \left (x\right ) - 36 \, \log \left (3\right )} + \frac {144 \, \log \left (x\right )}{x \log \left (x\right )^{3} - 3 \, {\left (3 \, x - 4\right )} \log \left (x\right )^{2} + 9 \, {\left (3 \, x - 8\right )} \log \left (x\right ) - 27 \, x + 108} + \frac {6 \, \log \left (x\right )}{x \log \left (3\right ) \log \left (x\right ) - 3 \, x \log \left (3\right ) + 12 \, \log \left (3\right )} - \frac {2 \, \log \left (x\right )}{\log \left (3\right ) \log \left (x\right ) - 3 \, \log \left (3\right )} - \frac {12 \, \log \left (x\right )}{\log \left (x\right )^{2} - 6 \, \log \left (x\right ) + 9} - \frac {432}{x \log \left (x\right )^{3} - 3 \, {\left (3 \, x - 4\right )} \log \left (x\right )^{2} + 9 \, {\left (3 \, x - 8\right )} \log \left (x\right ) - 27 \, x + 108} - \frac {144}{x \log \left (x\right )^{2} - 6 \, {\left (x - 2\right )} \log \left (x\right ) + 9 \, x - 36} + \frac {36}{\log \left (x\right )^{2} - 6 \, \log \left (x\right ) + 9} + \frac {12}{\log \left (x\right ) - 3}\right )}\right )} \]
integrate((((x^3*log(3)-6*x)*log(x)^2+((-6*x^3+24*x^2)*log(3)-6*x)*log(x)+ (9*x^3-72*x^2+144*x)*log(3)+6*x^2-42*x+72)*exp(((x^2*log(3)+6-2*x)*log(x)+ (-3*x^2+12*x)*log(3))/(x*log(3)*log(x)+(-3*x+12)*log(3)))*exp(exp(((x^2*lo g(3)+6-2*x)*log(x)+(-3*x^2+12*x)*log(3))/(x*log(3)*log(x)+(-3*x+12)*log(3) )))-x^3*log(3)*log(x)^2+(6*x^3-24*x^2)*log(3)*log(x)+(-9*x^3+72*x^2-144*x) *log(3))/(x^3*log(3)*log(x)^2+(-6*x^3+24*x^2)*log(3)*log(x)+(9*x^3-72*x^2+ 144*x)*log(3)),x, algorithm=\
-x + e^(e^(x*log(x)^2/(log(x)^2 - 6*log(x) + 9) - 6*x*log(x)/(log(x)^2 - 6 *log(x) + 9) + 9*x/(log(x)^2 - 6*log(x) + 9) + 24*log(x)/(x*log(3)*log(x)^ 2 + 9*x*log(3) - 6*(x*log(3) - 2*log(3))*log(x) - 36*log(3)) + 144*log(x)/ (x*log(x)^3 - 3*(3*x - 4)*log(x)^2 + 9*(3*x - 8)*log(x) - 27*x + 108) + 6* log(x)/(x*log(3)*log(x) - 3*x*log(3) + 12*log(3)) - 2*log(x)/(log(3)*log(x ) - 3*log(3)) - 12*log(x)/(log(x)^2 - 6*log(x) + 9) - 432/(x*log(x)^3 - 3* (3*x - 4)*log(x)^2 + 9*(3*x - 8)*log(x) - 27*x + 108) - 144/(x*log(x)^2 - 6*(x - 2)*log(x) + 9*x - 36) + 36/(log(x)^2 - 6*log(x) + 9) + 12/(log(x) - 3)))
\[ \int \frac {\left (-144 x+72 x^2-9 x^3\right ) \log (3)+\left (-24 x^2+6 x^3\right ) \log (3) \log (x)-x^3 \log (3) \log ^2(x)+e^{e^{\frac {\left (12 x-3 x^2\right ) \log (3)+\left (6-2 x+x^2 \log (3)\right ) \log (x)}{(12-3 x) \log (3)+x \log (3) \log (x)}}+\frac {\left (12 x-3 x^2\right ) \log (3)+\left (6-2 x+x^2 \log (3)\right ) \log (x)}{(12-3 x) \log (3)+x \log (3) \log (x)}} \left (72-42 x+6 x^2+\left (144 x-72 x^2+9 x^3\right ) \log (3)+\left (-6 x+\left (24 x^2-6 x^3\right ) \log (3)\right ) \log (x)+\left (-6 x+x^3 \log (3)\right ) \log ^2(x)\right )}{\left (144 x-72 x^2+9 x^3\right ) \log (3)+\left (24 x^2-6 x^3\right ) \log (3) \log (x)+x^3 \log (3) \log ^2(x)} \, dx=\int { -\frac {x^{3} \log \left (3\right ) \log \left (x\right )^{2} - 6 \, {\left (x^{3} - 4 \, x^{2}\right )} \log \left (3\right ) \log \left (x\right ) - {\left ({\left (x^{3} \log \left (3\right ) - 6 \, x\right )} \log \left (x\right )^{2} + 6 \, x^{2} + 9 \, {\left (x^{3} - 8 \, x^{2} + 16 \, x\right )} \log \left (3\right ) - 6 \, {\left ({\left (x^{3} - 4 \, x^{2}\right )} \log \left (3\right ) + x\right )} \log \left (x\right ) - 42 \, x + 72\right )} e^{\left (-\frac {3 \, {\left (x^{2} - 4 \, x\right )} \log \left (3\right ) - {\left (x^{2} \log \left (3\right ) - 2 \, x + 6\right )} \log \left (x\right )}{x \log \left (3\right ) \log \left (x\right ) - 3 \, {\left (x - 4\right )} \log \left (3\right )} + e^{\left (-\frac {3 \, {\left (x^{2} - 4 \, x\right )} \log \left (3\right ) - {\left (x^{2} \log \left (3\right ) - 2 \, x + 6\right )} \log \left (x\right )}{x \log \left (3\right ) \log \left (x\right ) - 3 \, {\left (x - 4\right )} \log \left (3\right )}\right )}\right )} + 9 \, {\left (x^{3} - 8 \, x^{2} + 16 \, x\right )} \log \left (3\right )}{x^{3} \log \left (3\right ) \log \left (x\right )^{2} - 6 \, {\left (x^{3} - 4 \, x^{2}\right )} \log \left (3\right ) \log \left (x\right ) + 9 \, {\left (x^{3} - 8 \, x^{2} + 16 \, x\right )} \log \left (3\right )} \,d x } \]
integrate((((x^3*log(3)-6*x)*log(x)^2+((-6*x^3+24*x^2)*log(3)-6*x)*log(x)+ (9*x^3-72*x^2+144*x)*log(3)+6*x^2-42*x+72)*exp(((x^2*log(3)+6-2*x)*log(x)+ (-3*x^2+12*x)*log(3))/(x*log(3)*log(x)+(-3*x+12)*log(3)))*exp(exp(((x^2*lo g(3)+6-2*x)*log(x)+(-3*x^2+12*x)*log(3))/(x*log(3)*log(x)+(-3*x+12)*log(3) )))-x^3*log(3)*log(x)^2+(6*x^3-24*x^2)*log(3)*log(x)+(-9*x^3+72*x^2-144*x) *log(3))/(x^3*log(3)*log(x)^2+(-6*x^3+24*x^2)*log(3)*log(x)+(9*x^3-72*x^2+ 144*x)*log(3)),x, algorithm=\
Time = 16.64 (sec) , antiderivative size = 130, normalized size of antiderivative = 3.71 \[ \int \frac {\left (-144 x+72 x^2-9 x^3\right ) \log (3)+\left (-24 x^2+6 x^3\right ) \log (3) \log (x)-x^3 \log (3) \log ^2(x)+e^{e^{\frac {\left (12 x-3 x^2\right ) \log (3)+\left (6-2 x+x^2 \log (3)\right ) \log (x)}{(12-3 x) \log (3)+x \log (3) \log (x)}}+\frac {\left (12 x-3 x^2\right ) \log (3)+\left (6-2 x+x^2 \log (3)\right ) \log (x)}{(12-3 x) \log (3)+x \log (3) \log (x)}} \left (72-42 x+6 x^2+\left (144 x-72 x^2+9 x^3\right ) \log (3)+\left (-6 x+\left (24 x^2-6 x^3\right ) \log (3)\right ) \log (x)+\left (-6 x+x^3 \log (3)\right ) \log ^2(x)\right )}{\left (144 x-72 x^2+9 x^3\right ) \log (3)+\left (24 x^2-6 x^3\right ) \log (3) \log (x)+x^3 \log (3) \log ^2(x)} \, dx={\mathrm {e}}^{{\mathrm {e}}^{-\frac {2\,x\,\ln \left (x\right )}{12\,\ln \left (3\right )-3\,x\,\ln \left (3\right )+x\,\ln \left (3\right )\,\ln \left (x\right )}}\,{\mathrm {e}}^{\frac {6\,\ln \left (x\right )}{12\,\ln \left (3\right )-3\,x\,\ln \left (3\right )+x\,\ln \left (3\right )\,\ln \left (x\right )}}\,{\mathrm {e}}^{\frac {12\,x\,\ln \left (3\right )}{12\,\ln \left (3\right )-3\,x\,\ln \left (3\right )+x\,\ln \left (3\right )\,\ln \left (x\right )}}\,{\mathrm {e}}^{\frac {x^2\,\ln \left (3\right )\,\ln \left (x\right )}{12\,\ln \left (3\right )-3\,x\,\ln \left (3\right )+x\,\ln \left (3\right )\,\ln \left (x\right )}}\,{\mathrm {e}}^{-\frac {3\,x^2\,\ln \left (3\right )}{12\,\ln \left (3\right )-3\,x\,\ln \left (3\right )+x\,\ln \left (3\right )\,\ln \left (x\right )}}}-x \]
int(-(log(3)*(144*x - 72*x^2 + 9*x^3) + log(3)*log(x)*(24*x^2 - 6*x^3) + x ^3*log(3)*log(x)^2 + exp(-(log(x)*(x^2*log(3) - 2*x + 6) + log(3)*(12*x - 3*x^2))/(log(3)*(3*x - 12) - x*log(3)*log(x)))*exp(exp(-(log(x)*(x^2*log(3 ) - 2*x + 6) + log(3)*(12*x - 3*x^2))/(log(3)*(3*x - 12) - x*log(3)*log(x) )))*(42*x + log(x)*(6*x - log(3)*(24*x^2 - 6*x^3)) - log(3)*(144*x - 72*x^ 2 + 9*x^3) + log(x)^2*(6*x - x^3*log(3)) - 6*x^2 - 72))/(log(3)*(144*x - 7 2*x^2 + 9*x^3) + log(3)*log(x)*(24*x^2 - 6*x^3) + x^3*log(3)*log(x)^2),x)
exp(exp(-(2*x*log(x))/(12*log(3) - 3*x*log(3) + x*log(3)*log(x)))*exp((6*l og(x))/(12*log(3) - 3*x*log(3) + x*log(3)*log(x)))*exp((12*x*log(3))/(12*l og(3) - 3*x*log(3) + x*log(3)*log(x)))*exp((x^2*log(3)*log(x))/(12*log(3) - 3*x*log(3) + x*log(3)*log(x)))*exp(-(3*x^2*log(3))/(12*log(3) - 3*x*log( 3) + x*log(3)*log(x)))) - x