\(\int \frac {24 e^{2 x}+(e^x (-120-24 e^5)+24 e^{2 x} x) \log (\frac {2}{x})+e^x (-120 x-24 e^5 x) \log ^2(\frac {2}{x})+(12 e^{3 x} x \log (\frac {2}{x})+e^{2 x} (-120 x-24 e^5 x) \log ^2(\frac {2}{x})+e^x (299 x+120 e^5 x+12 e^{10} x) \log ^3(\frac {2}{x})) \log (\frac {-12 e^{2 x}+e^x (120+24 e^5) \log (\frac {2}{x})+(-299-120 e^5-12 e^{10}) \log ^2(\frac {2}{x})}{\log ^2(\frac {2}{x})})}{(12 e^{2 x} x \log (\frac {2}{x})+e^x (-120 x-24 e^5 x) \log ^2(\frac {2}{x})+(299 x+120 e^5 x+12 e^{10} x) \log ^3(\frac {2}{x})) \log (\frac {-12 e^{2 x}+e^x (120+24 e^5) \log (\frac {2}{x})+(-299-120 e^5-12 e^{10}) \log ^2(\frac {2}{x})}{\log ^2(\frac {2}{x})})} \, dx\) [9420]

Optimal result

Integrand size = 304, antiderivative size = 31 \[ \int \frac {24 e^{2 x}+\left (e^x \left (-120-24 e^5\right )+24 e^{2 x} x\right ) \log \left (\frac {2}{x}\right )+e^x \left (-120 x-24 e^5 x\right ) \log ^2\left (\frac {2}{x}\right )+\left (12 e^{3 x} x \log \left (\frac {2}{x}\right )+e^{2 x} \left (-120 x-24 e^5 x\right ) \log ^2\left (\frac {2}{x}\right )+e^x \left (299 x+120 e^5 x+12 e^{10} x\right ) \log ^3\left (\frac {2}{x}\right )\right ) \log \left (\frac {-12 e^{2 x}+e^x \left (120+24 e^5\right ) \log \left (\frac {2}{x}\right )+\left (-299-120 e^5-12 e^{10}\right ) \log ^2\left (\frac {2}{x}\right )}{\log ^2\left (\frac {2}{x}\right )}\right )}{\left (12 e^{2 x} x \log \left (\frac {2}{x}\right )+e^x \left (-120 x-24 e^5 x\right ) \log ^2\left (\frac {2}{x}\right )+\left (299 x+120 e^5 x+12 e^{10} x\right ) \log ^3\left (\frac {2}{x}\right )\right ) \log \left (\frac {-12 e^{2 x}+e^x \left (120+24 e^5\right ) \log \left (\frac {2}{x}\right )+\left (-299-120 e^5-12 e^{10}\right ) \log ^2\left (\frac {2}{x}\right )}{\log ^2\left (\frac {2}{x}\right )}\right )} \, dx=e^x+\log \left (\log \left (1-12 \left (-5-e^5+\frac {e^x}{\log \left (\frac {2}{x}\right )}\right )^2\right )\right ) \]

[Out]

ln(ln(1-6*(exp(x)/ln(2/x)-exp(5)-5)*(2*exp(x)/ln(2/x)-2*exp(5)-10)))+exp(x)

Rubi [F]

\[ \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=\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 \]

[In]

Int[(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^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)*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]

[Out]

E^x + 2*Defer[Int][Log[-299*(1 + (12*E^5*(10 + E^5))/299) - (12*E^(2*x))/Log[2/x]^2 + (24*E^x*(5 + E^5))/Log[2
/x]]^(-1), x] + 2*Defer[Int][1/(x*Log[2/x]*Log[-299*(1 + (12*E^5*(10 + E^5))/299) - (12*E^(2*x))/Log[2/x]^2 +
(24*E^x*(5 + E^5))/Log[2/x]]), x] + 24*(5 + E^5)*Defer[Int][E^x/(x*(12*E^(2*x) - 120*E^x*(1 + E^5/5)*Log[2/x]
+ 299*(1 + (12*E^5*(10 + E^5))/299)*Log[2/x]^2)*Log[-299*(1 + (12*E^5*(10 + E^5))/299) - (12*E^(2*x))/Log[2/x]
^2 + (24*E^x*(5 + E^5))/Log[2/x]]), x] + 24*(5 + E^5)*Defer[Int][(E^x*Log[2/x])/((12*E^(2*x) - 120*E^x*(1 + E^
5/5)*Log[2/x] + 299*(1 + (12*E^5*(10 + E^5))/299)*Log[2/x]^2)*Log[-299*(1 + (12*E^5*(10 + E^5))/299) - (12*E^(
2*x))/Log[2/x]^2 + (24*E^x*(5 + E^5))/Log[2/x]]), x] - 2*(299 + 120*E^5 + 12*E^10)*Defer[Int][Log[2/x]/(x*(12*
E^(2*x) - 120*E^x*(1 + E^5/5)*Log[2/x] + 299*(1 + (12*E^5*(10 + E^5))/299)*Log[2/x]^2)*Log[-299*(1 + (12*E^5*(
10 + E^5))/299) - (12*E^(2*x))/Log[2/x]^2 + (24*E^x*(5 + E^5))/Log[2/x]]), x] - 2*(299 + 120*E^5 + 12*E^10)*De
fer[Int][Log[2/x]^2/((12*E^(2*x) - 120*E^x*(1 + E^5/5)*Log[2/x] + 299*(1 + (12*E^5*(10 + E^5))/299)*Log[2/x]^2
)*Log[-299*(1 + (12*E^5*(10 + E^5))/299) - (12*E^(2*x))/Log[2/x]^2 + (24*E^x*(5 + E^5))/Log[2/x]]), x]

Rubi steps \begin{align*} \text {integral}& = \int \left (e^x+\frac {2 \left (1+x \log \left (\frac {2}{x}\right )\right )}{x \log \left (\frac {2}{x}\right ) \log \left (-299 \left (1+\frac {12}{299} e^5 \left (10+e^5\right )\right )-\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 )}+\frac {2 \left (60 e^x \left (1+\frac {e^5}{5}\right )-299 \left (1+\frac {12}{299} e^5 \left (10+e^5\right )\right ) \log \left (\frac {2}{x}\right )\right ) \left (1+x \log \left (\frac {2}{x}\right )\right )}{x \left (12 e^{2 x}-120 e^x \left (1+\frac {e^5}{5}\right ) \log \left (\frac {2}{x}\right )+299 \left (1+\frac {12}{299} e^5 \left (10+e^5\right )\right ) \log ^2\left (\frac {2}{x}\right )\right ) \log \left (-299 \left (1+\frac {12}{299} e^5 \left (10+e^5\right )\right )-\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 ) \, dx \\ & = 2 \int \frac {1+x \log \left (\frac {2}{x}\right )}{x \log \left (\frac {2}{x}\right ) \log \left (-299 \left (1+\frac {12}{299} e^5 \left (10+e^5\right )\right )-\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 )} \, dx+2 \int \frac {\left (60 e^x \left (1+\frac {e^5}{5}\right )-299 \left (1+\frac {12}{299} e^5 \left (10+e^5\right )\right ) \log \left (\frac {2}{x}\right )\right ) \left (1+x \log \left (\frac {2}{x}\right )\right )}{x \left (12 e^{2 x}-120 e^x \left (1+\frac {e^5}{5}\right ) \log \left (\frac {2}{x}\right )+299 \left (1+\frac {12}{299} e^5 \left (10+e^5\right )\right ) \log ^2\left (\frac {2}{x}\right )\right ) \log \left (-299 \left (1+\frac {12}{299} e^5 \left (10+e^5\right )\right )-\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 )} \, dx+\int e^x \, dx \\ & = e^x+2 \int \left (\frac {1}{\log \left (-299 \left (1+\frac {12}{299} e^5 \left (10+e^5\right )\right )-\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 )}+\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 {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 ) \, dx+2 \int \left (\frac {12 e^x \left (5+e^5\right )}{x \left (12 e^{2 x}-120 e^x \left (1+\frac {e^5}{5}\right ) \log \left (\frac {2}{x}\right )+299 \left (1+\frac {12}{299} e^5 \left (10+e^5\right )\right ) \log ^2\left (\frac {2}{x}\right )\right ) \log \left (-299 \left (1+\frac {12}{299} e^5 \left (10+e^5\right )\right )-\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 )}+\frac {12 e^x \left (5+e^5\right ) \log \left (\frac {2}{x}\right )}{\left (12 e^{2 x}-120 e^x \left (1+\frac {e^5}{5}\right ) \log \left (\frac {2}{x}\right )+299 \left (1+\frac {12}{299} e^5 \left (10+e^5\right )\right ) \log ^2\left (\frac {2}{x}\right )\right ) \log \left (-299 \left (1+\frac {12}{299} e^5 \left (10+e^5\right )\right )-\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 )}+\frac {\left (-299-120 e^5-12 e^{10}\right ) \log \left (\frac {2}{x}\right )}{x \left (12 e^{2 x}-120 e^x \left (1+\frac {e^5}{5}\right ) \log \left (\frac {2}{x}\right )+299 \left (1+\frac {12}{299} e^5 \left (10+e^5\right )\right ) \log ^2\left (\frac {2}{x}\right )\right ) \log \left (-299 \left (1+\frac {12}{299} e^5 \left (10+e^5\right )\right )-\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 )}+\frac {\left (-299-120 e^5-12 e^{10}\right ) \log ^2\left (\frac {2}{x}\right )}{\left (12 e^{2 x}-120 e^x \left (1+\frac {e^5}{5}\right ) \log \left (\frac {2}{x}\right )+299 \left (1+\frac {12}{299} e^5 \left (10+e^5\right )\right ) \log ^2\left (\frac {2}{x}\right )\right ) \log \left (-299 \left (1+\frac {12}{299} e^5 \left (10+e^5\right )\right )-\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 ) \, dx \\ & = e^x+2 \int \frac {1}{\log \left (-299 \left (1+\frac {12}{299} e^5 \left (10+e^5\right )\right )-\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 )} \, 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 {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 )} \, dx+\left (24 \left (5+e^5\right )\right ) \int \frac {e^x}{x \left (12 e^{2 x}-120 e^x \left (1+\frac {e^5}{5}\right ) \log \left (\frac {2}{x}\right )+299 \left (1+\frac {12}{299} e^5 \left (10+e^5\right )\right ) \log ^2\left (\frac {2}{x}\right )\right ) \log \left (-299 \left (1+\frac {12}{299} e^5 \left (10+e^5\right )\right )-\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 )} \, dx+\left (24 \left (5+e^5\right )\right ) \int \frac {e^x \log \left (\frac {2}{x}\right )}{\left (12 e^{2 x}-120 e^x \left (1+\frac {e^5}{5}\right ) \log \left (\frac {2}{x}\right )+299 \left (1+\frac {12}{299} e^5 \left (10+e^5\right )\right ) \log ^2\left (\frac {2}{x}\right )\right ) \log \left (-299 \left (1+\frac {12}{299} e^5 \left (10+e^5\right )\right )-\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 )} \, dx-\left (2 \left (299+120 e^5+12 e^{10}\right )\right ) \int \frac {\log \left (\frac {2}{x}\right )}{x \left (12 e^{2 x}-120 e^x \left (1+\frac {e^5}{5}\right ) \log \left (\frac {2}{x}\right )+299 \left (1+\frac {12}{299} e^5 \left (10+e^5\right )\right ) \log ^2\left (\frac {2}{x}\right )\right ) \log \left (-299 \left (1+\frac {12}{299} e^5 \left (10+e^5\right )\right )-\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 )} \, dx-\left (2 \left (299+120 e^5+12 e^{10}\right )\right ) \int \frac {\log ^2\left (\frac {2}{x}\right )}{\left (12 e^{2 x}-120 e^x \left (1+\frac {e^5}{5}\right ) \log \left (\frac {2}{x}\right )+299 \left (1+\frac {12}{299} e^5 \left (10+e^5\right )\right ) \log ^2\left (\frac {2}{x}\right )\right ) \log \left (-299 \left (1+\frac {12}{299} e^5 \left (10+e^5\right )\right )-\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 )} \, dx \\ \end{align*}

Mathematica [A] (verified)

Time = 0.41 (sec) , antiderivative size = 51, normalized size of antiderivative = 1.65 \[ \int \frac {24 e^{2 x}+\left (e^x \left (-120-24 e^5\right )+24 e^{2 x} x\right ) \log \left (\frac {2}{x}\right )+e^x \left (-120 x-24 e^5 x\right ) \log ^2\left (\frac {2}{x}\right )+\left (12 e^{3 x} x \log \left (\frac {2}{x}\right )+e^{2 x} \left (-120 x-24 e^5 x\right ) \log ^2\left (\frac {2}{x}\right )+e^x \left (299 x+120 e^5 x+12 e^{10} x\right ) \log ^3\left (\frac {2}{x}\right )\right ) \log \left (\frac {-12 e^{2 x}+e^x \left (120+24 e^5\right ) \log \left (\frac {2}{x}\right )+\left (-299-120 e^5-12 e^{10}\right ) \log ^2\left (\frac {2}{x}\right )}{\log ^2\left (\frac {2}{x}\right )}\right )}{\left (12 e^{2 x} x \log \left (\frac {2}{x}\right )+e^x \left (-120 x-24 e^5 x\right ) \log ^2\left (\frac {2}{x}\right )+\left (299 x+120 e^5 x+12 e^{10} x\right ) \log ^3\left (\frac {2}{x}\right )\right ) \log \left (\frac {-12 e^{2 x}+e^x \left (120+24 e^5\right ) \log \left (\frac {2}{x}\right )+\left (-299-120 e^5-12 e^{10}\right ) \log ^2\left (\frac {2}{x}\right )}{\log ^2\left (\frac {2}{x}\right )}\right )} \, dx=e^x+\log \left (\log \left (-299-120 e^5-12 e^{10}-\frac {12 e^{2 x}}{\log ^2\left (\frac {2}{x}\right )}+\frac {24 e^x \left (5+e^5\right )}{\log \left (\frac {2}{x}\right )}\right )\right ) \]

[In]

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^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)*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]

[Out]

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]]]

Maple [A] (verified)

Time = 116.99 (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	\(\text {Expression too large to display}\)	\(1083\)

[In]

int((((12*x*exp(5)^2+120*x*exp(5)+299*x)*exp(x)*ln(2/x)^3+(-24*x*exp(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*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)

[Out]

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)

Fricas [A] (verification not implemented)

none

Time = 0.27 (sec) , antiderivative size = 55, normalized size of antiderivative = 1.77 \[ \int \frac {24 e^{2 x}+\left (e^x \left (-120-24 e^5\right )+24 e^{2 x} x\right ) \log \left (\frac {2}{x}\right )+e^x \left (-120 x-24 e^5 x\right ) \log ^2\left (\frac {2}{x}\right )+\left (12 e^{3 x} x \log \left (\frac {2}{x}\right )+e^{2 x} \left (-120 x-24 e^5 x\right ) \log ^2\left (\frac {2}{x}\right )+e^x \left (299 x+120 e^5 x+12 e^{10} x\right ) \log ^3\left (\frac {2}{x}\right )\right ) \log \left (\frac {-12 e^{2 x}+e^x \left (120+24 e^5\right ) \log \left (\frac {2}{x}\right )+\left (-299-120 e^5-12 e^{10}\right ) \log ^2\left (\frac {2}{x}\right )}{\log ^2\left (\frac {2}{x}\right )}\right )}{\left (12 e^{2 x} x \log \left (\frac {2}{x}\right )+e^x \left (-120 x-24 e^5 x\right ) \log ^2\left (\frac {2}{x}\right )+\left (299 x+120 e^5 x+12 e^{10} x\right ) \log ^3\left (\frac {2}{x}\right )\right ) \log \left (\frac {-12 e^{2 x}+e^x \left (120+24 e^5\right ) \log \left (\frac {2}{x}\right )+\left (-299-120 e^5-12 e^{10}\right ) \log ^2\left (\frac {2}{x}\right )}{\log ^2\left (\frac {2}{x}\right )}\right )} \, dx=e^{x} + \log \left (\log \left (\frac {24 \, {\left (e^{5} + 5\right )} e^{x} \log \left (\frac {2}{x}\right ) - {\left (12 \, e^{10} + 120 \, e^{5} + 299\right )} \log \left (\frac {2}{x}\right )^{2} - 12 \, e^{\left (2 \, x\right )}}{\log \left (\frac {2}{x}\right )^{2}}\right )\right ) \]

[In]

integrate((((12*x*exp(5)^2+120*x*exp(5)+299*x)*exp(x)*log(2/x)^3+(-24*x*exp(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)
/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,
algorithm="fricas")

[Out]

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))

Sympy [A] (verification not implemented)

Time = 3.30 (sec) , antiderivative size = 54, normalized size of antiderivative = 1.74 \[ \int \frac {24 e^{2 x}+\left (e^x \left (-120-24 e^5\right )+24 e^{2 x} x\right ) \log \left (\frac {2}{x}\right )+e^x \left (-120 x-24 e^5 x\right ) \log ^2\left (\frac {2}{x}\right )+\left (12 e^{3 x} x \log \left (\frac {2}{x}\right )+e^{2 x} \left (-120 x-24 e^5 x\right ) \log ^2\left (\frac {2}{x}\right )+e^x \left (299 x+120 e^5 x+12 e^{10} x\right ) \log ^3\left (\frac {2}{x}\right )\right ) \log \left (\frac {-12 e^{2 x}+e^x \left (120+24 e^5\right ) \log \left (\frac {2}{x}\right )+\left (-299-120 e^5-12 e^{10}\right ) \log ^2\left (\frac {2}{x}\right )}{\log ^2\left (\frac {2}{x}\right )}\right )}{\left (12 e^{2 x} x \log \left (\frac {2}{x}\right )+e^x \left (-120 x-24 e^5 x\right ) \log ^2\left (\frac {2}{x}\right )+\left (299 x+120 e^5 x+12 e^{10} x\right ) \log ^3\left (\frac {2}{x}\right )\right ) \log \left (\frac {-12 e^{2 x}+e^x \left (120+24 e^5\right ) \log \left (\frac {2}{x}\right )+\left (-299-120 e^5-12 e^{10}\right ) \log ^2\left (\frac {2}{x}\right )}{\log ^2\left (\frac {2}{x}\right )}\right )} \, dx=e^{x} + \log {\left (\log {\left (\frac {- 12 e^{2 x} + \left (120 + 24 e^{5}\right ) e^{x} \log {\left (\frac {2}{x} \right )} + \left (- 12 e^{10} - 120 e^{5} - 299\right ) \log {\left (\frac {2}{x} \right )}^{2}}{\log {\left (\frac {2}{x} \right )}^{2}} \right )} \right )} \]

[In]

integrate((((12*x*exp(5)**2+120*x*exp(5)+299*x)*exp(x)*ln(2/x)**3+(-24*x*exp(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*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*l
n(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)

[Out]

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))

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 92 vs. \(2 (28) = 56\).

Time = 0.44 (sec) , antiderivative size = 92, normalized size of antiderivative = 2.97 \[ \int \frac {24 e^{2 x}+\left (e^x \left (-120-24 e^5\right )+24 e^{2 x} x\right ) \log \left (\frac {2}{x}\right )+e^x \left (-120 x-24 e^5 x\right ) \log ^2\left (\frac {2}{x}\right )+\left (12 e^{3 x} x \log \left (\frac {2}{x}\right )+e^{2 x} \left (-120 x-24 e^5 x\right ) \log ^2\left (\frac {2}{x}\right )+e^x \left (299 x+120 e^5 x+12 e^{10} x\right ) \log ^3\left (\frac {2}{x}\right )\right ) \log \left (\frac {-12 e^{2 x}+e^x \left (120+24 e^5\right ) \log \left (\frac {2}{x}\right )+\left (-299-120 e^5-12 e^{10}\right ) \log ^2\left (\frac {2}{x}\right )}{\log ^2\left (\frac {2}{x}\right )}\right )}{\left (12 e^{2 x} x \log \left (\frac {2}{x}\right )+e^x \left (-120 x-24 e^5 x\right ) \log ^2\left (\frac {2}{x}\right )+\left (299 x+120 e^5 x+12 e^{10} x\right ) \log ^3\left (\frac {2}{x}\right )\right ) \log \left (\frac {-12 e^{2 x}+e^x \left (120+24 e^5\right ) \log \left (\frac {2}{x}\right )+\left (-299-120 e^5-12 e^{10}\right ) \log ^2\left (\frac {2}{x}\right )}{\log ^2\left (\frac {2}{x}\right )}\right )} \, dx=e^{x} + \log \left (\log \left (24 \, {\left (e^{5} + 5\right )} e^{x} \log \left (2\right ) - {\left (12 \, e^{10} + 120 \, e^{5} + 299\right )} \log \left (2\right )^{2} - {\left (12 \, e^{10} + 120 \, e^{5} + 299\right )} \log \left (x\right )^{2} - 2 \, {\left (12 \, {\left (e^{5} + 5\right )} e^{x} - {\left (12 \, e^{10} + 120 \, e^{5} + 299\right )} \log \left (2\right )\right )} \log \left (x\right ) - 12 \, e^{\left (2 \, x\right )}\right ) - 2 \, \log \left (-\log \left (2\right ) + \log \left (x\right )\right )\right ) \]

[In]

integrate((((12*x*exp(5)^2+120*x*exp(5)+299*x)*exp(x)*log(2/x)^3+(-24*x*exp(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)
/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,
algorithm="maxima")

[Out]

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 + 120*e^5 + 299)*log(2))*log(x) - 12*e^(2*x)) - 2*log(-log(2) + log(x)))

Giac [F(-1)]

Timed out. \[ \int \frac {24 e^{2 x}+\left (e^x \left (-120-24 e^5\right )+24 e^{2 x} x\right ) \log \left (\frac {2}{x}\right )+e^x \left (-120 x-24 e^5 x\right ) \log ^2\left (\frac {2}{x}\right )+\left (12 e^{3 x} x \log \left (\frac {2}{x}\right )+e^{2 x} \left (-120 x-24 e^5 x\right ) \log ^2\left (\frac {2}{x}\right )+e^x \left (299 x+120 e^5 x+12 e^{10} x\right ) \log ^3\left (\frac {2}{x}\right )\right ) \log \left (\frac {-12 e^{2 x}+e^x \left (120+24 e^5\right ) \log \left (\frac {2}{x}\right )+\left (-299-120 e^5-12 e^{10}\right ) \log ^2\left (\frac {2}{x}\right )}{\log ^2\left (\frac {2}{x}\right )}\right )}{\left (12 e^{2 x} x \log \left (\frac {2}{x}\right )+e^x \left (-120 x-24 e^5 x\right ) \log ^2\left (\frac {2}{x}\right )+\left (299 x+120 e^5 x+12 e^{10} x\right ) \log ^3\left (\frac {2}{x}\right )\right ) \log \left (\frac {-12 e^{2 x}+e^x \left (120+24 e^5\right ) \log \left (\frac {2}{x}\right )+\left (-299-120 e^5-12 e^{10}\right ) \log ^2\left (\frac {2}{x}\right )}{\log ^2\left (\frac {2}{x}\right )}\right )} \, dx=\text {Timed out} \]

[In]

integrate((((12*x*exp(5)^2+120*x*exp(5)+299*x)*exp(x)*log(2/x)^3+(-24*x*exp(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)
/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,
algorithm="giac")

[Out]

Timed out

Mupad [B] (verification not implemented)

Time = 15.60 (sec) , antiderivative size = 57, normalized size of antiderivative = 1.84 \[ \int \frac {24 e^{2 x}+\left (e^x \left (-120-24 e^5\right )+24 e^{2 x} x\right ) \log \left (\frac {2}{x}\right )+e^x \left (-120 x-24 e^5 x\right ) \log ^2\left (\frac {2}{x}\right )+\left (12 e^{3 x} x \log \left (\frac {2}{x}\right )+e^{2 x} \left (-120 x-24 e^5 x\right ) \log ^2\left (\frac {2}{x}\right )+e^x \left (299 x+120 e^5 x+12 e^{10} x\right ) \log ^3\left (\frac {2}{x}\right )\right ) \log \left (\frac {-12 e^{2 x}+e^x \left (120+24 e^5\right ) \log \left (\frac {2}{x}\right )+\left (-299-120 e^5-12 e^{10}\right ) \log ^2\left (\frac {2}{x}\right )}{\log ^2\left (\frac {2}{x}\right )}\right )}{\left (12 e^{2 x} x \log \left (\frac {2}{x}\right )+e^x \left (-120 x-24 e^5 x\right ) \log ^2\left (\frac {2}{x}\right )+\left (299 x+120 e^5 x+12 e^{10} x\right ) \log ^3\left (\frac {2}{x}\right )\right ) \log \left (\frac {-12 e^{2 x}+e^x \left (120+24 e^5\right ) \log \left (\frac {2}{x}\right )+\left (-299-120 e^5-12 e^{10}\right ) \log ^2\left (\frac {2}{x}\right )}{\log ^2\left (\frac {2}{x}\right )}\right )} \, dx=\ln \left (\ln \left (-\frac {\left (120\,{\mathrm {e}}^5+12\,{\mathrm {e}}^{10}+299\right )\,{\ln \left (\frac {2}{x}\right )}^2-{\mathrm {e}}^x\,\left (24\,{\mathrm {e}}^5+120\right )\,\ln \left (\frac {2}{x}\right )+12\,{\mathrm {e}}^{2\,x}}{{\ln \left (\frac {2}{x}\right )}^2}\right )\right )+{\mathrm {e}}^x \]

[In]

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)*log(2/x) - exp(2*x)*log(2/x)^2*(120*x + 24*x*exp(5)) + exp(x)*log(2/x)^3*(
299*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)

[Out]

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)