\(\int \frac {e^{\frac {3}{3+\log (\frac {9 x-6 x^2+x^3}{4-8 x+4 x^2})}} (18-36 x+6 x^2+(18-24 x+6 x^2) \log (\frac {9 x-6 x^2+x^3}{4-8 x+4 x^2})+(3-4 x+x^2) \log ^2(\frac {9 x-6 x^2+x^3}{4-8 x+4 x^2}))}{27-36 x+9 x^2+(18-24 x+6 x^2) \log (\frac {9 x-6 x^2+x^3}{4-8 x+4 x^2})+(3-4 x+x^2) \log ^2(\frac {9 x-6 x^2+x^3}{4-8 x+4 x^2})} \, dx\) [1726]

Optimal result

Integrand size = 205, antiderivative size = 34 \[ \int \frac {e^{\frac {3}{3+\log \left (\frac {9 x-6 x^2+x^3}{4-8 x+4 x^2}\right )}} \left (18-36 x+6 x^2+\left (18-24 x+6 x^2\right ) \log \left (\frac {9 x-6 x^2+x^3}{4-8 x+4 x^2}\right )+\left (3-4 x+x^2\right ) \log ^2\left (\frac {9 x-6 x^2+x^3}{4-8 x+4 x^2}\right )\right )}{27-36 x+9 x^2+\left (18-24 x+6 x^2\right ) \log \left (\frac {9 x-6 x^2+x^3}{4-8 x+4 x^2}\right )+\left (3-4 x+x^2\right ) \log ^2\left (\frac {9 x-6 x^2+x^3}{4-8 x+4 x^2}\right )} \, dx=e^{\frac {3}{3+\log \left (\frac {(3-x)^2 x^3}{4 \left (-x+x^2\right )^2}\right )}} x \] Output:

exp(3/(ln(1/4*x^3/(x^2-x)^2*(3-x)^2)+3))*x
 

Mathematica [A] (verified)

Time = 0.08 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.76 \[ \int \frac {e^{\frac {3}{3+\log \left (\frac {9 x-6 x^2+x^3}{4-8 x+4 x^2}\right )}} \left (18-36 x+6 x^2+\left (18-24 x+6 x^2\right ) \log \left (\frac {9 x-6 x^2+x^3}{4-8 x+4 x^2}\right )+\left (3-4 x+x^2\right ) \log ^2\left (\frac {9 x-6 x^2+x^3}{4-8 x+4 x^2}\right )\right )}{27-36 x+9 x^2+\left (18-24 x+6 x^2\right ) \log \left (\frac {9 x-6 x^2+x^3}{4-8 x+4 x^2}\right )+\left (3-4 x+x^2\right ) \log ^2\left (\frac {9 x-6 x^2+x^3}{4-8 x+4 x^2}\right )} \, dx=e^{\frac {3}{3+\log \left (\frac {(-3+x)^2 x}{4 (-1+x)^2}\right )}} x \] Input:

Integrate[(E^(3/(3 + Log[(9*x - 6*x^2 + x^3)/(4 - 8*x + 4*x^2)]))*(18 - 36 
*x + 6*x^2 + (18 - 24*x + 6*x^2)*Log[(9*x - 6*x^2 + x^3)/(4 - 8*x + 4*x^2) 
] + (3 - 4*x + x^2)*Log[(9*x - 6*x^2 + x^3)/(4 - 8*x + 4*x^2)]^2))/(27 - 3 
6*x + 9*x^2 + (18 - 24*x + 6*x^2)*Log[(9*x - 6*x^2 + x^3)/(4 - 8*x + 4*x^2 
)] + (3 - 4*x + x^2)*Log[(9*x - 6*x^2 + x^3)/(4 - 8*x + 4*x^2)]^2),x]
 

Output:

E^(3/(3 + Log[((-3 + x)^2*x)/(4*(-1 + x)^2)]))*x
 

Rubi [F]

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.

\(\displaystyle \int \frac {e^{\frac {3}{\log \left (\frac {x^3-6 x^2+9 x}{4 x^2-8 x+4}\right )+3}} \left (6 x^2+\left (x^2-4 x+3\right ) \log ^2\left (\frac {x^3-6 x^2+9 x}{4 x^2-8 x+4}\right )+\left (6 x^2-24 x+18\right ) \log \left (\frac {x^3-6 x^2+9 x}{4 x^2-8 x+4}\right )-36 x+18\right )}{9 x^2+\left (x^2-4 x+3\right ) \log ^2\left (\frac {x^3-6 x^2+9 x}{4 x^2-8 x+4}\right )+\left (6 x^2-24 x+18\right ) \log \left (\frac {x^3-6 x^2+9 x}{4 x^2-8 x+4}\right )-36 x+27} \, dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {e^{\frac {3}{\log \left (\frac {(x-3)^2 x}{4 (x-1)^2}\right )+3}} \left (6 \left (x^2-6 x+3\right )+\left (x^2-4 x+3\right ) \log ^2\left (\frac {(x-3)^2 x}{4 (x-1)^2}\right )+6 \left (x^2-4 x+3\right ) \log \left (\frac {(x-3)^2 x}{4 (x-1)^2}\right )\right )}{\left (x^2-4 x+3\right ) \left (\log \left (\frac {(x-3)^2 x}{4 (x-1)^2}\right )+3\right )^2}dx\)

\(\Big \downarrow \) 7279

\(\displaystyle \int \left (e^{\frac {3}{\log \left (\frac {(x-3)^2 x}{4 (x-1)^2}\right )+3}}-\frac {3 \left (x^2+3\right ) e^{\frac {3}{\log \left (\frac {(x-3)^2 x}{4 (x-1)^2}\right )+3}}}{(x-3) (x-1) \left (\log \left (\frac {(x-3)^2 x}{4 (x-1)^2}\right )+3\right )^2}\right )dx\)

\(\Big \downarrow \) 2009

\(\displaystyle \int e^{\frac {3}{\log \left (\frac {(x-3)^2 x}{4 (x-1)^2}\right )+3}}dx-3 \int \frac {e^{\frac {3}{\log \left (\frac {(x-3)^2 x}{4 (x-1)^2}\right )+3}}}{\left (\log \left (\frac {(x-3)^2 x}{4 (x-1)^2}\right )+3\right )^2}dx-18 \int \frac {e^{\frac {3}{\log \left (\frac {(x-3)^2 x}{4 (x-1)^2}\right )+3}}}{(x-3) \left (\log \left (\frac {(x-3)^2 x}{4 (x-1)^2}\right )+3\right )^2}dx+6 \int \frac {e^{\frac {3}{\log \left (\frac {(x-3)^2 x}{4 (x-1)^2}\right )+3}}}{(x-1) \left (\log \left (\frac {(x-3)^2 x}{4 (x-1)^2}\right )+3\right )^2}dx\)

Input:

Int[(E^(3/(3 + Log[(9*x - 6*x^2 + x^3)/(4 - 8*x + 4*x^2)]))*(18 - 36*x + 6 
*x^2 + (18 - 24*x + 6*x^2)*Log[(9*x - 6*x^2 + x^3)/(4 - 8*x + 4*x^2)] + (3 
 - 4*x + x^2)*Log[(9*x - 6*x^2 + x^3)/(4 - 8*x + 4*x^2)]^2))/(27 - 36*x + 
9*x^2 + (18 - 24*x + 6*x^2)*Log[(9*x - 6*x^2 + x^3)/(4 - 8*x + 4*x^2)] + ( 
3 - 4*x + x^2)*Log[(9*x - 6*x^2 + x^3)/(4 - 8*x + 4*x^2)]^2),x]
 

Output:

$Aborted
 

Maple [A] (verified)

Time = 25.24 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.06

method	result	size
risch	\(x \,{\mathrm e}^{\frac {3}{\ln \left (\frac {x^{3}-6 x^{2}+9 x}{4 x^{2}-8 x +4}\right )+3}}\)	\(36\)
norman	\(\frac {x \ln \left (\frac {x^{3}-6 x^{2}+9 x}{4 x^{2}-8 x +4}\right ) {\mathrm e}^{\frac {3}{\ln \left (\frac {x^{3}-6 x^{2}+9 x}{4 x^{2}-8 x +4}\right )+3}}+3 x \,{\mathrm e}^{\frac {3}{\ln \left (\frac {x^{3}-6 x^{2}+9 x}{4 x^{2}-8 x +4}\right )+3}}}{\ln \left (\frac {x^{3}-6 x^{2}+9 x}{4 x^{2}-8 x +4}\right )+3}\)	\(130\)

Input:

int(((x^2-4*x+3)*ln((x^3-6*x^2+9*x)/(4*x^2-8*x+4))^2+(6*x^2-24*x+18)*ln((x 
^3-6*x^2+9*x)/(4*x^2-8*x+4))+6*x^2-36*x+18)*exp(3/(ln((x^3-6*x^2+9*x)/(4*x 
^2-8*x+4))+3))/((x^2-4*x+3)*ln((x^3-6*x^2+9*x)/(4*x^2-8*x+4))^2+(6*x^2-24* 
x+18)*ln((x^3-6*x^2+9*x)/(4*x^2-8*x+4))+9*x^2-36*x+27),x,method=_RETURNVER 
BOSE)
 

Output:

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

Fricas [A] (verification not implemented)

Time = 0.10 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.00 \[ \int \frac {e^{\frac {3}{3+\log \left (\frac {9 x-6 x^2+x^3}{4-8 x+4 x^2}\right )}} \left (18-36 x+6 x^2+\left (18-24 x+6 x^2\right ) \log \left (\frac {9 x-6 x^2+x^3}{4-8 x+4 x^2}\right )+\left (3-4 x+x^2\right ) \log ^2\left (\frac {9 x-6 x^2+x^3}{4-8 x+4 x^2}\right )\right )}{27-36 x+9 x^2+\left (18-24 x+6 x^2\right ) \log \left (\frac {9 x-6 x^2+x^3}{4-8 x+4 x^2}\right )+\left (3-4 x+x^2\right ) \log ^2\left (\frac {9 x-6 x^2+x^3}{4-8 x+4 x^2}\right )} \, dx=x e^{\left (\frac {3}{\log \left (\frac {x^{3} - 6 \, x^{2} + 9 \, x}{4 \, {\left (x^{2} - 2 \, x + 1\right )}}\right ) + 3}\right )} \] Input:

integrate(((x^2-4*x+3)*log((x^3-6*x^2+9*x)/(4*x^2-8*x+4))^2+(6*x^2-24*x+18 
)*log((x^3-6*x^2+9*x)/(4*x^2-8*x+4))+6*x^2-36*x+18)*exp(3/(log((x^3-6*x^2+ 
9*x)/(4*x^2-8*x+4))+3))/((x^2-4*x+3)*log((x^3-6*x^2+9*x)/(4*x^2-8*x+4))^2+ 
(6*x^2-24*x+18)*log((x^3-6*x^2+9*x)/(4*x^2-8*x+4))+9*x^2-36*x+27),x, algor 
ithm="fricas")
 

Output:

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

Sympy [A] (verification not implemented)

Time = 8.53 (sec) , antiderivative size = 29, normalized size of antiderivative = 0.85 \[ \int \frac {e^{\frac {3}{3+\log \left (\frac {9 x-6 x^2+x^3}{4-8 x+4 x^2}\right )}} \left (18-36 x+6 x^2+\left (18-24 x+6 x^2\right ) \log \left (\frac {9 x-6 x^2+x^3}{4-8 x+4 x^2}\right )+\left (3-4 x+x^2\right ) \log ^2\left (\frac {9 x-6 x^2+x^3}{4-8 x+4 x^2}\right )\right )}{27-36 x+9 x^2+\left (18-24 x+6 x^2\right ) \log \left (\frac {9 x-6 x^2+x^3}{4-8 x+4 x^2}\right )+\left (3-4 x+x^2\right ) \log ^2\left (\frac {9 x-6 x^2+x^3}{4-8 x+4 x^2}\right )} \, dx=x e^{\frac {3}{\log {\left (\frac {x^{3} - 6 x^{2} + 9 x}{4 x^{2} - 8 x + 4} \right )} + 3}} \] Input:

integrate(((x**2-4*x+3)*ln((x**3-6*x**2+9*x)/(4*x**2-8*x+4))**2+(6*x**2-24 
*x+18)*ln((x**3-6*x**2+9*x)/(4*x**2-8*x+4))+6*x**2-36*x+18)*exp(3/(ln((x** 
3-6*x**2+9*x)/(4*x**2-8*x+4))+3))/((x**2-4*x+3)*ln((x**3-6*x**2+9*x)/(4*x* 
*2-8*x+4))**2+(6*x**2-24*x+18)*ln((x**3-6*x**2+9*x)/(4*x**2-8*x+4))+9*x**2 
-36*x+27),x)
 

Output:

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

Maxima [F]

\[ \int \frac {e^{\frac {3}{3+\log \left (\frac {9 x-6 x^2+x^3}{4-8 x+4 x^2}\right )}} \left (18-36 x+6 x^2+\left (18-24 x+6 x^2\right ) \log \left (\frac {9 x-6 x^2+x^3}{4-8 x+4 x^2}\right )+\left (3-4 x+x^2\right ) \log ^2\left (\frac {9 x-6 x^2+x^3}{4-8 x+4 x^2}\right )\right )}{27-36 x+9 x^2+\left (18-24 x+6 x^2\right ) \log \left (\frac {9 x-6 x^2+x^3}{4-8 x+4 x^2}\right )+\left (3-4 x+x^2\right ) \log ^2\left (\frac {9 x-6 x^2+x^3}{4-8 x+4 x^2}\right )} \, dx=\int { \frac {{\left ({\left (x^{2} - 4 \, x + 3\right )} \log \left (\frac {x^{3} - 6 \, x^{2} + 9 \, x}{4 \, {\left (x^{2} - 2 \, x + 1\right )}}\right )^{2} + 6 \, x^{2} + 6 \, {\left (x^{2} - 4 \, x + 3\right )} \log \left (\frac {x^{3} - 6 \, x^{2} + 9 \, x}{4 \, {\left (x^{2} - 2 \, x + 1\right )}}\right ) - 36 \, x + 18\right )} e^{\left (\frac {3}{\log \left (\frac {x^{3} - 6 \, x^{2} + 9 \, x}{4 \, {\left (x^{2} - 2 \, x + 1\right )}}\right ) + 3}\right )}}{{\left (x^{2} - 4 \, x + 3\right )} \log \left (\frac {x^{3} - 6 \, x^{2} + 9 \, x}{4 \, {\left (x^{2} - 2 \, x + 1\right )}}\right )^{2} + 9 \, x^{2} + 6 \, {\left (x^{2} - 4 \, x + 3\right )} \log \left (\frac {x^{3} - 6 \, x^{2} + 9 \, x}{4 \, {\left (x^{2} - 2 \, x + 1\right )}}\right ) - 36 \, x + 27} \,d x } \] Input:

integrate(((x^2-4*x+3)*log((x^3-6*x^2+9*x)/(4*x^2-8*x+4))^2+(6*x^2-24*x+18 
)*log((x^3-6*x^2+9*x)/(4*x^2-8*x+4))+6*x^2-36*x+18)*exp(3/(log((x^3-6*x^2+ 
9*x)/(4*x^2-8*x+4))+3))/((x^2-4*x+3)*log((x^3-6*x^2+9*x)/(4*x^2-8*x+4))^2+ 
(6*x^2-24*x+18)*log((x^3-6*x^2+9*x)/(4*x^2-8*x+4))+9*x^2-36*x+27),x, algor 
ithm="maxima")
 

Output:

-2*x^3*e^(-3/(2*log(2) + 2*log(x - 1) - 2*log(x - 3) - log(x) - 3))/(x^2 + 
 3) + 12*x^2*e^(-3/(2*log(2) + 2*log(x - 1) - 2*log(x - 3) - log(x) - 3))/ 
(x^2 + 3) - 6*x*e^(-3/(2*log(2) + 2*log(x - 1) - 2*log(x - 3) - log(x) - 3 
))/(x^2 + 3) + integrate((4*log(2)^2 + 4*(2*log(2) - 2*log(x - 3) - log(x) 
 - 3)*log(x - 1) + 4*log(x - 1)^2 - 4*(2*log(2) - log(x) - 3)*log(x - 3) + 
 4*log(x - 3)^2 - 2*(2*log(2) - 3)*log(x) + log(x)^2 - 12*log(2))*e^(-3/(2 
*log(2) + 2*log(x - 1) - 2*log(x - 3) - log(x) - 3))/(4*log(2)^2 + 4*(2*lo 
g(2) - 2*log(x - 3) - log(x) - 3)*log(x - 1) + 4*log(x - 1)^2 - 4*(2*log(2 
) - log(x) - 3)*log(x - 3) + 4*log(x - 3)^2 - 2*(2*log(2) - 3)*log(x) + lo 
g(x)^2 - 12*log(2) + 9), x)
 

Giac [F]

\[ \int \frac {e^{\frac {3}{3+\log \left (\frac {9 x-6 x^2+x^3}{4-8 x+4 x^2}\right )}} \left (18-36 x+6 x^2+\left (18-24 x+6 x^2\right ) \log \left (\frac {9 x-6 x^2+x^3}{4-8 x+4 x^2}\right )+\left (3-4 x+x^2\right ) \log ^2\left (\frac {9 x-6 x^2+x^3}{4-8 x+4 x^2}\right )\right )}{27-36 x+9 x^2+\left (18-24 x+6 x^2\right ) \log \left (\frac {9 x-6 x^2+x^3}{4-8 x+4 x^2}\right )+\left (3-4 x+x^2\right ) \log ^2\left (\frac {9 x-6 x^2+x^3}{4-8 x+4 x^2}\right )} \, dx=\int { \frac {{\left ({\left (x^{2} - 4 \, x + 3\right )} \log \left (\frac {x^{3} - 6 \, x^{2} + 9 \, x}{4 \, {\left (x^{2} - 2 \, x + 1\right )}}\right )^{2} + 6 \, x^{2} + 6 \, {\left (x^{2} - 4 \, x + 3\right )} \log \left (\frac {x^{3} - 6 \, x^{2} + 9 \, x}{4 \, {\left (x^{2} - 2 \, x + 1\right )}}\right ) - 36 \, x + 18\right )} e^{\left (\frac {3}{\log \left (\frac {x^{3} - 6 \, x^{2} + 9 \, x}{4 \, {\left (x^{2} - 2 \, x + 1\right )}}\right ) + 3}\right )}}{{\left (x^{2} - 4 \, x + 3\right )} \log \left (\frac {x^{3} - 6 \, x^{2} + 9 \, x}{4 \, {\left (x^{2} - 2 \, x + 1\right )}}\right )^{2} + 9 \, x^{2} + 6 \, {\left (x^{2} - 4 \, x + 3\right )} \log \left (\frac {x^{3} - 6 \, x^{2} + 9 \, x}{4 \, {\left (x^{2} - 2 \, x + 1\right )}}\right ) - 36 \, x + 27} \,d x } \] Input:

integrate(((x^2-4*x+3)*log((x^3-6*x^2+9*x)/(4*x^2-8*x+4))^2+(6*x^2-24*x+18 
)*log((x^3-6*x^2+9*x)/(4*x^2-8*x+4))+6*x^2-36*x+18)*exp(3/(log((x^3-6*x^2+ 
9*x)/(4*x^2-8*x+4))+3))/((x^2-4*x+3)*log((x^3-6*x^2+9*x)/(4*x^2-8*x+4))^2+ 
(6*x^2-24*x+18)*log((x^3-6*x^2+9*x)/(4*x^2-8*x+4))+9*x^2-36*x+27),x, algor 
ithm="giac")
 

Output:

integrate(((x^2 - 4*x + 3)*log(1/4*(x^3 - 6*x^2 + 9*x)/(x^2 - 2*x + 1))^2 
+ 6*x^2 + 6*(x^2 - 4*x + 3)*log(1/4*(x^3 - 6*x^2 + 9*x)/(x^2 - 2*x + 1)) - 
 36*x + 18)*e^(3/(log(1/4*(x^3 - 6*x^2 + 9*x)/(x^2 - 2*x + 1)) + 3))/((x^2 
 - 4*x + 3)*log(1/4*(x^3 - 6*x^2 + 9*x)/(x^2 - 2*x + 1))^2 + 9*x^2 + 6*(x^ 
2 - 4*x + 3)*log(1/4*(x^3 - 6*x^2 + 9*x)/(x^2 - 2*x + 1)) - 36*x + 27), x)
 

Mupad [F(-1)]

Timed out. \[ \int \frac {e^{\frac {3}{3+\log \left (\frac {9 x-6 x^2+x^3}{4-8 x+4 x^2}\right )}} \left (18-36 x+6 x^2+\left (18-24 x+6 x^2\right ) \log \left (\frac {9 x-6 x^2+x^3}{4-8 x+4 x^2}\right )+\left (3-4 x+x^2\right ) \log ^2\left (\frac {9 x-6 x^2+x^3}{4-8 x+4 x^2}\right )\right )}{27-36 x+9 x^2+\left (18-24 x+6 x^2\right ) \log \left (\frac {9 x-6 x^2+x^3}{4-8 x+4 x^2}\right )+\left (3-4 x+x^2\right ) \log ^2\left (\frac {9 x-6 x^2+x^3}{4-8 x+4 x^2}\right )} \, dx=\int \frac {{\mathrm {e}}^{\frac {3}{\ln \left (\frac {x^3-6\,x^2+9\,x}{4\,x^2-8\,x+4}\right )+3}}\,\left (\ln \left (\frac {x^3-6\,x^2+9\,x}{4\,x^2-8\,x+4}\right )\,\left (6\,x^2-24\,x+18\right )-36\,x+{\ln \left (\frac {x^3-6\,x^2+9\,x}{4\,x^2-8\,x+4}\right )}^2\,\left (x^2-4\,x+3\right )+6\,x^2+18\right )}{\ln \left (\frac {x^3-6\,x^2+9\,x}{4\,x^2-8\,x+4}\right )\,\left (6\,x^2-24\,x+18\right )-36\,x+{\ln \left (\frac {x^3-6\,x^2+9\,x}{4\,x^2-8\,x+4}\right )}^2\,\left (x^2-4\,x+3\right )+9\,x^2+27} \,d x \] Input:

int((exp(3/(log((9*x - 6*x^2 + x^3)/(4*x^2 - 8*x + 4)) + 3))*(log((9*x - 6 
*x^2 + x^3)/(4*x^2 - 8*x + 4))*(6*x^2 - 24*x + 18) - 36*x + log((9*x - 6*x 
^2 + x^3)/(4*x^2 - 8*x + 4))^2*(x^2 - 4*x + 3) + 6*x^2 + 18))/(log((9*x - 
6*x^2 + x^3)/(4*x^2 - 8*x + 4))*(6*x^2 - 24*x + 18) - 36*x + log((9*x - 6* 
x^2 + x^3)/(4*x^2 - 8*x + 4))^2*(x^2 - 4*x + 3) + 9*x^2 + 27),x)
 

Output:

int((exp(3/(log((9*x - 6*x^2 + x^3)/(4*x^2 - 8*x + 4)) + 3))*(log((9*x - 6 
*x^2 + x^3)/(4*x^2 - 8*x + 4))*(6*x^2 - 24*x + 18) - 36*x + log((9*x - 6*x 
^2 + x^3)/(4*x^2 - 8*x + 4))^2*(x^2 - 4*x + 3) + 6*x^2 + 18))/(log((9*x - 
6*x^2 + x^3)/(4*x^2 - 8*x + 4))*(6*x^2 - 24*x + 18) - 36*x + log((9*x - 6* 
x^2 + x^3)/(4*x^2 - 8*x + 4))^2*(x^2 - 4*x + 3) + 9*x^2 + 27), x)
 

Reduce [B] (verification not implemented)

Time = 0.21 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.06 \[ \int \frac {e^{\frac {3}{3+\log \left (\frac {9 x-6 x^2+x^3}{4-8 x+4 x^2}\right )}} \left (18-36 x+6 x^2+\left (18-24 x+6 x^2\right ) \log \left (\frac {9 x-6 x^2+x^3}{4-8 x+4 x^2}\right )+\left (3-4 x+x^2\right ) \log ^2\left (\frac {9 x-6 x^2+x^3}{4-8 x+4 x^2}\right )\right )}{27-36 x+9 x^2+\left (18-24 x+6 x^2\right ) \log \left (\frac {9 x-6 x^2+x^3}{4-8 x+4 x^2}\right )+\left (3-4 x+x^2\right ) \log ^2\left (\frac {9 x-6 x^2+x^3}{4-8 x+4 x^2}\right )} \, dx=e^{\frac {3}{\mathrm {log}\left (\frac {x^{3}-6 x^{2}+9 x}{4 x^{2}-8 x +4}\right )+3}} x \] Input:

int(((x^2-4*x+3)*log((x^3-6*x^2+9*x)/(4*x^2-8*x+4))^2+(6*x^2-24*x+18)*log( 
(x^3-6*x^2+9*x)/(4*x^2-8*x+4))+6*x^2-36*x+18)*exp(3/(log((x^3-6*x^2+9*x)/( 
4*x^2-8*x+4))+3))/((x^2-4*x+3)*log((x^3-6*x^2+9*x)/(4*x^2-8*x+4))^2+(6*x^2 
-24*x+18)*log((x^3-6*x^2+9*x)/(4*x^2-8*x+4))+9*x^2-36*x+27),x)
 

Output:

e**(3/(log((x**3 - 6*x**2 + 9*x)/(4*x**2 - 8*x + 4)) + 3))*x