Integrand size = 304, antiderivative size = 31 \[ \int \frac {24 e^{2 x}+\left (e^x \left (-120-24 e^5\right )+24 e^{2 x} x\right ) \log \left (\frac {2}{x}\right )+e^x \left (-120 x-24 e^5 x\right ) \log ^2\left (\frac {2}{x}\right )+\left (12 e^{3 x} x \log \left (\frac {2}{x}\right )+e^{2 x} \left (-120 x-24 e^5 x\right ) \log ^2\left (\frac {2}{x}\right )+e^x \left (299 x+120 e^5 x+12 e^{10} x\right ) \log ^3\left (\frac {2}{x}\right )\right ) \log \left (\frac {-12 e^{2 x}+e^x \left (120+24 e^5\right ) \log \left (\frac {2}{x}\right )+\left (-299-120 e^5-12 e^{10}\right ) \log ^2\left (\frac {2}{x}\right )}{\log ^2\left (\frac {2}{x}\right )}\right )}{\left (12 e^{2 x} x \log \left (\frac {2}{x}\right )+e^x \left (-120 x-24 e^5 x\right ) \log ^2\left (\frac {2}{x}\right )+\left (299 x+120 e^5 x+12 e^{10} x\right ) \log ^3\left (\frac {2}{x}\right )\right ) \log \left (\frac {-12 e^{2 x}+e^x \left (120+24 e^5\right ) \log \left (\frac {2}{x}\right )+\left (-299-120 e^5-12 e^{10}\right ) \log ^2\left (\frac {2}{x}\right )}{\log ^2\left (\frac {2}{x}\right )}\right )} \, dx=e^x+\log \left (\log \left (1-12 \left (-5-e^5+\frac {e^x}{\log \left (\frac {2}{x}\right )}\right )^2\right )\right ) \] Output:
ln(ln(1-6*(exp(x)/ln(2/x)-exp(5)-5)*(2*exp(x)/ln(2/x)-2*exp(5)-10)))+exp(x )
Time = 0.28 (sec) , antiderivative size = 51, normalized size of antiderivative = 1.65 \[ \int \frac {24 e^{2 x}+\left (e^x \left (-120-24 e^5\right )+24 e^{2 x} x\right ) \log \left (\frac {2}{x}\right )+e^x \left (-120 x-24 e^5 x\right ) \log ^2\left (\frac {2}{x}\right )+\left (12 e^{3 x} x \log \left (\frac {2}{x}\right )+e^{2 x} \left (-120 x-24 e^5 x\right ) \log ^2\left (\frac {2}{x}\right )+e^x \left (299 x+120 e^5 x+12 e^{10} x\right ) \log ^3\left (\frac {2}{x}\right )\right ) \log \left (\frac {-12 e^{2 x}+e^x \left (120+24 e^5\right ) \log \left (\frac {2}{x}\right )+\left (-299-120 e^5-12 e^{10}\right ) \log ^2\left (\frac {2}{x}\right )}{\log ^2\left (\frac {2}{x}\right )}\right )}{\left (12 e^{2 x} x \log \left (\frac {2}{x}\right )+e^x \left (-120 x-24 e^5 x\right ) \log ^2\left (\frac {2}{x}\right )+\left (299 x+120 e^5 x+12 e^{10} x\right ) \log ^3\left (\frac {2}{x}\right )\right ) \log \left (\frac {-12 e^{2 x}+e^x \left (120+24 e^5\right ) \log \left (\frac {2}{x}\right )+\left (-299-120 e^5-12 e^{10}\right ) \log ^2\left (\frac {2}{x}\right )}{\log ^2\left (\frac {2}{x}\right )}\right )} \, dx=e^x+\log \left (\log \left (-299-120 e^5-12 e^{10}-\frac {12 e^{2 x}}{\log ^2\left (\frac {2}{x}\right )}+\frac {24 e^x \left (5+e^5\right )}{\log \left (\frac {2}{x}\right )}\right )\right ) \] Input:
Integrate[(24*E^(2*x) + (E^x*(-120 - 24*E^5) + 24*E^(2*x)*x)*Log[2/x] + E^ x*(-120*x - 24*E^5*x)*Log[2/x]^2 + (12*E^(3*x)*x*Log[2/x] + E^(2*x)*(-120* x - 24*E^5*x)*Log[2/x]^2 + E^x*(299*x + 120*E^5*x + 12*E^10*x)*Log[2/x]^3) *Log[(-12*E^(2*x) + E^x*(120 + 24*E^5)*Log[2/x] + (-299 - 120*E^5 - 12*E^1 0)*Log[2/x]^2)/Log[2/x]^2])/((12*E^(2*x)*x*Log[2/x] + E^x*(-120*x - 24*E^5 *x)*Log[2/x]^2 + (299*x + 120*E^5*x + 12*E^10*x)*Log[2/x]^3)*Log[(-12*E^(2 *x) + E^x*(120 + 24*E^5)*Log[2/x] + (-299 - 120*E^5 - 12*E^10)*Log[2/x]^2) /Log[2/x]^2]),x]
Output:
E^x + Log[Log[-299 - 120*E^5 - 12*E^10 - (12*E^(2*x))/Log[2/x]^2 + (24*E^x *(5 + E^5))/Log[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.
| \(\displaystyle \int \frac {24 e^{2 x}+e^x \left (-24 e^5 x-120 x\right ) \log ^2\left (\frac {2}{x}\right )+\left (e^x \left (12 e^{10} x+120 e^5 x+299 x\right ) \log ^3\left (\frac {2}{x}\right )+e^{2 x} \left (-24 e^5 x-120 x\right ) \log ^2\left (\frac {2}{x}\right )+12 e^{3 x} x \log \left (\frac {2}{x}\right )\right ) \log \left (\frac {-12 e^{2 x}+\left (-299-120 e^5-12 e^{10}\right ) \log ^2\left (\frac {2}{x}\right )+\left (120+24 e^5\right ) e^x \log \left (\frac {2}{x}\right )}{\log ^2\left (\frac {2}{x}\right )}\right )+\left (24 e^{2 x} x+\left (-120-24 e^5\right ) e^x\right ) \log \left (\frac {2}{x}\right )}{\left (\left (12 e^{10} x+120 e^5 x+299 x\right ) \log ^3\left (\frac {2}{x}\right )+e^x \left (-24 e^5 x-120 x\right ) \log ^2\left (\frac {2}{x}\right )+12 e^{2 x} x \log \left (\frac {2}{x}\right )\right ) \log \left (\frac {-12 e^{2 x}+\left (-299-120 e^5-12 e^{10}\right ) \log ^2\left (\frac {2}{x}\right )+\left (120+24 e^5\right ) e^x \log \left (\frac {2}{x}\right )}{\log ^2\left (\frac {2}{x}\right )}\right )} \, dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (e^x+\frac {2 \left (x \log \left (\frac {2}{x}\right )+1\right )}{x \log \left (\frac {2}{x}\right ) \log \left (-\frac {12 e^{2 x}}{\log ^2\left (\frac {2}{x}\right )}+\frac {24 \left (5+e^5\right ) e^x}{\log \left (\frac {2}{x}\right )}-299 \left (1+\frac {12}{299} e^5 \left (10+e^5\right )\right )\right )}+\frac {2 \left (60 \left (1+\frac {e^5}{5}\right ) e^x-299 \left (1+\frac {12}{299} e^5 \left (10+e^5\right )\right ) \log \left (\frac {2}{x}\right )\right ) \left (x \log \left (\frac {2}{x}\right )+1\right )}{x \left (12 e^{2 x}+299 \left (1+\frac {12}{299} e^5 \left (10+e^5\right )\right ) \log ^2\left (\frac {2}{x}\right )-120 \left (1+\frac {e^5}{5}\right ) e^x \log \left (\frac {2}{x}\right )\right ) \log \left (-\frac {12 e^{2 x}}{\log ^2\left (\frac {2}{x}\right )}+\frac {24 \left (5+e^5\right ) e^x}{\log \left (\frac {2}{x}\right )}-299 \left (1+\frac {12}{299} e^5 \left (10+e^5\right )\right )\right )}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle 2 \int \frac {1}{\log \left (-299 \left (1+\frac {12}{299} e^5 \left (10+e^5\right )\right )+\frac {24 e^x \left (5+e^5\right )}{\log \left (\frac {2}{x}\right )}-\frac {12 e^{2 x}}{\log ^2\left (\frac {2}{x}\right )}\right )}dx+2 \int \frac {1}{x \log \left (\frac {2}{x}\right ) \log \left (-299 \left (1+\frac {12}{299} e^5 \left (10+e^5\right )\right )+\frac {24 e^x \left (5+e^5\right )}{\log \left (\frac {2}{x}\right )}-\frac {12 e^{2 x}}{\log ^2\left (\frac {2}{x}\right )}\right )}dx+24 \left (5+e^5\right ) \int \frac {e^x}{x \left (299 \left (1+\frac {12}{299} e^5 \left (10+e^5\right )\right ) \log ^2\left (\frac {2}{x}\right )-120 e^x \left (1+\frac {e^5}{5}\right ) \log \left (\frac {2}{x}\right )+12 e^{2 x}\right ) \log \left (-299 \left (1+\frac {12}{299} e^5 \left (10+e^5\right )\right )+\frac {24 e^x \left (5+e^5\right )}{\log \left (\frac {2}{x}\right )}-\frac {12 e^{2 x}}{\log ^2\left (\frac {2}{x}\right )}\right )}dx+24 \left (5+e^5\right ) \int \frac {e^x \log \left (\frac {2}{x}\right )}{\left (299 \left (1+\frac {12}{299} e^5 \left (10+e^5\right )\right ) \log ^2\left (\frac {2}{x}\right )-120 e^x \left (1+\frac {e^5}{5}\right ) \log \left (\frac {2}{x}\right )+12 e^{2 x}\right ) \log \left (-299 \left (1+\frac {12}{299} e^5 \left (10+e^5\right )\right )+\frac {24 e^x \left (5+e^5\right )}{\log \left (\frac {2}{x}\right )}-\frac {12 e^{2 x}}{\log ^2\left (\frac {2}{x}\right )}\right )}dx-2 \left (299+120 e^5+12 e^{10}\right ) \int \frac {\log \left (\frac {2}{x}\right )}{x \left (299 \left (1+\frac {12}{299} e^5 \left (10+e^5\right )\right ) \log ^2\left (\frac {2}{x}\right )-120 e^x \left (1+\frac {e^5}{5}\right ) \log \left (\frac {2}{x}\right )+12 e^{2 x}\right ) \log \left (-299 \left (1+\frac {12}{299} e^5 \left (10+e^5\right )\right )+\frac {24 e^x \left (5+e^5\right )}{\log \left (\frac {2}{x}\right )}-\frac {12 e^{2 x}}{\log ^2\left (\frac {2}{x}\right )}\right )}dx-2 \left (299+120 e^5+12 e^{10}\right ) \int \frac {\log ^2\left (\frac {2}{x}\right )}{\left (299 \left (1+\frac {12}{299} e^5 \left (10+e^5\right )\right ) \log ^2\left (\frac {2}{x}\right )-120 e^x \left (1+\frac {e^5}{5}\right ) \log \left (\frac {2}{x}\right )+12 e^{2 x}\right ) \log \left (-299 \left (1+\frac {12}{299} e^5 \left (10+e^5\right )\right )+\frac {24 e^x \left (5+e^5\right )}{\log \left (\frac {2}{x}\right )}-\frac {12 e^{2 x}}{\log ^2\left (\frac {2}{x}\right )}\right )}dx+e^x\) |
Input:
Int[(24*E^(2*x) + (E^x*(-120 - 24*E^5) + 24*E^(2*x)*x)*Log[2/x] + E^x*(-12 0*x - 24*E^5*x)*Log[2/x]^2 + (12*E^(3*x)*x*Log[2/x] + E^(2*x)*(-120*x - 24 *E^5*x)*Log[2/x]^2 + E^x*(299*x + 120*E^5*x + 12*E^10*x)*Log[2/x]^3)*Log[( -12*E^(2*x) + E^x*(120 + 24*E^5)*Log[2/x] + (-299 - 120*E^5 - 12*E^10)*Log [2/x]^2)/Log[2/x]^2])/((12*E^(2*x)*x*Log[2/x] + E^x*(-120*x - 24*E^5*x)*Lo g[2/x]^2 + (299*x + 120*E^5*x + 12*E^10*x)*Log[2/x]^3)*Log[(-12*E^(2*x) + E^x*(120 + 24*E^5)*Log[2/x] + (-299 - 120*E^5 - 12*E^10)*Log[2/x]^2)/Log[2 /x]^2]),x]
Output:
$Aborted
Time = 79.33 (sec) , antiderivative size = 58, normalized size of antiderivative = 1.87
| method | result | size |
| parallelrisch | \(\ln \left (\ln \left (\frac {\left (-12 \,{\mathrm e}^{10}-120 \,{\mathrm e}^{5}-299\right ) \ln \left (\frac {2}{x}\right )^{2}+\left (24 \,{\mathrm e}^{5}+120\right ) {\mathrm e}^{x} \ln \left (\frac {2}{x}\right )-12 \,{\mathrm e}^{2 x}}{\ln \left (\frac {2}{x}\right )^{2}}\right )\right )+{\mathrm e}^{x}\) | \(58\) |
| risch | \(\text {Expression too large to display}\) | \(1009\) |
Input:
int((((12*x*exp(5)^2+120*x*exp(5)+299*x)*exp(x)*ln(2/x)^3+(-24*x*exp(5)-12 0*x)*exp(x)^2*ln(2/x)^2+12*x*exp(x)^3*ln(2/x))*ln(((-12*exp(5)^2-120*exp(5 )-299)*ln(2/x)^2+(24*exp(5)+120)*exp(x)*ln(2/x)-12*exp(x)^2)/ln(2/x)^2)+(- 24*x*exp(5)-120*x)*exp(x)*ln(2/x)^2+(24*x*exp(x)^2+(-24*exp(5)-120)*exp(x) )*ln(2/x)+24*exp(x)^2)/((12*x*exp(5)^2+120*x*exp(5)+299*x)*ln(2/x)^3+(-24* x*exp(5)-120*x)*exp(x)*ln(2/x)^2+12*x*exp(x)^2*ln(2/x))/ln(((-12*exp(5)^2- 120*exp(5)-299)*ln(2/x)^2+(24*exp(5)+120)*exp(x)*ln(2/x)-12*exp(x)^2)/ln(2 /x)^2),x,method=_RETURNVERBOSE)
Output:
ln(ln(((-12*exp(5)^2-120*exp(5)-299)*ln(2/x)^2+(24*exp(5)+120)*exp(x)*ln(2 /x)-12*exp(x)^2)/ln(2/x)^2))+exp(x)
Time = 0.13 (sec) , antiderivative size = 55, normalized size of antiderivative = 1.77 \[ \int \frac {24 e^{2 x}+\left (e^x \left (-120-24 e^5\right )+24 e^{2 x} x\right ) \log \left (\frac {2}{x}\right )+e^x \left (-120 x-24 e^5 x\right ) \log ^2\left (\frac {2}{x}\right )+\left (12 e^{3 x} x \log \left (\frac {2}{x}\right )+e^{2 x} \left (-120 x-24 e^5 x\right ) \log ^2\left (\frac {2}{x}\right )+e^x \left (299 x+120 e^5 x+12 e^{10} x\right ) \log ^3\left (\frac {2}{x}\right )\right ) \log \left (\frac {-12 e^{2 x}+e^x \left (120+24 e^5\right ) \log \left (\frac {2}{x}\right )+\left (-299-120 e^5-12 e^{10}\right ) \log ^2\left (\frac {2}{x}\right )}{\log ^2\left (\frac {2}{x}\right )}\right )}{\left (12 e^{2 x} x \log \left (\frac {2}{x}\right )+e^x \left (-120 x-24 e^5 x\right ) \log ^2\left (\frac {2}{x}\right )+\left (299 x+120 e^5 x+12 e^{10} x\right ) \log ^3\left (\frac {2}{x}\right )\right ) \log \left (\frac {-12 e^{2 x}+e^x \left (120+24 e^5\right ) \log \left (\frac {2}{x}\right )+\left (-299-120 e^5-12 e^{10}\right ) \log ^2\left (\frac {2}{x}\right )}{\log ^2\left (\frac {2}{x}\right )}\right )} \, dx=e^{x} + \log \left (\log \left (\frac {24 \, {\left (e^{5} + 5\right )} e^{x} \log \left (\frac {2}{x}\right ) - {\left (12 \, e^{10} + 120 \, e^{5} + 299\right )} \log \left (\frac {2}{x}\right )^{2} - 12 \, e^{\left (2 \, x\right )}}{\log \left (\frac {2}{x}\right )^{2}}\right )\right ) \] Input:
integrate((((12*x*exp(5)^2+120*x*exp(5)+299*x)*exp(x)*log(2/x)^3+(-24*x*ex p(5)-120*x)*exp(x)^2*log(2/x)^2+12*x*exp(x)^3*log(2/x))*log(((-12*exp(5)^2 -120*exp(5)-299)*log(2/x)^2+(24*exp(5)+120)*exp(x)*log(2/x)-12*exp(x)^2)/l og(2/x)^2)+(-24*x*exp(5)-120*x)*exp(x)*log(2/x)^2+(24*x*exp(x)^2+(-24*exp( 5)-120)*exp(x))*log(2/x)+24*exp(x)^2)/((12*x*exp(5)^2+120*x*exp(5)+299*x)* log(2/x)^3+(-24*x*exp(5)-120*x)*exp(x)*log(2/x)^2+12*x*exp(x)^2*log(2/x))/ log(((-12*exp(5)^2-120*exp(5)-299)*log(2/x)^2+(24*exp(5)+120)*exp(x)*log(2 /x)-12*exp(x)^2)/log(2/x)^2),x, algorithm="fricas")
Output:
e^x + log(log((24*(e^5 + 5)*e^x*log(2/x) - (12*e^10 + 120*e^5 + 299)*log(2 /x)^2 - 12*e^(2*x))/log(2/x)^2))
Time = 3.45 (sec) , antiderivative size = 54, normalized size of antiderivative = 1.74 \[ \int \frac {24 e^{2 x}+\left (e^x \left (-120-24 e^5\right )+24 e^{2 x} x\right ) \log \left (\frac {2}{x}\right )+e^x \left (-120 x-24 e^5 x\right ) \log ^2\left (\frac {2}{x}\right )+\left (12 e^{3 x} x \log \left (\frac {2}{x}\right )+e^{2 x} \left (-120 x-24 e^5 x\right ) \log ^2\left (\frac {2}{x}\right )+e^x \left (299 x+120 e^5 x+12 e^{10} x\right ) \log ^3\left (\frac {2}{x}\right )\right ) \log \left (\frac {-12 e^{2 x}+e^x \left (120+24 e^5\right ) \log \left (\frac {2}{x}\right )+\left (-299-120 e^5-12 e^{10}\right ) \log ^2\left (\frac {2}{x}\right )}{\log ^2\left (\frac {2}{x}\right )}\right )}{\left (12 e^{2 x} x \log \left (\frac {2}{x}\right )+e^x \left (-120 x-24 e^5 x\right ) \log ^2\left (\frac {2}{x}\right )+\left (299 x+120 e^5 x+12 e^{10} x\right ) \log ^3\left (\frac {2}{x}\right )\right ) \log \left (\frac {-12 e^{2 x}+e^x \left (120+24 e^5\right ) \log \left (\frac {2}{x}\right )+\left (-299-120 e^5-12 e^{10}\right ) \log ^2\left (\frac {2}{x}\right )}{\log ^2\left (\frac {2}{x}\right )}\right )} \, dx=e^{x} + \log {\left (\log {\left (\frac {- 12 e^{2 x} + \left (120 + 24 e^{5}\right ) e^{x} \log {\left (\frac {2}{x} \right )} + \left (- 12 e^{10} - 120 e^{5} - 299\right ) \log {\left (\frac {2}{x} \right )}^{2}}{\log {\left (\frac {2}{x} \right )}^{2}} \right )} \right )} \] Input:
integrate((((12*x*exp(5)**2+120*x*exp(5)+299*x)*exp(x)*ln(2/x)**3+(-24*x*e xp(5)-120*x)*exp(x)**2*ln(2/x)**2+12*x*exp(x)**3*ln(2/x))*ln(((-12*exp(5)* *2-120*exp(5)-299)*ln(2/x)**2+(24*exp(5)+120)*exp(x)*ln(2/x)-12*exp(x)**2) /ln(2/x)**2)+(-24*x*exp(5)-120*x)*exp(x)*ln(2/x)**2+(24*x*exp(x)**2+(-24*e xp(5)-120)*exp(x))*ln(2/x)+24*exp(x)**2)/((12*x*exp(5)**2+120*x*exp(5)+299 *x)*ln(2/x)**3+(-24*x*exp(5)-120*x)*exp(x)*ln(2/x)**2+12*x*exp(x)**2*ln(2/ x))/ln(((-12*exp(5)**2-120*exp(5)-299)*ln(2/x)**2+(24*exp(5)+120)*exp(x)*l n(2/x)-12*exp(x)**2)/ln(2/x)**2),x)
Output:
exp(x) + log(log((-12*exp(2*x) + (120 + 24*exp(5))*exp(x)*log(2/x) + (-12* exp(10) - 120*exp(5) - 299)*log(2/x)**2)/log(2/x)**2))
Leaf count of result is larger than twice the leaf count of optimal. 92 vs. \(2 (28) = 56\).
Time = 0.26 (sec) , antiderivative size = 92, normalized size of antiderivative = 2.97 \[ \int \frac {24 e^{2 x}+\left (e^x \left (-120-24 e^5\right )+24 e^{2 x} x\right ) \log \left (\frac {2}{x}\right )+e^x \left (-120 x-24 e^5 x\right ) \log ^2\left (\frac {2}{x}\right )+\left (12 e^{3 x} x \log \left (\frac {2}{x}\right )+e^{2 x} \left (-120 x-24 e^5 x\right ) \log ^2\left (\frac {2}{x}\right )+e^x \left (299 x+120 e^5 x+12 e^{10} x\right ) \log ^3\left (\frac {2}{x}\right )\right ) \log \left (\frac {-12 e^{2 x}+e^x \left (120+24 e^5\right ) \log \left (\frac {2}{x}\right )+\left (-299-120 e^5-12 e^{10}\right ) \log ^2\left (\frac {2}{x}\right )}{\log ^2\left (\frac {2}{x}\right )}\right )}{\left (12 e^{2 x} x \log \left (\frac {2}{x}\right )+e^x \left (-120 x-24 e^5 x\right ) \log ^2\left (\frac {2}{x}\right )+\left (299 x+120 e^5 x+12 e^{10} x\right ) \log ^3\left (\frac {2}{x}\right )\right ) \log \left (\frac {-12 e^{2 x}+e^x \left (120+24 e^5\right ) \log \left (\frac {2}{x}\right )+\left (-299-120 e^5-12 e^{10}\right ) \log ^2\left (\frac {2}{x}\right )}{\log ^2\left (\frac {2}{x}\right )}\right )} \, dx=e^{x} + \log \left (\log \left (24 \, {\left (e^{5} + 5\right )} e^{x} \log \left (2\right ) - {\left (12 \, e^{10} + 120 \, e^{5} + 299\right )} \log \left (2\right )^{2} - {\left (12 \, e^{10} + 120 \, e^{5} + 299\right )} \log \left (x\right )^{2} - 2 \, {\left (12 \, {\left (e^{5} + 5\right )} e^{x} - {\left (12 \, e^{10} + 120 \, e^{5} + 299\right )} \log \left (2\right )\right )} \log \left (x\right ) - 12 \, e^{\left (2 \, x\right )}\right ) - 2 \, \log \left (-\log \left (2\right ) + \log \left (x\right )\right )\right ) \] Input:
integrate((((12*x*exp(5)^2+120*x*exp(5)+299*x)*exp(x)*log(2/x)^3+(-24*x*ex p(5)-120*x)*exp(x)^2*log(2/x)^2+12*x*exp(x)^3*log(2/x))*log(((-12*exp(5)^2 -120*exp(5)-299)*log(2/x)^2+(24*exp(5)+120)*exp(x)*log(2/x)-12*exp(x)^2)/l og(2/x)^2)+(-24*x*exp(5)-120*x)*exp(x)*log(2/x)^2+(24*x*exp(x)^2+(-24*exp( 5)-120)*exp(x))*log(2/x)+24*exp(x)^2)/((12*x*exp(5)^2+120*x*exp(5)+299*x)* log(2/x)^3+(-24*x*exp(5)-120*x)*exp(x)*log(2/x)^2+12*x*exp(x)^2*log(2/x))/ log(((-12*exp(5)^2-120*exp(5)-299)*log(2/x)^2+(24*exp(5)+120)*exp(x)*log(2 /x)-12*exp(x)^2)/log(2/x)^2),x, algorithm="maxima")
Output:
e^x + log(log(24*(e^5 + 5)*e^x*log(2) - (12*e^10 + 120*e^5 + 299)*log(2)^2 - (12*e^10 + 120*e^5 + 299)*log(x)^2 - 2*(12*(e^5 + 5)*e^x - (12*e^10 + 1 20*e^5 + 299)*log(2))*log(x) - 12*e^(2*x)) - 2*log(-log(2) + log(x)))
Timed out. \[ \int \frac {24 e^{2 x}+\left (e^x \left (-120-24 e^5\right )+24 e^{2 x} x\right ) \log \left (\frac {2}{x}\right )+e^x \left (-120 x-24 e^5 x\right ) \log ^2\left (\frac {2}{x}\right )+\left (12 e^{3 x} x \log \left (\frac {2}{x}\right )+e^{2 x} \left (-120 x-24 e^5 x\right ) \log ^2\left (\frac {2}{x}\right )+e^x \left (299 x+120 e^5 x+12 e^{10} x\right ) \log ^3\left (\frac {2}{x}\right )\right ) \log \left (\frac {-12 e^{2 x}+e^x \left (120+24 e^5\right ) \log \left (\frac {2}{x}\right )+\left (-299-120 e^5-12 e^{10}\right ) \log ^2\left (\frac {2}{x}\right )}{\log ^2\left (\frac {2}{x}\right )}\right )}{\left (12 e^{2 x} x \log \left (\frac {2}{x}\right )+e^x \left (-120 x-24 e^5 x\right ) \log ^2\left (\frac {2}{x}\right )+\left (299 x+120 e^5 x+12 e^{10} x\right ) \log ^3\left (\frac {2}{x}\right )\right ) \log \left (\frac {-12 e^{2 x}+e^x \left (120+24 e^5\right ) \log \left (\frac {2}{x}\right )+\left (-299-120 e^5-12 e^{10}\right ) \log ^2\left (\frac {2}{x}\right )}{\log ^2\left (\frac {2}{x}\right )}\right )} \, dx=\text {Timed out} \] Input:
integrate((((12*x*exp(5)^2+120*x*exp(5)+299*x)*exp(x)*log(2/x)^3+(-24*x*ex p(5)-120*x)*exp(x)^2*log(2/x)^2+12*x*exp(x)^3*log(2/x))*log(((-12*exp(5)^2 -120*exp(5)-299)*log(2/x)^2+(24*exp(5)+120)*exp(x)*log(2/x)-12*exp(x)^2)/l og(2/x)^2)+(-24*x*exp(5)-120*x)*exp(x)*log(2/x)^2+(24*x*exp(x)^2+(-24*exp( 5)-120)*exp(x))*log(2/x)+24*exp(x)^2)/((12*x*exp(5)^2+120*x*exp(5)+299*x)* log(2/x)^3+(-24*x*exp(5)-120*x)*exp(x)*log(2/x)^2+12*x*exp(x)^2*log(2/x))/ log(((-12*exp(5)^2-120*exp(5)-299)*log(2/x)^2+(24*exp(5)+120)*exp(x)*log(2 /x)-12*exp(x)^2)/log(2/x)^2),x, algorithm="giac")
Output:
Timed out
Time = 4.59 (sec) , antiderivative size = 57, normalized size of antiderivative = 1.84 \[ \int \frac {24 e^{2 x}+\left (e^x \left (-120-24 e^5\right )+24 e^{2 x} x\right ) \log \left (\frac {2}{x}\right )+e^x \left (-120 x-24 e^5 x\right ) \log ^2\left (\frac {2}{x}\right )+\left (12 e^{3 x} x \log \left (\frac {2}{x}\right )+e^{2 x} \left (-120 x-24 e^5 x\right ) \log ^2\left (\frac {2}{x}\right )+e^x \left (299 x+120 e^5 x+12 e^{10} x\right ) \log ^3\left (\frac {2}{x}\right )\right ) \log \left (\frac {-12 e^{2 x}+e^x \left (120+24 e^5\right ) \log \left (\frac {2}{x}\right )+\left (-299-120 e^5-12 e^{10}\right ) \log ^2\left (\frac {2}{x}\right )}{\log ^2\left (\frac {2}{x}\right )}\right )}{\left (12 e^{2 x} x \log \left (\frac {2}{x}\right )+e^x \left (-120 x-24 e^5 x\right ) \log ^2\left (\frac {2}{x}\right )+\left (299 x+120 e^5 x+12 e^{10} x\right ) \log ^3\left (\frac {2}{x}\right )\right ) \log \left (\frac {-12 e^{2 x}+e^x \left (120+24 e^5\right ) \log \left (\frac {2}{x}\right )+\left (-299-120 e^5-12 e^{10}\right ) \log ^2\left (\frac {2}{x}\right )}{\log ^2\left (\frac {2}{x}\right )}\right )} \, dx=\ln \left (\ln \left (-\frac {\left (120\,{\mathrm {e}}^5+12\,{\mathrm {e}}^{10}+299\right )\,{\ln \left (\frac {2}{x}\right )}^2-{\mathrm {e}}^x\,\left (24\,{\mathrm {e}}^5+120\right )\,\ln \left (\frac {2}{x}\right )+12\,{\mathrm {e}}^{2\,x}}{{\ln \left (\frac {2}{x}\right )}^2}\right )\right )+{\mathrm {e}}^x \] Input:
int((24*exp(2*x) + log(-(12*exp(2*x) + log(2/x)^2*(120*exp(5) + 12*exp(10) + 299) - exp(x)*log(2/x)*(24*exp(5) + 120))/log(2/x)^2)*(12*x*exp(3*x)*lo g(2/x) - exp(2*x)*log(2/x)^2*(120*x + 24*x*exp(5)) + exp(x)*log(2/x)^3*(29 9*x + 120*x*exp(5) + 12*x*exp(10))) + log(2/x)*(24*x*exp(2*x) - exp(x)*(24 *exp(5) + 120)) - exp(x)*log(2/x)^2*(120*x + 24*x*exp(5)))/(log(-(12*exp(2 *x) + log(2/x)^2*(120*exp(5) + 12*exp(10) + 299) - exp(x)*log(2/x)*(24*exp (5) + 120))/log(2/x)^2)*(log(2/x)^3*(299*x + 120*x*exp(5) + 12*x*exp(10)) - exp(x)*log(2/x)^2*(120*x + 24*x*exp(5)) + 12*x*exp(2*x)*log(2/x))),x)
Output:
log(log(-(12*exp(2*x) + log(2/x)^2*(120*exp(5) + 12*exp(10) + 299) - exp(x )*log(2/x)*(24*exp(5) + 120))/log(2/x)^2)) + exp(x)
Time = 0.17 (sec) , antiderivative size = 84, normalized size of antiderivative = 2.71 \[ \int \frac {24 e^{2 x}+\left (e^x \left (-120-24 e^5\right )+24 e^{2 x} x\right ) \log \left (\frac {2}{x}\right )+e^x \left (-120 x-24 e^5 x\right ) \log ^2\left (\frac {2}{x}\right )+\left (12 e^{3 x} x \log \left (\frac {2}{x}\right )+e^{2 x} \left (-120 x-24 e^5 x\right ) \log ^2\left (\frac {2}{x}\right )+e^x \left (299 x+120 e^5 x+12 e^{10} x\right ) \log ^3\left (\frac {2}{x}\right )\right ) \log \left (\frac {-12 e^{2 x}+e^x \left (120+24 e^5\right ) \log \left (\frac {2}{x}\right )+\left (-299-120 e^5-12 e^{10}\right ) \log ^2\left (\frac {2}{x}\right )}{\log ^2\left (\frac {2}{x}\right )}\right )}{\left (12 e^{2 x} x \log \left (\frac {2}{x}\right )+e^x \left (-120 x-24 e^5 x\right ) \log ^2\left (\frac {2}{x}\right )+\left (299 x+120 e^5 x+12 e^{10} x\right ) \log ^3\left (\frac {2}{x}\right )\right ) \log \left (\frac {-12 e^{2 x}+e^x \left (120+24 e^5\right ) \log \left (\frac {2}{x}\right )+\left (-299-120 e^5-12 e^{10}\right ) \log ^2\left (\frac {2}{x}\right )}{\log ^2\left (\frac {2}{x}\right )}\right )} \, dx=e^{x}+\mathrm {log}\left (\mathrm {log}\left (\frac {-12 e^{2 x}+24 e^{x} \mathrm {log}\left (\frac {2}{x}\right ) e^{5}+120 e^{x} \mathrm {log}\left (\frac {2}{x}\right )-12 \mathrm {log}\left (\frac {2}{x}\right )^{2} e^{10}-120 \mathrm {log}\left (\frac {2}{x}\right )^{2} e^{5}-299 \mathrm {log}\left (\frac {2}{x}\right )^{2}}{\mathrm {log}\left (\frac {2}{x}\right )^{2}}\right )\right ) \] Input:
int((((12*x*exp(5)^2+120*x*exp(5)+299*x)*exp(x)*log(2/x)^3+(-24*x*exp(5)-1 20*x)*exp(x)^2*log(2/x)^2+12*x*exp(x)^3*log(2/x))*log(((-12*exp(5)^2-120*e xp(5)-299)*log(2/x)^2+(24*exp(5)+120)*exp(x)*log(2/x)-12*exp(x)^2)/log(2/x )^2)+(-24*x*exp(5)-120*x)*exp(x)*log(2/x)^2+(24*x*exp(x)^2+(-24*exp(5)-120 )*exp(x))*log(2/x)+24*exp(x)^2)/((12*x*exp(5)^2+120*x*exp(5)+299*x)*log(2/ x)^3+(-24*x*exp(5)-120*x)*exp(x)*log(2/x)^2+12*x*exp(x)^2*log(2/x))/log((( -12*exp(5)^2-120*exp(5)-299)*log(2/x)^2+(24*exp(5)+120)*exp(x)*log(2/x)-12 *exp(x)^2)/log(2/x)^2),x)
Output:
e**x + log(log(( - 12*e**(2*x) + 24*e**x*log(2/x)*e**5 + 120*e**x*log(2/x) - 12*log(2/x)**2*e**10 - 120*log(2/x)**2*e**5 - 299*log(2/x)**2)/log(2/x) **2))