Integrand size = 121, antiderivative size = 27 \[ \int \frac {x^3 \log ^3(x)+e^{\frac {144+(-120-120 x+24 \log (3)) \log (x)+\left (25+50 x+25 x^2+(-10-10 x) \log (3)+\log ^2(3)\right ) \log ^2(x)}{x^2 \log ^2(x)}} \left (-288+(-168+120 x-24 \log (3)) \log (x)+(240+120 x-48 \log (3)) \log ^2(x)+\left (-50-50 x+(20+10 x) \log (3)-2 \log ^2(3)\right ) \log ^3(x)\right )}{x^3 \log ^3(x)} \, dx=e^{\left (6+\frac {5-x-\log (3)-\frac {12}{\log (x)}}{x}\right )^2}+x \] Output:
x+exp(((5-ln(3)-x-12/ln(x))/x+6)^2)
Leaf count is larger than twice the leaf count of optimal. \(65\) vs. \(2(27)=54\).
Time = 0.24 (sec) , antiderivative size = 65, normalized size of antiderivative = 2.41 \[ \int \frac {x^3 \log ^3(x)+e^{\frac {144+(-120-120 x+24 \log (3)) \log (x)+\left (25+50 x+25 x^2+(-10-10 x) \log (3)+\log ^2(3)\right ) \log ^2(x)}{x^2 \log ^2(x)}} \left (-288+(-168+120 x-24 \log (3)) \log (x)+(240+120 x-48 \log (3)) \log ^2(x)+\left (-50-50 x+(20+10 x) \log (3)-2 \log ^2(3)\right ) \log ^3(x)\right )}{x^3 \log ^3(x)} \, dx=3^{-\frac {10}{x^2}-\frac {10}{x}+\frac {24}{x^2 \log (x)}} e^{25+\frac {50}{x}+\frac {25+\log ^2(3)}{x^2}+\frac {144}{x^2 \log ^2(x)}-\frac {120 (1+x)}{x^2 \log (x)}}+x \] Input:
Integrate[(x^3*Log[x]^3 + E^((144 + (-120 - 120*x + 24*Log[3])*Log[x] + (2 5 + 50*x + 25*x^2 + (-10 - 10*x)*Log[3] + Log[3]^2)*Log[x]^2)/(x^2*Log[x]^ 2))*(-288 + (-168 + 120*x - 24*Log[3])*Log[x] + (240 + 120*x - 48*Log[3])* Log[x]^2 + (-50 - 50*x + (20 + 10*x)*Log[3] - 2*Log[3]^2)*Log[x]^3))/(x^3* Log[x]^3),x]
Output:
3^(-10/x^2 - 10/x + 24/(x^2*Log[x]))*E^(25 + 50/x + (25 + Log[3]^2)/x^2 + 144/(x^2*Log[x]^2) - (120*(1 + x))/(x^2*Log[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.
| \(\displaystyle \int \frac {\left ((120 x+240-48 \log (3)) \log ^2(x)+\left (-50 x+(10 x+20) \log (3)-50-2 \log ^2(3)\right ) \log ^3(x)+(120 x-168-24 \log (3)) \log (x)-288\right ) \exp \left (\frac {\left (25 x^2+50 x+(-10 x-10) \log (3)+25+\log ^2(3)\right ) \log ^2(x)+(-120 x-120+24 \log (3)) \log (x)+144}{x^2 \log ^2(x)}\right )+x^3 \log ^3(x)}{x^3 \log ^3(x)} \, dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {2\ 3^{-\frac {2 (5 x \log (x)+5 \log (x)-12)}{x^2 \log (x)}} \left (-5 x \log (x)-5 \left (1-\frac {\log (3)}{5}\right ) \log (x)+12\right ) \left (5 \left (1-\frac {\log (3)}{5}\right ) \log ^2(x)-12 \log (x)-12\right ) \exp \left (\frac {144}{x^2 \log ^2(x)}+\frac {25 \left (1+\frac {\log ^2(3)}{25}\right )}{x^2}-\frac {120}{x^2 \log (x)}+\frac {50}{x}-\frac {120}{x \log (x)}+25\right )}{x^3 \log ^3(x)}+1\right )dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \left (\frac {2\ 3^{-\frac {2 (5 x \log (x)+5 \log (x)-12)}{x^2 \log (x)}} \left (-5 x \log (x)-5 \left (1-\frac {\log (3)}{5}\right ) \log (x)+12\right ) \left (5 \left (1-\frac {\log (3)}{5}\right ) \log ^2(x)-12 \log (x)-12\right ) \exp \left (\frac {25 x^2 \log ^2(x)+50 x \log ^2(x)+25 \left (1+\frac {\log ^2(3)}{25}\right ) \log ^2(x)-120 x \log (x)-120 \log (x)+144}{x^2 \log ^2(x)}\right )}{x^3 \log ^3(x)}+1\right )dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {2\ 3^{-\frac {2 (5 x \log (x)+5 \log (x)-12)}{x^2 \log (x)}} \left (-5 x \log (x)-5 \left (1-\frac {\log (3)}{5}\right ) \log (x)+12\right ) \left (5 \left (1-\frac {\log (3)}{5}\right ) \log ^2(x)-12 \log (x)-12\right ) \exp \left (\frac {144}{x^2 \log ^2(x)}+\frac {25 \left (1+\frac {\log ^2(3)}{25}\right )}{x^2}-\frac {120}{x^2 \log (x)}+\frac {50}{x}-\frac {120}{x \log (x)}+25\right )}{x^3 \log ^3(x)}+1\right )dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \left (\frac {2\ 3^{-\frac {2 (5 x \log (x)+5 \log (x)-12)}{x^2 \log (x)}} \left (-5 x \log (x)-5 \left (1-\frac {\log (3)}{5}\right ) \log (x)+12\right ) \left (5 \left (1-\frac {\log (3)}{5}\right ) \log ^2(x)-12 \log (x)-12\right ) \exp \left (\frac {25 x^2 \log ^2(x)+50 x \log ^2(x)+25 \left (1+\frac {\log ^2(3)}{25}\right ) \log ^2(x)-120 x \log (x)-120 \log (x)+144}{x^2 \log ^2(x)}\right )}{x^3 \log ^3(x)}+1\right )dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {2\ 3^{-\frac {2 (5 x \log (x)+5 \log (x)-12)}{x^2 \log (x)}} \left (-5 x \log (x)-5 \left (1-\frac {\log (3)}{5}\right ) \log (x)+12\right ) \left (5 \left (1-\frac {\log (3)}{5}\right ) \log ^2(x)-12 \log (x)-12\right ) \exp \left (\frac {144}{x^2 \log ^2(x)}+\frac {25 \left (1+\frac {\log ^2(3)}{25}\right )}{x^2}-\frac {120}{x^2 \log (x)}+\frac {50}{x}-\frac {120}{x \log (x)}+25\right )}{x^3 \log ^3(x)}+1\right )dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \left (\frac {2\ 3^{-\frac {2 (5 x \log (x)+5 \log (x)-12)}{x^2 \log (x)}} \left (-5 x \log (x)-5 \left (1-\frac {\log (3)}{5}\right ) \log (x)+12\right ) \left (5 \left (1-\frac {\log (3)}{5}\right ) \log ^2(x)-12 \log (x)-12\right ) \exp \left (\frac {25 x^2 \log ^2(x)+50 x \log ^2(x)+25 \left (1+\frac {\log ^2(3)}{25}\right ) \log ^2(x)-120 x \log (x)-120 \log (x)+144}{x^2 \log ^2(x)}\right )}{x^3 \log ^3(x)}+1\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle -10 (5-\log (3)) \int \frac {3^{-\frac {2 (5 x \log (x)+5 \log (x)-12)}{x^2 \log (x)}} \exp \left (\frac {25 x^2 \log ^2(x)+50 x \log ^2(x)+25 \left (1+\frac {\log ^2(3)}{25}\right ) \log ^2(x)-120 x \log (x)-120 \log (x)+144}{x^2 \log ^2(x)}\right )}{x^2}dx+40 \int \frac {3^{1-\frac {2 (5 x \log (x)+5 \log (x)-12)}{x^2 \log (x)}} \exp \left (\frac {25 x^2 \log ^2(x)+50 x \log ^2(x)+25 \left (1+\frac {\log ^2(3)}{25}\right ) \log ^2(x)-120 x \log (x)-120 \log (x)+144}{x^2 \log ^2(x)}\right )}{x^2 \log ^2(x)}dx+40 \int \frac {3^{1-\frac {2 (5 x \log (x)+5 \log (x)-12)}{x^2 \log (x)}} \exp \left (\frac {25 x^2 \log ^2(x)+50 x \log ^2(x)+25 \left (1+\frac {\log ^2(3)}{25}\right ) \log ^2(x)-120 x \log (x)-120 \log (x)+144}{x^2 \log ^2(x)}\right )}{x^2 \log (x)}dx-2 (5-\log (3))^2 \int \frac {3^{-\frac {2 (5 x \log (x)+5 \log (x)-12)}{x^2 \log (x)}} \exp \left (\frac {25 x^2 \log ^2(x)+50 x \log ^2(x)+25 \left (1+\frac {\log ^2(3)}{25}\right ) \log ^2(x)-120 x \log (x)-120 \log (x)+144}{x^2 \log ^2(x)}\right )}{x^3}dx-8 (7+\log (3)) \int \frac {3^{1-\frac {2 (5 x \log (x)+5 \log (x)-12)}{x^2 \log (x)}} \exp \left (\frac {25 x^2 \log ^2(x)+50 x \log ^2(x)+25 \left (1+\frac {\log ^2(3)}{25}\right ) \log ^2(x)-120 x \log (x)-120 \log (x)+144}{x^2 \log ^2(x)}\right )}{x^3 \log ^2(x)}dx+8 (10-\log (9)) \int \frac {3^{1-\frac {2 (5 x \log (x)+5 \log (x)-12)}{x^2 \log (x)}} \exp \left (\frac {25 x^2 \log ^2(x)+50 x \log ^2(x)+25 \left (1+\frac {\log ^2(3)}{25}\right ) \log ^2(x)-120 x \log (x)-120 \log (x)+144}{x^2 \log ^2(x)}\right )}{x^3 \log (x)}dx-32 \int \frac {3^{2-\frac {2 (5 x \log (x)+5 \log (x)-12)}{x^2 \log (x)}} \exp \left (\frac {25 x^2 \log ^2(x)+50 x \log ^2(x)+25 \left (1+\frac {\log ^2(3)}{25}\right ) \log ^2(x)-120 x \log (x)-120 \log (x)+144}{x^2 \log ^2(x)}\right )}{x^3 \log ^3(x)}dx+x\) |
Input:
Int[(x^3*Log[x]^3 + E^((144 + (-120 - 120*x + 24*Log[3])*Log[x] + (25 + 50 *x + 25*x^2 + (-10 - 10*x)*Log[3] + Log[3]^2)*Log[x]^2)/(x^2*Log[x]^2))*(- 288 + (-168 + 120*x - 24*Log[3])*Log[x] + (240 + 120*x - 48*Log[3])*Log[x] ^2 + (-50 - 50*x + (20 + 10*x)*Log[3] - 2*Log[3]^2)*Log[x]^3))/(x^3*Log[x] ^3),x]
Output:
$Aborted
Time = 11.36 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.11
| method | result | size |
| risch | \(x +{\mathrm e}^{\frac {\left (\ln \left (3\right ) \ln \left (x \right )-5 x \ln \left (x \right )-5 \ln \left (x \right )+12\right )^{2}}{x^{2} \ln \left (x \right )^{2}}}\) | \(30\) |
| parallelrisch | \(x +{\mathrm e}^{\frac {\left (\ln \left (3\right )^{2}+\left (-10 x -10\right ) \ln \left (3\right )+25 x^{2}+50 x +25\right ) \ln \left (x \right )^{2}+\left (24 \ln \left (3\right )-120 x -120\right ) \ln \left (x \right )+144}{x^{2} \ln \left (x \right )^{2}}}\) | \(53\) |
Input:
int((((-2*ln(3)^2+(10*x+20)*ln(3)-50*x-50)*ln(x)^3+(-48*ln(3)+120*x+240)*l n(x)^2+(-24*ln(3)+120*x-168)*ln(x)-288)*exp(((ln(3)^2+(-10*x-10)*ln(3)+25* x^2+50*x+25)*ln(x)^2+(24*ln(3)-120*x-120)*ln(x)+144)/x^2/ln(x)^2)+x^3*ln(x )^3)/x^3/ln(x)^3,x,method=_RETURNVERBOSE)
Output:
x+exp((ln(3)*ln(x)-5*x*ln(x)-5*ln(x)+12)^2/x^2/ln(x)^2)
Leaf count of result is larger than twice the leaf count of optimal. 52 vs. \(2 (22) = 44\).
Time = 0.09 (sec) , antiderivative size = 52, normalized size of antiderivative = 1.93 \[ \int \frac {x^3 \log ^3(x)+e^{\frac {144+(-120-120 x+24 \log (3)) \log (x)+\left (25+50 x+25 x^2+(-10-10 x) \log (3)+\log ^2(3)\right ) \log ^2(x)}{x^2 \log ^2(x)}} \left (-288+(-168+120 x-24 \log (3)) \log (x)+(240+120 x-48 \log (3)) \log ^2(x)+\left (-50-50 x+(20+10 x) \log (3)-2 \log ^2(3)\right ) \log ^3(x)\right )}{x^3 \log ^3(x)} \, dx=x + e^{\left (\frac {{\left (25 \, x^{2} - 10 \, {\left (x + 1\right )} \log \left (3\right ) + \log \left (3\right )^{2} + 50 \, x + 25\right )} \log \left (x\right )^{2} - 24 \, {\left (5 \, x - \log \left (3\right ) + 5\right )} \log \left (x\right ) + 144}{x^{2} \log \left (x\right )^{2}}\right )} \] Input:
integrate((((-2*log(3)^2+(10*x+20)*log(3)-50*x-50)*log(x)^3+(-48*log(3)+12 0*x+240)*log(x)^2+(-24*log(3)+120*x-168)*log(x)-288)*exp(((log(3)^2+(-10*x -10)*log(3)+25*x^2+50*x+25)*log(x)^2+(24*log(3)-120*x-120)*log(x)+144)/x^2 /log(x)^2)+x^3*log(x)^3)/x^3/log(x)^3,x, algorithm="fricas")
Output:
x + e^(((25*x^2 - 10*(x + 1)*log(3) + log(3)^2 + 50*x + 25)*log(x)^2 - 24* (5*x - log(3) + 5)*log(x) + 144)/(x^2*log(x)^2))
Leaf count of result is larger than twice the leaf count of optimal. 56 vs. \(2 (19) = 38\).
Time = 0.41 (sec) , antiderivative size = 56, normalized size of antiderivative = 2.07 \[ \int \frac {x^3 \log ^3(x)+e^{\frac {144+(-120-120 x+24 \log (3)) \log (x)+\left (25+50 x+25 x^2+(-10-10 x) \log (3)+\log ^2(3)\right ) \log ^2(x)}{x^2 \log ^2(x)}} \left (-288+(-168+120 x-24 \log (3)) \log (x)+(240+120 x-48 \log (3)) \log ^2(x)+\left (-50-50 x+(20+10 x) \log (3)-2 \log ^2(3)\right ) \log ^3(x)\right )}{x^3 \log ^3(x)} \, dx=x + e^{\frac {\left (- 120 x - 120 + 24 \log {\left (3 \right )}\right ) \log {\left (x \right )} + \left (25 x^{2} + 50 x + \left (- 10 x - 10\right ) \log {\left (3 \right )} + \log {\left (3 \right )}^{2} + 25\right ) \log {\left (x \right )}^{2} + 144}{x^{2} \log {\left (x \right )}^{2}}} \] Input:
integrate((((-2*ln(3)**2+(10*x+20)*ln(3)-50*x-50)*ln(x)**3+(-48*ln(3)+120* x+240)*ln(x)**2+(-24*ln(3)+120*x-168)*ln(x)-288)*exp(((ln(3)**2+(-10*x-10) *ln(3)+25*x**2+50*x+25)*ln(x)**2+(24*ln(3)-120*x-120)*ln(x)+144)/x**2/ln(x )**2)+x**3*ln(x)**3)/x**3/ln(x)**3,x)
Output:
x + exp(((-120*x - 120 + 24*log(3))*log(x) + (25*x**2 + 50*x + (-10*x - 10 )*log(3) + log(3)**2 + 25)*log(x)**2 + 144)/(x**2*log(x)**2))
Leaf count of result is larger than twice the leaf count of optimal. 75 vs. \(2 (22) = 44\).
Time = 0.34 (sec) , antiderivative size = 75, normalized size of antiderivative = 2.78 \[ \int \frac {x^3 \log ^3(x)+e^{\frac {144+(-120-120 x+24 \log (3)) \log (x)+\left (25+50 x+25 x^2+(-10-10 x) \log (3)+\log ^2(3)\right ) \log ^2(x)}{x^2 \log ^2(x)}} \left (-288+(-168+120 x-24 \log (3)) \log (x)+(240+120 x-48 \log (3)) \log ^2(x)+\left (-50-50 x+(20+10 x) \log (3)-2 \log ^2(3)\right ) \log ^3(x)\right )}{x^3 \log ^3(x)} \, dx=x + e^{\left (-\frac {10 \, \log \left (3\right )}{x} + \frac {\log \left (3\right )^{2}}{x^{2}} + \frac {50}{x} - \frac {10 \, \log \left (3\right )}{x^{2}} + \frac {25}{x^{2}} - \frac {120}{x \log \left (x\right )} + \frac {24 \, \log \left (3\right )}{x^{2} \log \left (x\right )} - \frac {120}{x^{2} \log \left (x\right )} + \frac {144}{x^{2} \log \left (x\right )^{2}} + 25\right )} \] Input:
integrate((((-2*log(3)^2+(10*x+20)*log(3)-50*x-50)*log(x)^3+(-48*log(3)+12 0*x+240)*log(x)^2+(-24*log(3)+120*x-168)*log(x)-288)*exp(((log(3)^2+(-10*x -10)*log(3)+25*x^2+50*x+25)*log(x)^2+(24*log(3)-120*x-120)*log(x)+144)/x^2 /log(x)^2)+x^3*log(x)^3)/x^3/log(x)^3,x, algorithm="maxima")
Output:
x + e^(-10*log(3)/x + log(3)^2/x^2 + 50/x - 10*log(3)/x^2 + 25/x^2 - 120/( x*log(x)) + 24*log(3)/(x^2*log(x)) - 120/(x^2*log(x)) + 144/(x^2*log(x)^2) + 25)
\[ \int \frac {x^3 \log ^3(x)+e^{\frac {144+(-120-120 x+24 \log (3)) \log (x)+\left (25+50 x+25 x^2+(-10-10 x) \log (3)+\log ^2(3)\right ) \log ^2(x)}{x^2 \log ^2(x)}} \left (-288+(-168+120 x-24 \log (3)) \log (x)+(240+120 x-48 \log (3)) \log ^2(x)+\left (-50-50 x+(20+10 x) \log (3)-2 \log ^2(3)\right ) \log ^3(x)\right )}{x^3 \log ^3(x)} \, dx=\int { \frac {x^{3} \log \left (x\right )^{3} + 2 \, {\left ({\left (5 \, {\left (x + 2\right )} \log \left (3\right ) - \log \left (3\right )^{2} - 25 \, x - 25\right )} \log \left (x\right )^{3} + 12 \, {\left (5 \, x - 2 \, \log \left (3\right ) + 10\right )} \log \left (x\right )^{2} + 12 \, {\left (5 \, x - \log \left (3\right ) - 7\right )} \log \left (x\right ) - 144\right )} e^{\left (\frac {{\left (25 \, x^{2} - 10 \, {\left (x + 1\right )} \log \left (3\right ) + \log \left (3\right )^{2} + 50 \, x + 25\right )} \log \left (x\right )^{2} - 24 \, {\left (5 \, x - \log \left (3\right ) + 5\right )} \log \left (x\right ) + 144}{x^{2} \log \left (x\right )^{2}}\right )}}{x^{3} \log \left (x\right )^{3}} \,d x } \] Input:
integrate((((-2*log(3)^2+(10*x+20)*log(3)-50*x-50)*log(x)^3+(-48*log(3)+12 0*x+240)*log(x)^2+(-24*log(3)+120*x-168)*log(x)-288)*exp(((log(3)^2+(-10*x -10)*log(3)+25*x^2+50*x+25)*log(x)^2+(24*log(3)-120*x-120)*log(x)+144)/x^2 /log(x)^2)+x^3*log(x)^3)/x^3/log(x)^3,x, algorithm="giac")
Output:
undef
Time = 4.13 (sec) , antiderivative size = 85, normalized size of antiderivative = 3.15 \[ \int \frac {x^3 \log ^3(x)+e^{\frac {144+(-120-120 x+24 \log (3)) \log (x)+\left (25+50 x+25 x^2+(-10-10 x) \log (3)+\log ^2(3)\right ) \log ^2(x)}{x^2 \log ^2(x)}} \left (-288+(-168+120 x-24 \log (3)) \log (x)+(240+120 x-48 \log (3)) \log ^2(x)+\left (-50-50 x+(20+10 x) \log (3)-2 \log ^2(3)\right ) \log ^3(x)\right )}{x^3 \log ^3(x)} \, dx=x+\frac {3^{\frac {24}{x^2\,\ln \left (x\right )}}\,{\mathrm {e}}^{25}\,{\mathrm {e}}^{\frac {{\ln \left (3\right )}^2}{x^2}}\,{\mathrm {e}}^{\frac {25}{x^2}}\,{\mathrm {e}}^{50/x}\,{\mathrm {e}}^{-\frac {120}{x\,\ln \left (x\right )}}\,{\mathrm {e}}^{-\frac {120}{x^2\,\ln \left (x\right )}}\,{\mathrm {e}}^{\frac {144}{x^2\,{\ln \left (x\right )}^2}}}{3^{10/x}\,3^{\frac {10}{x^2}}} \] Input:
int(-(exp((log(x)^2*(50*x - log(3)*(10*x + 10) + log(3)^2 + 25*x^2 + 25) - log(x)*(120*x - 24*log(3) + 120) + 144)/(x^2*log(x)^2))*(log(x)^3*(50*x - log(3)*(10*x + 20) + 2*log(3)^2 + 50) + log(x)*(24*log(3) - 120*x + 168) - log(x)^2*(120*x - 48*log(3) + 240) + 288) - x^3*log(x)^3)/(x^3*log(x)^3) ,x)
Output:
x + (3^(24/(x^2*log(x)))*exp(25)*exp(log(3)^2/x^2)*exp(25/x^2)*exp(50/x)*e xp(-120/(x*log(x)))*exp(-120/(x^2*log(x)))*exp(144/(x^2*log(x)^2)))/(3^(10 /x)*3^(10/x^2))
Time = 1.05 (sec) , antiderivative size = 106, normalized size of antiderivative = 3.93 \[ \int \frac {x^3 \log ^3(x)+e^{\frac {144+(-120-120 x+24 \log (3)) \log (x)+\left (25+50 x+25 x^2+(-10-10 x) \log (3)+\log ^2(3)\right ) \log ^2(x)}{x^2 \log ^2(x)}} \left (-288+(-168+120 x-24 \log (3)) \log (x)+(240+120 x-48 \log (3)) \log ^2(x)+\left (-50-50 x+(20+10 x) \log (3)-2 \log ^2(3)\right ) \log ^3(x)\right )}{x^3 \log ^3(x)} \, dx=\frac {e^{\frac {\mathrm {log}\left (x \right )^{2} \mathrm {log}\left (3\right )^{2}+50 \mathrm {log}\left (x \right )^{2} x +25 \mathrm {log}\left (x \right )^{2}+24 \,\mathrm {log}\left (x \right ) \mathrm {log}\left (3\right )+144}{\mathrm {log}\left (x \right )^{2} x^{2}}} e^{25}+e^{\frac {10 \,\mathrm {log}\left (x \right ) \mathrm {log}\left (3\right ) x +10 \,\mathrm {log}\left (x \right ) \mathrm {log}\left (3\right )+120 x +120}{\mathrm {log}\left (x \right ) x^{2}}} x}{e^{\frac {10 \,\mathrm {log}\left (x \right ) \mathrm {log}\left (3\right ) x +10 \,\mathrm {log}\left (x \right ) \mathrm {log}\left (3\right )+120 x +120}{\mathrm {log}\left (x \right ) x^{2}}}} \] Input:
int((((-2*log(3)^2+(10*x+20)*log(3)-50*x-50)*log(x)^3+(-48*log(3)+120*x+24 0)*log(x)^2+(-24*log(3)+120*x-168)*log(x)-288)*exp(((log(3)^2+(-10*x-10)*l og(3)+25*x^2+50*x+25)*log(x)^2+(24*log(3)-120*x-120)*log(x)+144)/x^2/log(x )^2)+x^3*log(x)^3)/x^3/log(x)^3,x)
Output:
(e**((log(x)**2*log(3)**2 + 50*log(x)**2*x + 25*log(x)**2 + 24*log(x)*log( 3) + 144)/(log(x)**2*x**2))*e**25 + e**((10*log(x)*log(3)*x + 10*log(x)*lo g(3) + 120*x + 120)/(log(x)*x**2))*x)/e**((10*log(x)*log(3)*x + 10*log(x)* log(3) + 120*x + 120)/(log(x)*x**2))