Integrand size = 209, antiderivative size = 30 \[ \int \frac {-720+540 x+3 e^{4+x} x^3+\left (180 x-6 e^{4+x} x^2\right ) \log \left (\frac {x}{\log (5)}\right )+3 e^{4+x} x \log ^2\left (\frac {x}{\log (5)}\right )+\left (-720 x-180 x^2+3 e^{4+x} x^2+\left (720+180 x-6 e^{4+x} x\right ) \log \left (\frac {x}{\log (5)}\right )+3 e^{4+x} \log ^2\left (\frac {x}{\log (5)}\right )\right ) \log \left (\frac {-240-60 x+e^{4+x} x-e^{4+x} \log \left (\frac {x}{\log (5)}\right )}{-x+\log \left (\frac {x}{\log (5)}\right )}\right )}{-240 x-60 x^2+e^{4+x} x^2+\left (240+60 x-2 e^{4+x} x\right ) \log \left (\frac {x}{\log (5)}\right )+e^{4+x} \log ^2\left (\frac {x}{\log (5)}\right )} \, dx=3 x \log \left (-e^{4+x}+\frac {60 (4+x)}{x-\log \left (\frac {x}{\log (5)}\right )}\right ) \]
\[ \int \frac {-720+540 x+3 e^{4+x} x^3+\left (180 x-6 e^{4+x} x^2\right ) \log \left (\frac {x}{\log (5)}\right )+3 e^{4+x} x \log ^2\left (\frac {x}{\log (5)}\right )+\left (-720 x-180 x^2+3 e^{4+x} x^2+\left (720+180 x-6 e^{4+x} x\right ) \log \left (\frac {x}{\log (5)}\right )+3 e^{4+x} \log ^2\left (\frac {x}{\log (5)}\right )\right ) \log \left (\frac {-240-60 x+e^{4+x} x-e^{4+x} \log \left (\frac {x}{\log (5)}\right )}{-x+\log \left (\frac {x}{\log (5)}\right )}\right )}{-240 x-60 x^2+e^{4+x} x^2+\left (240+60 x-2 e^{4+x} x\right ) \log \left (\frac {x}{\log (5)}\right )+e^{4+x} \log ^2\left (\frac {x}{\log (5)}\right )} \, dx=\int \frac {-720+540 x+3 e^{4+x} x^3+\left (180 x-6 e^{4+x} x^2\right ) \log \left (\frac {x}{\log (5)}\right )+3 e^{4+x} x \log ^2\left (\frac {x}{\log (5)}\right )+\left (-720 x-180 x^2+3 e^{4+x} x^2+\left (720+180 x-6 e^{4+x} x\right ) \log \left (\frac {x}{\log (5)}\right )+3 e^{4+x} \log ^2\left (\frac {x}{\log (5)}\right )\right ) \log \left (\frac {-240-60 x+e^{4+x} x-e^{4+x} \log \left (\frac {x}{\log (5)}\right )}{-x+\log \left (\frac {x}{\log (5)}\right )}\right )}{-240 x-60 x^2+e^{4+x} x^2+\left (240+60 x-2 e^{4+x} x\right ) \log \left (\frac {x}{\log (5)}\right )+e^{4+x} \log ^2\left (\frac {x}{\log (5)}\right )} \, dx \]
Integrate[(-720 + 540*x + 3*E^(4 + x)*x^3 + (180*x - 6*E^(4 + x)*x^2)*Log[ x/Log[5]] + 3*E^(4 + x)*x*Log[x/Log[5]]^2 + (-720*x - 180*x^2 + 3*E^(4 + x )*x^2 + (720 + 180*x - 6*E^(4 + x)*x)*Log[x/Log[5]] + 3*E^(4 + x)*Log[x/Lo g[5]]^2)*Log[(-240 - 60*x + E^(4 + x)*x - E^(4 + x)*Log[x/Log[5]])/(-x + L og[x/Log[5]])])/(-240*x - 60*x^2 + E^(4 + x)*x^2 + (240 + 60*x - 2*E^(4 + x)*x)*Log[x/Log[5]] + E^(4 + x)*Log[x/Log[5]]^2),x]
Integrate[(-720 + 540*x + 3*E^(4 + x)*x^3 + (180*x - 6*E^(4 + x)*x^2)*Log[ x/Log[5]] + 3*E^(4 + x)*x*Log[x/Log[5]]^2 + (-720*x - 180*x^2 + 3*E^(4 + x )*x^2 + (720 + 180*x - 6*E^(4 + x)*x)*Log[x/Log[5]] + 3*E^(4 + x)*Log[x/Lo g[5]]^2)*Log[(-240 - 60*x + E^(4 + x)*x - E^(4 + x)*Log[x/Log[5]])/(-x + L og[x/Log[5]])])/(-240*x - 60*x^2 + E^(4 + x)*x^2 + (240 + 60*x - 2*E^(4 + x)*x)*Log[x/Log[5]] + E^(4 + x)*Log[x/Log[5]]^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.
| \(\displaystyle \int \frac {3 e^{x+4} x^3+\left (3 e^{x+4} x^2-180 x^2-720 x+3 e^{x+4} \log ^2\left (\frac {x}{\log (5)}\right )+\left (-6 e^{x+4} x+180 x+720\right ) \log \left (\frac {x}{\log (5)}\right )\right ) \log \left (\frac {e^{x+4} x-60 x-e^{x+4} \log \left (\frac {x}{\log (5)}\right )-240}{\log \left (\frac {x}{\log (5)}\right )-x}\right )+\left (180 x-6 e^{x+4} x^2\right ) \log \left (\frac {x}{\log (5)}\right )+540 x+3 e^{x+4} x \log ^2\left (\frac {x}{\log (5)}\right )-720}{e^{x+4} x^2-60 x^2-240 x+e^{x+4} \log ^2\left (\frac {x}{\log (5)}\right )+\left (-2 e^{x+4} x+60 x+240\right ) \log \left (\frac {x}{\log (5)}\right )} \, dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {-3 e^{x+4} x^3-\left (3 e^{x+4} x^2-180 x^2-720 x+3 e^{x+4} \log ^2\left (\frac {x}{\log (5)}\right )+\left (-6 e^{x+4} x+180 x+720\right ) \log \left (\frac {x}{\log (5)}\right )\right ) \log \left (\frac {e^{x+4} x-60 x-e^{x+4} \log \left (\frac {x}{\log (5)}\right )-240}{\log \left (\frac {x}{\log (5)}\right )-x}\right )-\left (180 x-6 e^{x+4} x^2\right ) \log \left (\frac {x}{\log (5)}\right )-540 x-3 e^{x+4} x \log ^2\left (\frac {x}{\log (5)}\right )+720}{\left (-e^{x+4} x+60 x+e^{x+4} \log \left (\frac {x}{\log (5)}\right )+240\right ) (x-\log (x)+\log (\log (5)))}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {180 \left (x^3+4 x^2-x^2 \log \left (\frac {x}{\log (5)}\right )+3 x-3 x \log \left (\frac {x}{\log (5)}\right )-4\right )}{\left (e^{x+4} x-60 x-e^{x+4} \log \left (\frac {x}{\log (5)}\right )-240\right ) (x-\log (x)+\log (\log (5)))}+3 \left (x+\log \left (\frac {-e^{x+4} x+60 x+e^{x+4} \log \left (\frac {x}{\log (5)}\right )+240}{x-\log (x)+\log (\log (5))}\right )\right )\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle -180 (4+\log (\log (5))) \int \frac {x^2}{\left (e^{x+4} x-60 x-e^{x+4} \log \left (\frac {x}{\log (5)}\right )-240\right ) (x-\log (x)+\log (\log (5)))}dx+720 \int \frac {x^2}{\left (e^{x+4} x-60 x-e^{x+4} \log \left (\frac {x}{\log (5)}\right )-240\right ) (x-\log (x)+\log (\log (5)))}dx+180 \int \frac {x^2 \log (x)}{\left (e^{x+4} x-60 x-e^{x+4} \log \left (\frac {x}{\log (5)}\right )-240\right ) (x-\log (x)+\log (\log (5)))}dx-180 \int \frac {x^2 \log \left (\frac {x}{\log (5)}\right )}{\left (e^{x+4} x-60 x-e^{x+4} \log \left (\frac {x}{\log (5)}\right )-240\right ) (x-\log (x)+\log (\log (5)))}dx-540 (1+\log (\log (5))) \int \frac {x}{\left (e^{x+4} x-60 x-e^{x+4} \log \left (\frac {x}{\log (5)}\right )-240\right ) (x-\log (x)+\log (\log (5)))}dx+540 \int \frac {x}{\left (e^{x+4} x-60 x-e^{x+4} \log \left (\frac {x}{\log (5)}\right )-240\right ) (x-\log (x)+\log (\log (5)))}dx+540 \int \frac {x \log (x)}{\left (e^{x+4} x-60 x-e^{x+4} \log \left (\frac {x}{\log (5)}\right )-240\right ) (x-\log (x)+\log (\log (5)))}dx-540 \int \frac {x \log \left (\frac {x}{\log (5)}\right )}{\left (e^{x+4} x-60 x-e^{x+4} \log \left (\frac {x}{\log (5)}\right )-240\right ) (x-\log (x)+\log (\log (5)))}dx+3 x \log \left (\frac {-e^{x+4} x+60 x+e^{x+4} \log \left (\frac {x}{\log (5)}\right )+240}{x-\log (x)+\log (\log (5))}\right )\) |
Int[(-720 + 540*x + 3*E^(4 + x)*x^3 + (180*x - 6*E^(4 + x)*x^2)*Log[x/Log[ 5]] + 3*E^(4 + x)*x*Log[x/Log[5]]^2 + (-720*x - 180*x^2 + 3*E^(4 + x)*x^2 + (720 + 180*x - 6*E^(4 + x)*x)*Log[x/Log[5]] + 3*E^(4 + x)*Log[x/Log[5]]^ 2)*Log[(-240 - 60*x + E^(4 + x)*x - E^(4 + x)*Log[x/Log[5]])/(-x + Log[x/L og[5]])])/(-240*x - 60*x^2 + E^(4 + x)*x^2 + (240 + 60*x - 2*E^(4 + x)*x)* Log[x/Log[5]] + E^(4 + x)*Log[x/Log[5]]^2),x]
3.24.92.3.1 Defintions of rubi rules used
Time = 11.23 (sec) , antiderivative size = 44, normalized size of antiderivative = 1.47
| method | result | size |
| parallelrisch | \(3 \ln \left (-\frac {{\mathrm e}^{4+x} \ln \left (\frac {x}{\ln \left (5\right )}\right )-x \,{\mathrm e}^{4+x}+60 x +240}{\ln \left (\frac {x}{\ln \left (5\right )}\right )-x}\right ) x\) | \(44\) |
| risch | \(3 x \ln \left (\left ({\mathrm e}^{4+x}-60\right ) x -{\mathrm e}^{4+x} \ln \left (\frac {x}{\ln \left (5\right )}\right )-240\right )-3 x \ln \left (-\ln \left (\frac {x}{\ln \left (5\right )}\right )+x \right )-3 i \pi x {\operatorname {csgn}\left (\frac {i \left (\left ({\mathrm e}^{4+x}-60\right ) x -{\mathrm e}^{4+x} \ln \left (\frac {x}{\ln \left (5\right )}\right )-240\right )}{-\ln \left (\frac {x}{\ln \left (5\right )}\right )+x}\right )}^{2}-\frac {3 i \pi x \,\operatorname {csgn}\left (\frac {i}{-\ln \left (\frac {x}{\ln \left (5\right )}\right )+x}\right ) \operatorname {csgn}\left (i \left (\left ({\mathrm e}^{4+x}-60\right ) x -{\mathrm e}^{4+x} \ln \left (\frac {x}{\ln \left (5\right )}\right )-240\right )\right ) \operatorname {csgn}\left (\frac {i \left (\left ({\mathrm e}^{4+x}-60\right ) x -{\mathrm e}^{4+x} \ln \left (\frac {x}{\ln \left (5\right )}\right )-240\right )}{-\ln \left (\frac {x}{\ln \left (5\right )}\right )+x}\right )}{2}+\frac {3 i \pi x \,\operatorname {csgn}\left (\frac {i}{-\ln \left (\frac {x}{\ln \left (5\right )}\right )+x}\right ) {\operatorname {csgn}\left (\frac {i \left (\left ({\mathrm e}^{4+x}-60\right ) x -{\mathrm e}^{4+x} \ln \left (\frac {x}{\ln \left (5\right )}\right )-240\right )}{-\ln \left (\frac {x}{\ln \left (5\right )}\right )+x}\right )}^{2}}{2}+\frac {3 i \pi x \,\operatorname {csgn}\left (i \left (\left ({\mathrm e}^{4+x}-60\right ) x -{\mathrm e}^{4+x} \ln \left (\frac {x}{\ln \left (5\right )}\right )-240\right )\right ) {\operatorname {csgn}\left (\frac {i \left (\left ({\mathrm e}^{4+x}-60\right ) x -{\mathrm e}^{4+x} \ln \left (\frac {x}{\ln \left (5\right )}\right )-240\right )}{-\ln \left (\frac {x}{\ln \left (5\right )}\right )+x}\right )}^{2}}{2}+\frac {3 i \pi x {\operatorname {csgn}\left (\frac {i \left (\left ({\mathrm e}^{4+x}-60\right ) x -{\mathrm e}^{4+x} \ln \left (\frac {x}{\ln \left (5\right )}\right )-240\right )}{-\ln \left (\frac {x}{\ln \left (5\right )}\right )+x}\right )}^{3}}{2}+3 i \pi x\) | \(370\) |
int(((3*exp(4+x)*ln(x/ln(5))^2+(-6*x*exp(4+x)+180*x+720)*ln(x/ln(5))+3*x^2 *exp(4+x)-180*x^2-720*x)*ln((-exp(4+x)*ln(x/ln(5))+x*exp(4+x)-60*x-240)/(l n(x/ln(5))-x))+3*x*exp(4+x)*ln(x/ln(5))^2+(-6*x^2*exp(4+x)+180*x)*ln(x/ln( 5))+3*x^3*exp(4+x)+540*x-720)/(exp(4+x)*ln(x/ln(5))^2+(-2*x*exp(4+x)+60*x+ 240)*ln(x/ln(5))+x^2*exp(4+x)-60*x^2-240*x),x,method=_RETURNVERBOSE)
Time = 0.25 (sec) , antiderivative size = 43, normalized size of antiderivative = 1.43 \[ \int \frac {-720+540 x+3 e^{4+x} x^3+\left (180 x-6 e^{4+x} x^2\right ) \log \left (\frac {x}{\log (5)}\right )+3 e^{4+x} x \log ^2\left (\frac {x}{\log (5)}\right )+\left (-720 x-180 x^2+3 e^{4+x} x^2+\left (720+180 x-6 e^{4+x} x\right ) \log \left (\frac {x}{\log (5)}\right )+3 e^{4+x} \log ^2\left (\frac {x}{\log (5)}\right )\right ) \log \left (\frac {-240-60 x+e^{4+x} x-e^{4+x} \log \left (\frac {x}{\log (5)}\right )}{-x+\log \left (\frac {x}{\log (5)}\right )}\right )}{-240 x-60 x^2+e^{4+x} x^2+\left (240+60 x-2 e^{4+x} x\right ) \log \left (\frac {x}{\log (5)}\right )+e^{4+x} \log ^2\left (\frac {x}{\log (5)}\right )} \, dx=3 \, x \log \left (-\frac {x e^{\left (x + 4\right )} - e^{\left (x + 4\right )} \log \left (\frac {x}{\log \left (5\right )}\right ) - 60 \, x - 240}{x - \log \left (\frac {x}{\log \left (5\right )}\right )}\right ) \]
integrate(((3*exp(4+x)*log(x/log(5))^2+(-6*x*exp(4+x)+180*x+720)*log(x/log (5))+3*x^2*exp(4+x)-180*x^2-720*x)*log((-exp(4+x)*log(x/log(5))+x*exp(4+x) -60*x-240)/(log(x/log(5))-x))+3*x*exp(4+x)*log(x/log(5))^2+(-6*x^2*exp(4+x )+180*x)*log(x/log(5))+3*x^3*exp(4+x)+540*x-720)/(exp(4+x)*log(x/log(5))^2 +(-2*x*exp(4+x)+60*x+240)*log(x/log(5))+x^2*exp(4+x)-60*x^2-240*x),x, algo rithm=\
Exception generated. \[ \int \frac {-720+540 x+3 e^{4+x} x^3+\left (180 x-6 e^{4+x} x^2\right ) \log \left (\frac {x}{\log (5)}\right )+3 e^{4+x} x \log ^2\left (\frac {x}{\log (5)}\right )+\left (-720 x-180 x^2+3 e^{4+x} x^2+\left (720+180 x-6 e^{4+x} x\right ) \log \left (\frac {x}{\log (5)}\right )+3 e^{4+x} \log ^2\left (\frac {x}{\log (5)}\right )\right ) \log \left (\frac {-240-60 x+e^{4+x} x-e^{4+x} \log \left (\frac {x}{\log (5)}\right )}{-x+\log \left (\frac {x}{\log (5)}\right )}\right )}{-240 x-60 x^2+e^{4+x} x^2+\left (240+60 x-2 e^{4+x} x\right ) \log \left (\frac {x}{\log (5)}\right )+e^{4+x} \log ^2\left (\frac {x}{\log (5)}\right )} \, dx=\text {Exception raised: TypeError} \]
integrate(((3*exp(4+x)*ln(x/ln(5))**2+(-6*x*exp(4+x)+180*x+720)*ln(x/ln(5) )+3*x**2*exp(4+x)-180*x**2-720*x)*ln((-exp(4+x)*ln(x/ln(5))+x*exp(4+x)-60* x-240)/(ln(x/ln(5))-x))+3*x*exp(4+x)*ln(x/ln(5))**2+(-6*x**2*exp(4+x)+180* x)*ln(x/ln(5))+3*x**3*exp(4+x)+540*x-720)/(exp(4+x)*ln(x/ln(5))**2+(-2*x*e xp(4+x)+60*x+240)*ln(x/ln(5))+x**2*exp(4+x)-60*x**2-240*x),x)
Time = 0.34 (sec) , antiderivative size = 45, normalized size of antiderivative = 1.50 \[ \int \frac {-720+540 x+3 e^{4+x} x^3+\left (180 x-6 e^{4+x} x^2\right ) \log \left (\frac {x}{\log (5)}\right )+3 e^{4+x} x \log ^2\left (\frac {x}{\log (5)}\right )+\left (-720 x-180 x^2+3 e^{4+x} x^2+\left (720+180 x-6 e^{4+x} x\right ) \log \left (\frac {x}{\log (5)}\right )+3 e^{4+x} \log ^2\left (\frac {x}{\log (5)}\right )\right ) \log \left (\frac {-240-60 x+e^{4+x} x-e^{4+x} \log \left (\frac {x}{\log (5)}\right )}{-x+\log \left (\frac {x}{\log (5)}\right )}\right )}{-240 x-60 x^2+e^{4+x} x^2+\left (240+60 x-2 e^{4+x} x\right ) \log \left (\frac {x}{\log (5)}\right )+e^{4+x} \log ^2\left (\frac {x}{\log (5)}\right )} \, dx=3 \, x \log \left (-{\left (x e^{4} + e^{4} \log \left (\log \left (5\right )\right )\right )} e^{x} + e^{\left (x + 4\right )} \log \left (x\right ) + 60 \, x + 240\right ) - 3 \, x \log \left (x - \log \left (x\right ) + \log \left (\log \left (5\right )\right )\right ) \]
integrate(((3*exp(4+x)*log(x/log(5))^2+(-6*x*exp(4+x)+180*x+720)*log(x/log (5))+3*x^2*exp(4+x)-180*x^2-720*x)*log((-exp(4+x)*log(x/log(5))+x*exp(4+x) -60*x-240)/(log(x/log(5))-x))+3*x*exp(4+x)*log(x/log(5))^2+(-6*x^2*exp(4+x )+180*x)*log(x/log(5))+3*x^3*exp(4+x)+540*x-720)/(exp(4+x)*log(x/log(5))^2 +(-2*x*exp(4+x)+60*x+240)*log(x/log(5))+x^2*exp(4+x)-60*x^2-240*x),x, algo rithm=\
3*x*log(-(x*e^4 + e^4*log(log(5)))*e^x + e^(x + 4)*log(x) + 60*x + 240) - 3*x*log(x - log(x) + log(log(5)))
Leaf count of result is larger than twice the leaf count of optimal. 109 vs. \(2 (29) = 58\).
Time = 0.84 (sec) , antiderivative size = 109, normalized size of antiderivative = 3.63 \[ \int \frac {-720+540 x+3 e^{4+x} x^3+\left (180 x-6 e^{4+x} x^2\right ) \log \left (\frac {x}{\log (5)}\right )+3 e^{4+x} x \log ^2\left (\frac {x}{\log (5)}\right )+\left (-720 x-180 x^2+3 e^{4+x} x^2+\left (720+180 x-6 e^{4+x} x\right ) \log \left (\frac {x}{\log (5)}\right )+3 e^{4+x} \log ^2\left (\frac {x}{\log (5)}\right )\right ) \log \left (\frac {-240-60 x+e^{4+x} x-e^{4+x} \log \left (\frac {x}{\log (5)}\right )}{-x+\log \left (\frac {x}{\log (5)}\right )}\right )}{-240 x-60 x^2+e^{4+x} x^2+\left (240+60 x-2 e^{4+x} x\right ) \log \left (\frac {x}{\log (5)}\right )+e^{4+x} \log ^2\left (\frac {x}{\log (5)}\right )} \, dx=3 \, {\left (x + 4\right )} \log \left (-{\left (x + 4\right )} e^{\left (x + 4\right )} + e^{\left (x + 4\right )} \log \left (x\right ) - e^{\left (x + 4\right )} \log \left (\log \left (5\right )\right ) + 60 \, x + 4 \, e^{\left (x + 4\right )} + 240\right ) - 3 \, {\left (x + 4\right )} \log \left (x - \log \left (x\right ) + \log \left (\log \left (5\right )\right )\right ) - 12 \, \log \left (-{\left (x + 4\right )} e^{\left (x + 4\right )} + e^{\left (x + 4\right )} \log \left (x\right ) - e^{\left (x + 4\right )} \log \left (\log \left (5\right )\right ) + 60 \, x + 4 \, e^{\left (x + 4\right )} + 240\right ) + 12 \, \log \left (x - \log \left (x\right ) + \log \left (\log \left (5\right )\right )\right ) \]
integrate(((3*exp(4+x)*log(x/log(5))^2+(-6*x*exp(4+x)+180*x+720)*log(x/log (5))+3*x^2*exp(4+x)-180*x^2-720*x)*log((-exp(4+x)*log(x/log(5))+x*exp(4+x) -60*x-240)/(log(x/log(5))-x))+3*x*exp(4+x)*log(x/log(5))^2+(-6*x^2*exp(4+x )+180*x)*log(x/log(5))+3*x^3*exp(4+x)+540*x-720)/(exp(4+x)*log(x/log(5))^2 +(-2*x*exp(4+x)+60*x+240)*log(x/log(5))+x^2*exp(4+x)-60*x^2-240*x),x, algo rithm=\
3*(x + 4)*log(-(x + 4)*e^(x + 4) + e^(x + 4)*log(x) - e^(x + 4)*log(log(5) ) + 60*x + 4*e^(x + 4) + 240) - 3*(x + 4)*log(x - log(x) + log(log(5))) - 12*log(-(x + 4)*e^(x + 4) + e^(x + 4)*log(x) - e^(x + 4)*log(log(5)) + 60* x + 4*e^(x + 4) + 240) + 12*log(x - log(x) + log(log(5)))
Time = 14.20 (sec) , antiderivative size = 42, normalized size of antiderivative = 1.40 \[ \int \frac {-720+540 x+3 e^{4+x} x^3+\left (180 x-6 e^{4+x} x^2\right ) \log \left (\frac {x}{\log (5)}\right )+3 e^{4+x} x \log ^2\left (\frac {x}{\log (5)}\right )+\left (-720 x-180 x^2+3 e^{4+x} x^2+\left (720+180 x-6 e^{4+x} x\right ) \log \left (\frac {x}{\log (5)}\right )+3 e^{4+x} \log ^2\left (\frac {x}{\log (5)}\right )\right ) \log \left (\frac {-240-60 x+e^{4+x} x-e^{4+x} \log \left (\frac {x}{\log (5)}\right )}{-x+\log \left (\frac {x}{\log (5)}\right )}\right )}{-240 x-60 x^2+e^{4+x} x^2+\left (240+60 x-2 e^{4+x} x\right ) \log \left (\frac {x}{\log (5)}\right )+e^{4+x} \log ^2\left (\frac {x}{\log (5)}\right )} \, dx=3\,x\,\ln \left (\frac {60\,x-x\,{\mathrm {e}}^4\,{\mathrm {e}}^x+\ln \left (\frac {x}{\ln \left (5\right )}\right )\,{\mathrm {e}}^4\,{\mathrm {e}}^x+240}{x-\ln \left (\frac {x}{\ln \left (5\right )}\right )}\right ) \]
int((540*x + log(x/log(5))*(180*x - 6*x^2*exp(x + 4)) + log((60*x - x*exp( x + 4) + log(x/log(5))*exp(x + 4) + 240)/(x - log(x/log(5))))*(3*log(x/log (5))^2*exp(x + 4) - 720*x + 3*x^2*exp(x + 4) + log(x/log(5))*(180*x - 6*x* exp(x + 4) + 720) - 180*x^2) + 3*x^3*exp(x + 4) + 3*x*log(x/log(5))^2*exp( x + 4) - 720)/(log(x/log(5))^2*exp(x + 4) - 240*x + x^2*exp(x + 4) + log(x /log(5))*(60*x - 2*x*exp(x + 4) + 240) - 60*x^2),x)