Integrand size = 196, antiderivative size = 30 \[ \int \frac {e^{\frac {-23+12 x+\left (-18-21 x+9 x^2+3 x^3\right ) \log (3)+\left (-8+4 x+\left (-6-7 x+3 x^2+x^3\right ) \log (3)\right ) \log (x)}{-6+3 x+(-2+x) \log (x)}} \left (2-4 x+\left (180 x-108 x^2-27 x^3+18 x^4\right ) \log (3)+\left (-x+\left (120 x-72 x^2-18 x^3+12 x^4\right ) \log (3)\right ) \log (x)+\left (20 x-12 x^2-3 x^3+2 x^4\right ) \log (3) \log ^2(x)\right )}{36 x-36 x^2+9 x^3+\left (24 x-24 x^2+6 x^3\right ) \log (x)+\left (4 x-4 x^2+x^3\right ) \log ^2(x)} \, dx=e^{4+\left (3+5 x+x^2\right ) \log (3)-\frac {1}{(2-x) (3+\log (x))}} \] Output:
exp(4-1/(2-x)/(3+ln(x))+ln(3)*(x^2+5*x+3))
\[ \int \frac {e^{\frac {-23+12 x+\left (-18-21 x+9 x^2+3 x^3\right ) \log (3)+\left (-8+4 x+\left (-6-7 x+3 x^2+x^3\right ) \log (3)\right ) \log (x)}{-6+3 x+(-2+x) \log (x)}} \left (2-4 x+\left (180 x-108 x^2-27 x^3+18 x^4\right ) \log (3)+\left (-x+\left (120 x-72 x^2-18 x^3+12 x^4\right ) \log (3)\right ) \log (x)+\left (20 x-12 x^2-3 x^3+2 x^4\right ) \log (3) \log ^2(x)\right )}{36 x-36 x^2+9 x^3+\left (24 x-24 x^2+6 x^3\right ) \log (x)+\left (4 x-4 x^2+x^3\right ) \log ^2(x)} \, dx=\int \frac {e^{\frac {-23+12 x+\left (-18-21 x+9 x^2+3 x^3\right ) \log (3)+\left (-8+4 x+\left (-6-7 x+3 x^2+x^3\right ) \log (3)\right ) \log (x)}{-6+3 x+(-2+x) \log (x)}} \left (2-4 x+\left (180 x-108 x^2-27 x^3+18 x^4\right ) \log (3)+\left (-x+\left (120 x-72 x^2-18 x^3+12 x^4\right ) \log (3)\right ) \log (x)+\left (20 x-12 x^2-3 x^3+2 x^4\right ) \log (3) \log ^2(x)\right )}{36 x-36 x^2+9 x^3+\left (24 x-24 x^2+6 x^3\right ) \log (x)+\left (4 x-4 x^2+x^3\right ) \log ^2(x)} \, dx \] Input:
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)*L og[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]
Output:
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)*L og[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]
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.
| \(\displaystyle \int \frac {\left (\left (2 x^4-3 x^3-12 x^2+20 x\right ) \log (3) \log ^2(x)+\left (\left (12 x^4-18 x^3-72 x^2+120 x\right ) \log (3)-x\right ) \log (x)+\left (18 x^4-27 x^3-108 x^2+180 x\right ) \log (3)-4 x+2\right ) \exp \left (\frac {\left (\left (x^3+3 x^2-7 x-6\right ) \log (3)+4 x-8\right ) \log (x)+\left (3 x^3+9 x^2-21 x-18\right ) \log (3)+12 x-23}{3 x+(x-2) \log (x)-6}\right )}{9 x^3-36 x^2+\left (x^3-4 x^2+4 x\right ) \log ^2(x)+\left (6 x^3-24 x^2+24 x\right ) \log (x)+36 x} \, dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {\left (\left (2 x^4-3 x^3-12 x^2+20 x\right ) \log (3) \log ^2(x)+\left (\left (12 x^4-18 x^3-72 x^2+120 x\right ) \log (3)-x\right ) \log (x)+\left (18 x^4-27 x^3-108 x^2+180 x\right ) \log (3)-4 x+2\right ) \exp \left (\frac {\left (\left (x^3+3 x^2-7 x-6\right ) \log (3)+4 x-8\right ) \log (x)+\left (3 x^3+9 x^2-21 x-18\right ) \log (3)+12 x-23}{(x-2) (\log (x)+3)}\right )}{(2-x)^2 x (\log (x)+3)^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left ((2 x+5) \log (3) \exp \left (\frac {\left (\left (x^3+3 x^2-7 x-6\right ) \log (3)+4 x-8\right ) \log (x)+\left (3 x^3+9 x^2-21 x-18\right ) \log (3)+12 x-23}{(x-2) (\log (x)+3)}\right )-\frac {\exp \left (\frac {\left (\left (x^3+3 x^2-7 x-6\right ) \log (3)+4 x-8\right ) \log (x)+\left (3 x^3+9 x^2-21 x-18\right ) \log (3)+12 x-23}{(x-2) (\log (x)+3)}\right )}{(x-2)^2 (\log (x)+3)}-\frac {\exp \left (\frac {\left (\left (x^3+3 x^2-7 x-6\right ) \log (3)+4 x-8\right ) \log (x)+\left (3 x^3+9 x^2-21 x-18\right ) \log (3)+12 x-23}{(x-2) (\log (x)+3)}\right )}{(x-2) x (\log (x)+3)^2}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle 5 \log (3) \int \exp \left (\frac {12 x+\left (4 x+\left (x^3+3 x^2-7 x-6\right ) \log (3)-8\right ) \log (x)+\left (3 x^3+9 x^2-21 x-18\right ) \log (3)-23}{(x-2) (\log (x)+3)}\right )dx+2 \log (3) \int \exp \left (\frac {12 x+\left (4 x+\left (x^3+3 x^2-7 x-6\right ) \log (3)-8\right ) \log (x)+\left (3 x^3+9 x^2-21 x-18\right ) \log (3)-23}{(x-2) (\log (x)+3)}\right ) xdx-\frac {1}{2} \int \frac {\exp \left (\frac {12 x+\left (4 x+\left (x^3+3 x^2-7 x-6\right ) \log (3)-8\right ) \log (x)+\left (3 x^3+9 x^2-21 x-18\right ) \log (3)-23}{(x-2) (\log (x)+3)}\right )}{(x-2) (\log (x)+3)^2}dx+\frac {1}{2} \int \frac {\exp \left (\frac {12 x+\left (4 x+\left (x^3+3 x^2-7 x-6\right ) \log (3)-8\right ) \log (x)+\left (3 x^3+9 x^2-21 x-18\right ) \log (3)-23}{(x-2) (\log (x)+3)}\right )}{x (\log (x)+3)^2}dx-\int \frac {\exp \left (\frac {12 x+\left (4 x+\left (x^3+3 x^2-7 x-6\right ) \log (3)-8\right ) \log (x)+\left (3 x^3+9 x^2-21 x-18\right ) \log (3)-23}{(x-2) (\log (x)+3)}\right )}{(x-2)^2 (\log (x)+3)}dx\) |
Input:
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]
Output:
$Aborted
Leaf count of result is larger than twice the leaf count of optimal. \(64\) vs. \(2(29)=58\).
Time = 14.07 (sec) , antiderivative size = 65, normalized size of antiderivative = 2.17
| method | result | size |
| parallelrisch | \({\mathrm e}^{\frac {\left (\left (x^{3}+3 x^{2}-7 x -6\right ) \ln \left (3\right )+4 x -8\right ) \ln \left (x \right )+\left (3 x^{3}+9 x^{2}-21 x -18\right ) \ln \left (3\right )+12 x -23}{x \ln \left (x \right )-2 \ln \left (x \right )+3 x -6}}\) | \(65\) |
| risch | \({\mathrm e}^{\frac {\ln \left (3\right ) \ln \left (x \right ) x^{3}+3 x^{2} \ln \left (3\right ) \ln \left (x \right )+3 x^{3} \ln \left (3\right )-7 x \ln \left (3\right ) \ln \left (x \right )+9 x^{2} \ln \left (3\right )-6 \ln \left (x \right ) \ln \left (3\right )-21 x \ln \left (3\right )+4 x \ln \left (x \right )-18 \ln \left (3\right )-8 \ln \left (x \right )+12 x -23}{\left (-2+x \right ) \left (3+\ln \left (x \right )\right )}}\) | \(81\) |
Input:
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)/((-2+x)*l n(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)
Output:
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*ln(x)-2*ln(x)+3*x-6))
Leaf count of result is larger than twice the leaf count of optimal. 61 vs. \(2 (26) = 52\).
Time = 0.09 (sec) , antiderivative size = 61, normalized size of antiderivative = 2.03 \[ \int \frac {e^{\frac {-23+12 x+\left (-18-21 x+9 x^2+3 x^3\right ) \log (3)+\left (-8+4 x+\left (-6-7 x+3 x^2+x^3\right ) \log (3)\right ) \log (x)}{-6+3 x+(-2+x) \log (x)}} \left (2-4 x+\left (180 x-108 x^2-27 x^3+18 x^4\right ) \log (3)+\left (-x+\left (120 x-72 x^2-18 x^3+12 x^4\right ) \log (3)\right ) \log (x)+\left (20 x-12 x^2-3 x^3+2 x^4\right ) \log (3) \log ^2(x)\right )}{36 x-36 x^2+9 x^3+\left (24 x-24 x^2+6 x^3\right ) \log (x)+\left (4 x-4 x^2+x^3\right ) \log ^2(x)} \, dx=e^{\left (\frac {3 \, {\left (x^{3} + 3 \, x^{2} - 7 \, x - 6\right )} \log \left (3\right ) + {\left ({\left (x^{3} + 3 \, x^{2} - 7 \, x - 6\right )} \log \left (3\right ) + 4 \, x - 8\right )} \log \left (x\right ) + 12 \, x - 23}{{\left (x - 2\right )} \log \left (x\right ) + 3 \, x - 6}\right )} \] Input:
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)/((-2+x)*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, algorithm="fricas")
Output:
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))
Leaf count of result is larger than twice the leaf count of optimal. 61 vs. \(2 (24) = 48\).
Time = 0.71 (sec) , antiderivative size = 61, normalized size of antiderivative = 2.03 \[ \int \frac {e^{\frac {-23+12 x+\left (-18-21 x+9 x^2+3 x^3\right ) \log (3)+\left (-8+4 x+\left (-6-7 x+3 x^2+x^3\right ) \log (3)\right ) \log (x)}{-6+3 x+(-2+x) \log (x)}} \left (2-4 x+\left (180 x-108 x^2-27 x^3+18 x^4\right ) \log (3)+\left (-x+\left (120 x-72 x^2-18 x^3+12 x^4\right ) \log (3)\right ) \log (x)+\left (20 x-12 x^2-3 x^3+2 x^4\right ) \log (3) \log ^2(x)\right )}{36 x-36 x^2+9 x^3+\left (24 x-24 x^2+6 x^3\right ) \log (x)+\left (4 x-4 x^2+x^3\right ) \log ^2(x)} \, dx=e^{\frac {12 x + \left (4 x + \left (x^{3} + 3 x^{2} - 7 x - 6\right ) \log {\left (3 \right )} - 8\right ) \log {\left (x \right )} + \left (3 x^{3} + 9 x^{2} - 21 x - 18\right ) \log {\left (3 \right )} - 23}{3 x + \left (x - 2\right ) \log {\left (x \right )} - 6}} \] Input:
integrate(((2*x**4-3*x**3-12*x**2+20*x)*ln(3)*ln(x)**2+((12*x**4-18*x**3-7 2*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)/((-2+x)*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)
Output:
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))
Leaf count of result is larger than twice the leaf count of optimal. 106 vs. \(2 (26) = 52\).
Time = 0.61 (sec) , antiderivative size = 106, normalized size of antiderivative = 3.53 \[ \int \frac {e^{\frac {-23+12 x+\left (-18-21 x+9 x^2+3 x^3\right ) \log (3)+\left (-8+4 x+\left (-6-7 x+3 x^2+x^3\right ) \log (3)\right ) \log (x)}{-6+3 x+(-2+x) \log (x)}} \left (2-4 x+\left (180 x-108 x^2-27 x^3+18 x^4\right ) \log (3)+\left (-x+\left (120 x-72 x^2-18 x^3+12 x^4\right ) \log (3)\right ) \log (x)+\left (20 x-12 x^2-3 x^3+2 x^4\right ) \log (3) \log ^2(x)\right )}{36 x-36 x^2+9 x^3+\left (24 x-24 x^2+6 x^3\right ) \log (x)+\left (4 x-4 x^2+x^3\right ) \log ^2(x)} \, dx=e^{\left (\frac {x^{2} \log \left (3\right ) \log \left (x\right )}{\log \left (x\right ) + 3} + \frac {3 \, x^{2} \log \left (3\right )}{\log \left (x\right ) + 3} + \frac {5 \, x \log \left (3\right ) \log \left (x\right )}{\log \left (x\right ) + 3} + \frac {15 \, x \log \left (3\right )}{\log \left (x\right ) + 3} + \frac {3 \, \log \left (3\right ) \log \left (x\right )}{\log \left (x\right ) + 3} + \frac {9 \, \log \left (3\right )}{\log \left (x\right ) + 3} + \frac {4 \, \log \left (x\right )}{\log \left (x\right ) + 3} + \frac {1}{{\left (x - 2\right )} \log \left (x\right ) + 3 \, x - 6} + \frac {12}{\log \left (x\right ) + 3}\right )} \] Input:
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)/((-2+x)*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, algorithm="maxima")
Output:
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))
Leaf count of result is larger than twice the leaf count of optimal. 249 vs. \(2 (26) = 52\).
Time = 0.26 (sec) , antiderivative size = 249, normalized size of antiderivative = 8.30 \[ \int \frac {e^{\frac {-23+12 x+\left (-18-21 x+9 x^2+3 x^3\right ) \log (3)+\left (-8+4 x+\left (-6-7 x+3 x^2+x^3\right ) \log (3)\right ) \log (x)}{-6+3 x+(-2+x) \log (x)}} \left (2-4 x+\left (180 x-108 x^2-27 x^3+18 x^4\right ) \log (3)+\left (-x+\left (120 x-72 x^2-18 x^3+12 x^4\right ) \log (3)\right ) \log (x)+\left (20 x-12 x^2-3 x^3+2 x^4\right ) \log (3) \log ^2(x)\right )}{36 x-36 x^2+9 x^3+\left (24 x-24 x^2+6 x^3\right ) \log (x)+\left (4 x-4 x^2+x^3\right ) \log ^2(x)} \, dx=e^{\left (\frac {x^{3} \log \left (3\right ) \log \left (x\right )}{x \log \left (x\right ) + 3 \, x - 2 \, \log \left (x\right ) - 6} + \frac {3 \, x^{3} \log \left (3\right )}{x \log \left (x\right ) + 3 \, x - 2 \, \log \left (x\right ) - 6} + \frac {3 \, x^{2} \log \left (3\right ) \log \left (x\right )}{x \log \left (x\right ) + 3 \, x - 2 \, \log \left (x\right ) - 6} + \frac {9 \, x^{2} \log \left (3\right )}{x \log \left (x\right ) + 3 \, x - 2 \, \log \left (x\right ) - 6} - \frac {7 \, x \log \left (3\right ) \log \left (x\right )}{x \log \left (x\right ) + 3 \, x - 2 \, \log \left (x\right ) - 6} - \frac {21 \, x \log \left (3\right )}{x \log \left (x\right ) + 3 \, x - 2 \, \log \left (x\right ) - 6} + \frac {4 \, x \log \left (x\right )}{x \log \left (x\right ) + 3 \, x - 2 \, \log \left (x\right ) - 6} - \frac {6 \, \log \left (3\right ) \log \left (x\right )}{x \log \left (x\right ) + 3 \, x - 2 \, \log \left (x\right ) - 6} + \frac {12 \, x}{x \log \left (x\right ) + 3 \, x - 2 \, \log \left (x\right ) - 6} - \frac {18 \, \log \left (3\right )}{x \log \left (x\right ) + 3 \, x - 2 \, \log \left (x\right ) - 6} - \frac {8 \, \log \left (x\right )}{x \log \left (x\right ) + 3 \, x - 2 \, \log \left (x\right ) - 6} - \frac {23}{x \log \left (x\right ) + 3 \, x - 2 \, \log \left (x\right ) - 6}\right )} \] Input:
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)/((-2+x)*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, algorithm="giac")
Output:
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*log(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*log(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))
Time = 4.21 (sec) , antiderivative size = 81, normalized size of antiderivative = 2.70 \[ \int \frac {e^{\frac {-23+12 x+\left (-18-21 x+9 x^2+3 x^3\right ) \log (3)+\left (-8+4 x+\left (-6-7 x+3 x^2+x^3\right ) \log (3)\right ) \log (x)}{-6+3 x+(-2+x) \log (x)}} \left (2-4 x+\left (180 x-108 x^2-27 x^3+18 x^4\right ) \log (3)+\left (-x+\left (120 x-72 x^2-18 x^3+12 x^4\right ) \log (3)\right ) \log (x)+\left (20 x-12 x^2-3 x^3+2 x^4\right ) \log (3) \log ^2(x)\right )}{36 x-36 x^2+9 x^3+\left (24 x-24 x^2+6 x^3\right ) \log (x)+\left (4 x-4 x^2+x^3\right ) \log ^2(x)} \, dx={27}^{\frac {x^2+5\,x+3}{\ln \left (x\right )+3}}\,x^{\frac {\ln \left (3\right )\,x^2+5\,\ln \left (3\right )\,x+3\,\ln \left (3\right )+4}{\ln \left (x\right )+3}}\,{\mathrm {e}}^{\frac {12\,x}{3\,x-2\,\ln \left (x\right )+x\,\ln \left (x\right )-6}-\frac {23}{3\,x-2\,\ln \left (x\right )+x\,\ln \left (x\right )-6}} \] Input:
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 - 72* 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)
Output:
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))
\[ \int \frac {e^{\frac {-23+12 x+\left (-18-21 x+9 x^2+3 x^3\right ) \log (3)+\left (-8+4 x+\left (-6-7 x+3 x^2+x^3\right ) \log (3)\right ) \log (x)}{-6+3 x+(-2+x) \log (x)}} \left (2-4 x+\left (180 x-108 x^2-27 x^3+18 x^4\right ) \log (3)+\left (-x+\left (120 x-72 x^2-18 x^3+12 x^4\right ) \log (3)\right ) \log (x)+\left (20 x-12 x^2-3 x^3+2 x^4\right ) \log (3) \log ^2(x)\right )}{36 x-36 x^2+9 x^3+\left (24 x-24 x^2+6 x^3\right ) \log (x)+\left (4 x-4 x^2+x^3\right ) \log ^2(x)} \, dx=\int \frac {\left (\left (2 x^{4}-3 x^{3}-12 x^{2}+20 x \right ) \mathrm {log}\left (3\right ) \mathrm {log}\left (x \right )^{2}+\left (\left (12 x^{4}-18 x^{3}-72 x^{2}+120 x \right ) \mathrm {log}\left (3\right )-x \right ) \mathrm {log}\left (x \right )+\left (18 x^{4}-27 x^{3}-108 x^{2}+180 x \right ) \mathrm {log}\left (3\right )-4 x +2\right ) {\mathrm e}^{\frac {\left (\left (x^{3}+3 x^{2}-7 x -6\right ) \mathrm {log}\left (3\right )+4 x -8\right ) \mathrm {log}\left (x \right )+\left (3 x^{3}+9 x^{2}-21 x -18\right ) \mathrm {log}\left (3\right )+12 x -23}{\left (x -2\right ) \mathrm {log}\left (x \right )+3 x -6}}}{\left (x^{3}-4 x^{2}+4 x \right ) \mathrm {log}\left (x \right )^{2}+\left (6 x^{3}-24 x^{2}+24 x \right ) \mathrm {log}\left (x \right )+9 x^{3}-36 x^{2}+36 x}d x \] Input:
int(((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)/( (-2+x)*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)
Output:
int(((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)/( (-2+x)*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)