Integrand size = 210, antiderivative size = 25 \[ \int \frac {-10+8 x+12 e^x x+12 x^2+\left (\frac {-5+4 x+6 e^x x+6 x^2}{x}\right )^x \left (-5-x+6 x^2-6 x^3+e^x \left (6 x-6 x^3\right )+\left (5 x-4 x^2-6 e^x x^2-6 x^3\right ) \log \left (\frac {-5+4 x+6 e^x x+6 x^2}{x}\right )\right )}{-60+48 x+72 e^x x+72 x^2+\left (\frac {-5+4 x+6 e^x x+6 x^2}{x}\right )^{2 x} \left (-15+12 x+18 e^x x+18 x^2\right )+\left (\frac {-5+4 x+6 e^x x+6 x^2}{x}\right )^x \left (-60+48 x+72 e^x x+72 x^2\right )} \, dx=\frac {x}{3 \left (2+\left (4-\frac {5}{x}+6 \left (e^x+x\right )\right )^x\right )} \] Output:
x/(3*exp(x*ln(4-5/x+6*exp(x)+6*x))+6)
Time = 0.14 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.04 \[ \int \frac {-10+8 x+12 e^x x+12 x^2+\left (\frac {-5+4 x+6 e^x x+6 x^2}{x}\right )^x \left (-5-x+6 x^2-6 x^3+e^x \left (6 x-6 x^3\right )+\left (5 x-4 x^2-6 e^x x^2-6 x^3\right ) \log \left (\frac {-5+4 x+6 e^x x+6 x^2}{x}\right )\right )}{-60+48 x+72 e^x x+72 x^2+\left (\frac {-5+4 x+6 e^x x+6 x^2}{x}\right )^{2 x} \left (-15+12 x+18 e^x x+18 x^2\right )+\left (\frac {-5+4 x+6 e^x x+6 x^2}{x}\right )^x \left (-60+48 x+72 e^x x+72 x^2\right )} \, dx=\frac {x}{3 \left (2+\left (4+6 e^x-\frac {5}{x}+6 x\right )^x\right )} \] Input:
Integrate[(-10 + 8*x + 12*E^x*x + 12*x^2 + ((-5 + 4*x + 6*E^x*x + 6*x^2)/x )^x*(-5 - x + 6*x^2 - 6*x^3 + E^x*(6*x - 6*x^3) + (5*x - 4*x^2 - 6*E^x*x^2 - 6*x^3)*Log[(-5 + 4*x + 6*E^x*x + 6*x^2)/x]))/(-60 + 48*x + 72*E^x*x + 7 2*x^2 + ((-5 + 4*x + 6*E^x*x + 6*x^2)/x)^(2*x)*(-15 + 12*x + 18*E^x*x + 18 *x^2) + ((-5 + 4*x + 6*E^x*x + 6*x^2)/x)^x*(-60 + 48*x + 72*E^x*x + 72*x^2 )),x]
Output:
x/(3*(2 + (4 + 6*E^x - 5/x + 6*x)^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.
| \(\displaystyle \int \frac {12 x^2+\left (\frac {6 x^2+6 e^x x+4 x-5}{x}\right )^x \left (-6 x^3+e^x \left (6 x-6 x^3\right )+6 x^2+\left (-6 x^3-6 e^x x^2-4 x^2+5 x\right ) \log \left (\frac {6 x^2+6 e^x x+4 x-5}{x}\right )-x-5\right )+12 e^x x+8 x-10}{\left (72 x^2+72 e^x x+48 x-60\right ) \left (\frac {6 x^2+6 e^x x+4 x-5}{x}\right )^x+\left (18 x^2+18 e^x x+12 x-15\right ) \left (\frac {6 x^2+6 e^x x+4 x-5}{x}\right )^{2 x}+72 x^2+72 e^x x+48 x-60} \, dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {-12 x^2-\left (\left (\frac {6 x^2+6 e^x x+4 x-5}{x}\right )^x \left (-6 x^3+e^x \left (6 x-6 x^3\right )+6 x^2+\left (-6 x^3-6 e^x x^2-4 x^2+5 x\right ) \log \left (\frac {6 x^2+6 e^x x+4 x-5}{x}\right )-x-5\right )\right )-12 e^x x-8 x+10}{3 \left (-6 x^2-6 e^x x-4 x+5\right ) \left (\left (6 x+6 e^x-\frac {5}{x}+4\right )^x+2\right )^2}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {1}{3} \int \frac {\left (6 x^3-6 x^2+x-6 e^x \left (x-x^3\right )-\left (-6 x^3-6 e^x x^2-4 x^2+5 x\right ) \log \left (-\frac {-6 x^2-6 e^x x-4 x+5}{x}\right )+5\right ) \left (-\frac {-6 x^2-6 e^x x-4 x+5}{x}\right )^x-12 x^2-12 e^x x-8 x+10}{\left (-6 x^2-6 e^x x-4 x+5\right ) \left (\left (6 x+6 e^x+4-\frac {5}{x}\right )^x+2\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {1}{3} \int \left (-\frac {\left (6 e^x x^3+6 \log \left (6 x+6 e^x+4-\frac {5}{x}\right ) x^3+6 x^3+6 e^x \log \left (6 x+6 e^x+4-\frac {5}{x}\right ) x^2+4 \log \left (6 x+6 e^x+4-\frac {5}{x}\right ) x^2-6 x^2-6 e^x x-5 \log \left (6 x+6 e^x+4-\frac {5}{x}\right ) x+x+5\right ) \left (6 x+6 e^x+4-\frac {5}{x}\right )^x}{\left (6 x^2+6 e^x x+4 x-5\right ) \left (\left (6 x+6 e^x+4-\frac {5}{x}\right )^x+2\right )^2}+\frac {12 x^2}{\left (6 x^2+6 e^x x+4 x-5\right ) \left (\left (6 x+6 e^x+4-\frac {5}{x}\right )^x+2\right )^2}+\frac {12 e^x x}{\left (6 x^2+6 e^x x+4 x-5\right ) \left (\left (6 x+6 e^x+4-\frac {5}{x}\right )^x+2\right )^2}+\frac {8 x}{\left (6 x^2+6 e^x x+4 x-5\right ) \left (\left (6 x+6 e^x+4-\frac {5}{x}\right )^x+2\right )^2}-\frac {10}{\left (6 x^2+6 e^x x+4 x-5\right ) \left (\left (6 x+6 e^x+4-\frac {5}{x}\right )^x+2\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7299 |
| \(\displaystyle \frac {1}{3} \int \left (-\frac {\left (6 e^x x^3+6 \log \left (6 x+6 e^x+4-\frac {5}{x}\right ) x^3+6 x^3+6 e^x \log \left (6 x+6 e^x+4-\frac {5}{x}\right ) x^2+4 \log \left (6 x+6 e^x+4-\frac {5}{x}\right ) x^2-6 x^2-6 e^x x-5 \log \left (6 x+6 e^x+4-\frac {5}{x}\right ) x+x+5\right ) \left (6 x+6 e^x+4-\frac {5}{x}\right )^x}{\left (6 x^2+6 e^x x+4 x-5\right ) \left (\left (6 x+6 e^x+4-\frac {5}{x}\right )^x+2\right )^2}+\frac {12 x^2}{\left (6 x^2+6 e^x x+4 x-5\right ) \left (\left (6 x+6 e^x+4-\frac {5}{x}\right )^x+2\right )^2}+\frac {12 e^x x}{\left (6 x^2+6 e^x x+4 x-5\right ) \left (\left (6 x+6 e^x+4-\frac {5}{x}\right )^x+2\right )^2}+\frac {8 x}{\left (6 x^2+6 e^x x+4 x-5\right ) \left (\left (6 x+6 e^x+4-\frac {5}{x}\right )^x+2\right )^2}-\frac {10}{\left (6 x^2+6 e^x x+4 x-5\right ) \left (\left (6 x+6 e^x+4-\frac {5}{x}\right )^x+2\right )^2}\right )dx\) |
Input:
Int[(-10 + 8*x + 12*E^x*x + 12*x^2 + ((-5 + 4*x + 6*E^x*x + 6*x^2)/x)^x*(- 5 - x + 6*x^2 - 6*x^3 + E^x*(6*x - 6*x^3) + (5*x - 4*x^2 - 6*E^x*x^2 - 6*x ^3)*Log[(-5 + 4*x + 6*E^x*x + 6*x^2)/x]))/(-60 + 48*x + 72*E^x*x + 72*x^2 + ((-5 + 4*x + 6*E^x*x + 6*x^2)/x)^(2*x)*(-15 + 12*x + 18*E^x*x + 18*x^2) + ((-5 + 4*x + 6*E^x*x + 6*x^2)/x)^x*(-60 + 48*x + 72*E^x*x + 72*x^2)),x]
Output:
$Aborted
Time = 14.84 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.24
| method | result | size |
| parallelrisch | \(\frac {x}{3 \,{\mathrm e}^{x \ln \left (\frac {6 \,{\mathrm e}^{x} x +6 x^{2}+4 x -5}{x}\right )}+6}\) | \(31\) |
| risch | \(\frac {x}{3 x^{-x} 3^{x} 2^{x} \left (-\frac {5}{6}+x^{2}+\left ({\mathrm e}^{x}+\frac {2}{3}\right ) x \right )^{x} {\mathrm e}^{-\frac {i \pi \,\operatorname {csgn}\left (\frac {i \left (-\frac {5}{6}+x^{2}+\left ({\mathrm e}^{x}+\frac {2}{3}\right ) x \right )}{x}\right ) x \left (-\operatorname {csgn}\left (\frac {i \left (-\frac {5}{6}+x^{2}+\left ({\mathrm e}^{x}+\frac {2}{3}\right ) x \right )}{x}\right )+\operatorname {csgn}\left (i \left (-\frac {5}{6}+x^{2}+\left ({\mathrm e}^{x}+\frac {2}{3}\right ) x \right )\right )\right ) \left (-\operatorname {csgn}\left (\frac {i \left (-\frac {5}{6}+x^{2}+\left ({\mathrm e}^{x}+\frac {2}{3}\right ) x \right )}{x}\right )+\operatorname {csgn}\left (\frac {i}{x}\right )\right )}{2}}+6}\) | \(121\) |
Input:
int((((-6*exp(x)*x^2-6*x^3-4*x^2+5*x)*ln((6*exp(x)*x+6*x^2+4*x-5)/x)+(-6*x ^3+6*x)*exp(x)-6*x^3+6*x^2-x-5)*exp(x*ln((6*exp(x)*x+6*x^2+4*x-5)/x))+12*e xp(x)*x+12*x^2+8*x-10)/((18*exp(x)*x+18*x^2+12*x-15)*exp(x*ln((6*exp(x)*x+ 6*x^2+4*x-5)/x))^2+(72*exp(x)*x+72*x^2+48*x-60)*exp(x*ln((6*exp(x)*x+6*x^2 +4*x-5)/x))+72*exp(x)*x+72*x^2+48*x-60),x,method=_RETURNVERBOSE)
Output:
1/3*x/(exp(x*ln((6*exp(x)*x+6*x^2+4*x-5)/x))+2)
Time = 0.09 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.12 \[ \int \frac {-10+8 x+12 e^x x+12 x^2+\left (\frac {-5+4 x+6 e^x x+6 x^2}{x}\right )^x \left (-5-x+6 x^2-6 x^3+e^x \left (6 x-6 x^3\right )+\left (5 x-4 x^2-6 e^x x^2-6 x^3\right ) \log \left (\frac {-5+4 x+6 e^x x+6 x^2}{x}\right )\right )}{-60+48 x+72 e^x x+72 x^2+\left (\frac {-5+4 x+6 e^x x+6 x^2}{x}\right )^{2 x} \left (-15+12 x+18 e^x x+18 x^2\right )+\left (\frac {-5+4 x+6 e^x x+6 x^2}{x}\right )^x \left (-60+48 x+72 e^x x+72 x^2\right )} \, dx=\frac {x}{3 \, {\left (\left (\frac {6 \, x^{2} + 6 \, x e^{x} + 4 \, x - 5}{x}\right )^{x} + 2\right )}} \] Input:
integrate((((-6*exp(x)*x^2-6*x^3-4*x^2+5*x)*log((6*exp(x)*x+6*x^2+4*x-5)/x )+(-6*x^3+6*x)*exp(x)-6*x^3+6*x^2-x-5)*exp(x*log((6*exp(x)*x+6*x^2+4*x-5)/ x))+12*exp(x)*x+12*x^2+8*x-10)/((18*exp(x)*x+18*x^2+12*x-15)*exp(x*log((6* exp(x)*x+6*x^2+4*x-5)/x))^2+(72*exp(x)*x+72*x^2+48*x-60)*exp(x*log((6*exp( x)*x+6*x^2+4*x-5)/x))+72*exp(x)*x+72*x^2+48*x-60),x, algorithm="fricas")
Output:
1/3*x/(((6*x^2 + 6*x*e^x + 4*x - 5)/x)^x + 2)
Timed out. \[ \int \frac {-10+8 x+12 e^x x+12 x^2+\left (\frac {-5+4 x+6 e^x x+6 x^2}{x}\right )^x \left (-5-x+6 x^2-6 x^3+e^x \left (6 x-6 x^3\right )+\left (5 x-4 x^2-6 e^x x^2-6 x^3\right ) \log \left (\frac {-5+4 x+6 e^x x+6 x^2}{x}\right )\right )}{-60+48 x+72 e^x x+72 x^2+\left (\frac {-5+4 x+6 e^x x+6 x^2}{x}\right )^{2 x} \left (-15+12 x+18 e^x x+18 x^2\right )+\left (\frac {-5+4 x+6 e^x x+6 x^2}{x}\right )^x \left (-60+48 x+72 e^x x+72 x^2\right )} \, dx=\text {Timed out} \] Input:
integrate((((-6*exp(x)*x**2-6*x**3-4*x**2+5*x)*ln((6*exp(x)*x+6*x**2+4*x-5 )/x)+(-6*x**3+6*x)*exp(x)-6*x**3+6*x**2-x-5)*exp(x*ln((6*exp(x)*x+6*x**2+4 *x-5)/x))+12*exp(x)*x+12*x**2+8*x-10)/((18*exp(x)*x+18*x**2+12*x-15)*exp(x *ln((6*exp(x)*x+6*x**2+4*x-5)/x))**2+(72*exp(x)*x+72*x**2+48*x-60)*exp(x*l n((6*exp(x)*x+6*x**2+4*x-5)/x))+72*exp(x)*x+72*x**2+48*x-60),x)
Output:
Timed out
Time = 0.19 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.24 \[ \int \frac {-10+8 x+12 e^x x+12 x^2+\left (\frac {-5+4 x+6 e^x x+6 x^2}{x}\right )^x \left (-5-x+6 x^2-6 x^3+e^x \left (6 x-6 x^3\right )+\left (5 x-4 x^2-6 e^x x^2-6 x^3\right ) \log \left (\frac {-5+4 x+6 e^x x+6 x^2}{x}\right )\right )}{-60+48 x+72 e^x x+72 x^2+\left (\frac {-5+4 x+6 e^x x+6 x^2}{x}\right )^{2 x} \left (-15+12 x+18 e^x x+18 x^2\right )+\left (\frac {-5+4 x+6 e^x x+6 x^2}{x}\right )^x \left (-60+48 x+72 e^x x+72 x^2\right )} \, dx=\frac {x x^{x}}{3 \, {\left ({\left (6 \, x^{2} + 6 \, x e^{x} + 4 \, x - 5\right )}^{x} + 2 \, x^{x}\right )}} \] Input:
integrate((((-6*exp(x)*x^2-6*x^3-4*x^2+5*x)*log((6*exp(x)*x+6*x^2+4*x-5)/x )+(-6*x^3+6*x)*exp(x)-6*x^3+6*x^2-x-5)*exp(x*log((6*exp(x)*x+6*x^2+4*x-5)/ x))+12*exp(x)*x+12*x^2+8*x-10)/((18*exp(x)*x+18*x^2+12*x-15)*exp(x*log((6* exp(x)*x+6*x^2+4*x-5)/x))^2+(72*exp(x)*x+72*x^2+48*x-60)*exp(x*log((6*exp( x)*x+6*x^2+4*x-5)/x))+72*exp(x)*x+72*x^2+48*x-60),x, algorithm="maxima")
Output:
1/3*x*x^x/((6*x^2 + 6*x*e^x + 4*x - 5)^x + 2*x^x)
\[ \int \frac {-10+8 x+12 e^x x+12 x^2+\left (\frac {-5+4 x+6 e^x x+6 x^2}{x}\right )^x \left (-5-x+6 x^2-6 x^3+e^x \left (6 x-6 x^3\right )+\left (5 x-4 x^2-6 e^x x^2-6 x^3\right ) \log \left (\frac {-5+4 x+6 e^x x+6 x^2}{x}\right )\right )}{-60+48 x+72 e^x x+72 x^2+\left (\frac {-5+4 x+6 e^x x+6 x^2}{x}\right )^{2 x} \left (-15+12 x+18 e^x x+18 x^2\right )+\left (\frac {-5+4 x+6 e^x x+6 x^2}{x}\right )^x \left (-60+48 x+72 e^x x+72 x^2\right )} \, dx=\int { \frac {12 \, x^{2} - {\left (6 \, x^{3} - 6 \, x^{2} + 6 \, {\left (x^{3} - x\right )} e^{x} + {\left (6 \, x^{3} + 6 \, x^{2} e^{x} + 4 \, x^{2} - 5 \, x\right )} \log \left (\frac {6 \, x^{2} + 6 \, x e^{x} + 4 \, x - 5}{x}\right ) + x + 5\right )} \left (\frac {6 \, x^{2} + 6 \, x e^{x} + 4 \, x - 5}{x}\right )^{x} + 12 \, x e^{x} + 8 \, x - 10}{3 \, {\left (24 \, x^{2} + {\left (6 \, x^{2} + 6 \, x e^{x} + 4 \, x - 5\right )} \left (\frac {6 \, x^{2} + 6 \, x e^{x} + 4 \, x - 5}{x}\right )^{2 \, x} + 4 \, {\left (6 \, x^{2} + 6 \, x e^{x} + 4 \, x - 5\right )} \left (\frac {6 \, x^{2} + 6 \, x e^{x} + 4 \, x - 5}{x}\right )^{x} + 24 \, x e^{x} + 16 \, x - 20\right )}} \,d x } \] Input:
integrate((((-6*exp(x)*x^2-6*x^3-4*x^2+5*x)*log((6*exp(x)*x+6*x^2+4*x-5)/x )+(-6*x^3+6*x)*exp(x)-6*x^3+6*x^2-x-5)*exp(x*log((6*exp(x)*x+6*x^2+4*x-5)/ x))+12*exp(x)*x+12*x^2+8*x-10)/((18*exp(x)*x+18*x^2+12*x-15)*exp(x*log((6* exp(x)*x+6*x^2+4*x-5)/x))^2+(72*exp(x)*x+72*x^2+48*x-60)*exp(x*log((6*exp( x)*x+6*x^2+4*x-5)/x))+72*exp(x)*x+72*x^2+48*x-60),x, algorithm="giac")
Output:
integrate(1/3*(12*x^2 - (6*x^3 - 6*x^2 + 6*(x^3 - x)*e^x + (6*x^3 + 6*x^2* e^x + 4*x^2 - 5*x)*log((6*x^2 + 6*x*e^x + 4*x - 5)/x) + x + 5)*((6*x^2 + 6 *x*e^x + 4*x - 5)/x)^x + 12*x*e^x + 8*x - 10)/(24*x^2 + (6*x^2 + 6*x*e^x + 4*x - 5)*((6*x^2 + 6*x*e^x + 4*x - 5)/x)^(2*x) + 4*(6*x^2 + 6*x*e^x + 4*x - 5)*((6*x^2 + 6*x*e^x + 4*x - 5)/x)^x + 24*x*e^x + 16*x - 20), x)
Time = 3.39 (sec) , antiderivative size = 254, normalized size of antiderivative = 10.16 \[ \int \frac {-10+8 x+12 e^x x+12 x^2+\left (\frac {-5+4 x+6 e^x x+6 x^2}{x}\right )^x \left (-5-x+6 x^2-6 x^3+e^x \left (6 x-6 x^3\right )+\left (5 x-4 x^2-6 e^x x^2-6 x^3\right ) \log \left (\frac {-5+4 x+6 e^x x+6 x^2}{x}\right )\right )}{-60+48 x+72 e^x x+72 x^2+\left (\frac {-5+4 x+6 e^x x+6 x^2}{x}\right )^{2 x} \left (-15+12 x+18 e^x x+18 x^2\right )+\left (\frac {-5+4 x+6 e^x x+6 x^2}{x}\right )^x \left (-60+48 x+72 e^x x+72 x^2\right )} \, dx=\frac {5\,x+6\,x^3\,{\mathrm {e}}^x-5\,x\,\ln \left (\frac {4\,x+6\,x\,{\mathrm {e}}^x+6\,x^2-5}{x}\right )+6\,x^3+4\,x^2\,\ln \left (\frac {4\,x+6\,x\,{\mathrm {e}}^x+6\,x^2-5}{x}\right )+6\,x^3\,\ln \left (\frac {4\,x+6\,x\,{\mathrm {e}}^x+6\,x^2-5}{x}\right )+6\,x^2\,{\mathrm {e}}^x\,\ln \left (\frac {4\,x+6\,x\,{\mathrm {e}}^x+6\,x^2-5}{x}\right )}{3\,\left ({\left (\frac {4\,x+6\,x\,{\mathrm {e}}^x+6\,x^2-5}{x}\right )}^x+2\right )\,\left (6\,x^2\,{\mathrm {e}}^x-5\,\ln \left (\frac {4\,x+6\,x\,{\mathrm {e}}^x+6\,x^2-5}{x}\right )+4\,x\,\ln \left (\frac {4\,x+6\,x\,{\mathrm {e}}^x+6\,x^2-5}{x}\right )+6\,x^2+6\,x^2\,\ln \left (\frac {4\,x+6\,x\,{\mathrm {e}}^x+6\,x^2-5}{x}\right )+6\,x\,{\mathrm {e}}^x\,\ln \left (\frac {4\,x+6\,x\,{\mathrm {e}}^x+6\,x^2-5}{x}\right )+5\right )} \] Input:
int((8*x - exp(x*log((4*x + 6*x*exp(x) + 6*x^2 - 5)/x))*(x - exp(x)*(6*x - 6*x^3) - 6*x^2 + 6*x^3 + log((4*x + 6*x*exp(x) + 6*x^2 - 5)/x)*(6*x^2*exp (x) - 5*x + 4*x^2 + 6*x^3) + 5) + 12*x*exp(x) + 12*x^2 - 10)/(48*x + exp(2 *x*log((4*x + 6*x*exp(x) + 6*x^2 - 5)/x))*(12*x + 18*x*exp(x) + 18*x^2 - 1 5) + exp(x*log((4*x + 6*x*exp(x) + 6*x^2 - 5)/x))*(48*x + 72*x*exp(x) + 72 *x^2 - 60) + 72*x*exp(x) + 72*x^2 - 60),x)
Output:
(5*x + 6*x^3*exp(x) - 5*x*log((4*x + 6*x*exp(x) + 6*x^2 - 5)/x) + 6*x^3 + 4*x^2*log((4*x + 6*x*exp(x) + 6*x^2 - 5)/x) + 6*x^3*log((4*x + 6*x*exp(x) + 6*x^2 - 5)/x) + 6*x^2*exp(x)*log((4*x + 6*x*exp(x) + 6*x^2 - 5)/x))/(3*( ((4*x + 6*x*exp(x) + 6*x^2 - 5)/x)^x + 2)*(6*x^2*exp(x) - 5*log((4*x + 6*x *exp(x) + 6*x^2 - 5)/x) + 4*x*log((4*x + 6*x*exp(x) + 6*x^2 - 5)/x) + 6*x^ 2 + 6*x^2*log((4*x + 6*x*exp(x) + 6*x^2 - 5)/x) + 6*x*exp(x)*log((4*x + 6* x*exp(x) + 6*x^2 - 5)/x) + 5))
\[ \int \frac {-10+8 x+12 e^x x+12 x^2+\left (\frac {-5+4 x+6 e^x x+6 x^2}{x}\right )^x \left (-5-x+6 x^2-6 x^3+e^x \left (6 x-6 x^3\right )+\left (5 x-4 x^2-6 e^x x^2-6 x^3\right ) \log \left (\frac {-5+4 x+6 e^x x+6 x^2}{x}\right )\right )}{-60+48 x+72 e^x x+72 x^2+\left (\frac {-5+4 x+6 e^x x+6 x^2}{x}\right )^{2 x} \left (-15+12 x+18 e^x x+18 x^2\right )+\left (\frac {-5+4 x+6 e^x x+6 x^2}{x}\right )^x \left (-60+48 x+72 e^x x+72 x^2\right )} \, dx=\int \frac {\left (\left (-6 \,{\mathrm e}^{x} x^{2}-6 x^{3}-4 x^{2}+5 x \right ) \mathrm {log}\left (\frac {6 \,{\mathrm e}^{x} x +6 x^{2}+4 x -5}{x}\right )+\left (-6 x^{3}+6 x \right ) {\mathrm e}^{x}-6 x^{3}+6 x^{2}-x -5\right ) {\mathrm e}^{x \,\mathrm {log}\left (\frac {6 \,{\mathrm e}^{x} x +6 x^{2}+4 x -5}{x}\right )}+12 \,{\mathrm e}^{x} x +12 x^{2}+8 x -10}{\left (18 \,{\mathrm e}^{x} x +18 x^{2}+12 x -15\right ) \left ({\mathrm e}^{x \,\mathrm {log}\left (\frac {6 \,{\mathrm e}^{x} x +6 x^{2}+4 x -5}{x}\right )}\right )^{2}+\left (72 \,{\mathrm e}^{x} x +72 x^{2}+48 x -60\right ) {\mathrm e}^{x \,\mathrm {log}\left (\frac {6 \,{\mathrm e}^{x} x +6 x^{2}+4 x -5}{x}\right )}+72 \,{\mathrm e}^{x} x +72 x^{2}+48 x -60}d x \] Input:
int((((-6*exp(x)*x^2-6*x^3-4*x^2+5*x)*log((6*exp(x)*x+6*x^2+4*x-5)/x)+(-6* x^3+6*x)*exp(x)-6*x^3+6*x^2-x-5)*exp(x*log((6*exp(x)*x+6*x^2+4*x-5)/x))+12 *exp(x)*x+12*x^2+8*x-10)/((18*exp(x)*x+18*x^2+12*x-15)*exp(x*log((6*exp(x) *x+6*x^2+4*x-5)/x))^2+(72*exp(x)*x+72*x^2+48*x-60)*exp(x*log((6*exp(x)*x+6 *x^2+4*x-5)/x))+72*exp(x)*x+72*x^2+48*x-60),x)
Output:
int((((-6*exp(x)*x^2-6*x^3-4*x^2+5*x)*log((6*exp(x)*x+6*x^2+4*x-5)/x)+(-6* x^3+6*x)*exp(x)-6*x^3+6*x^2-x-5)*exp(x*log((6*exp(x)*x+6*x^2+4*x-5)/x))+12 *exp(x)*x+12*x^2+8*x-10)/((18*exp(x)*x+18*x^2+12*x-15)*exp(x*log((6*exp(x) *x+6*x^2+4*x-5)/x))^2+(72*exp(x)*x+72*x^2+48*x-60)*exp(x*log((6*exp(x)*x+6 *x^2+4*x-5)/x))+72*exp(x)*x+72*x^2+48*x-60),x)