\[ \int \frac {-54 x-6 e^6 x+162 x^2-108 x^3+e^3 \left (-36 x+54 x^2\right )+2^{60/x} x^{60/x} \left (2 x-6 x^2+4 x^3\right )+2^{20/x} x^{20/x} \left (54 x-162 x^2+108 x^3+e^6 (-40+2 x)+e^3 \left (-120+144 x-36 x^2\right )+\left (40 e^6+e^3 (120-120 x)\right ) \log (2 x)\right )+2^{40/x} x^{40/x} \left (-18 x+54 x^2-36 x^3+e^3 \left (40-44 x+6 x^2\right )+e^3 (-40+40 x) \log (2 x)\right )}{-27+27\ 2^{20/x} x^{20/x}-9\ 2^{40/x} x^{40/x}+2^{60/x} x^{60/x}} \, dx \]
Optimal antiderivative \[ \left (\frac {{\mathrm e}^{3}}{3-{\mathrm e}^{\frac {20 \ln \left (2 x \right )}{x}}}-x +1\right )^{2} x^{2} \]
command
integrate(((4*x^3-6*x^2+2*x)*exp(20*log(2*x)/x)^3+((40*x-40)*exp(3)*log(2*x)+(6*x^2-44*x+40)*exp(3)-36*x^3+54*x^2-18*x)*exp(20*log(2*x)/x)^2+((40*exp(3)^2+(-120*x+120)*exp(3))*log(2*x)+(2*x-40)*exp(3)^2+(-36*x^2+144*x-120)*exp(3)+108*x^3-162*x^2+54*x)*exp(20*log(2*x)/x)-6*x*exp(3)^2+(54*x^2-36*x)*exp(3)-108*x^3+162*x^2-54*x)/(exp(20*log(2*x)/x)^3-9*exp(20*log(2*x)/x)^2+27*exp(20*log(2*x)/x)-27),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {\left (2 \, x\right )^{\frac {40}{x}}}{\frac {\left (2 \, x\right )^{\frac {40}{x}}}{x^{4}} - \frac {6 \, \left (2 \, x\right )^{\frac {20}{x}}}{x^{4}} + \frac {9}{x^{4}}} - \frac {6 \, \left (2 \, x\right )^{\frac {20}{x}}}{\frac {\left (2 \, x\right )^{\frac {40}{x}}}{x^{4}} - \frac {6 \, \left (2 \, x\right )^{\frac {20}{x}}}{x^{4}} + \frac {9}{x^{4}}} + \frac {2 \, \left (2 \, x\right )^{\frac {20}{x}} e^{3}}{x {\left (\frac {\left (2 \, x\right )^{\frac {40}{x}}}{x^{4}} - \frac {6 \, \left (2 \, x\right )^{\frac {20}{x}}}{x^{4}} + \frac {9}{x^{4}}\right )}} - \frac {2 \, \left (2 \, x\right )^{\frac {40}{x}}}{x {\left (\frac {\left (2 \, x\right )^{\frac {40}{x}}}{x^{4}} - \frac {6 \, \left (2 \, x\right )^{\frac {20}{x}}}{x^{4}} + \frac {9}{x^{4}}\right )}} + \frac {12 \, \left (2 \, x\right )^{\frac {20}{x}}}{x {\left (\frac {\left (2 \, x\right )^{\frac {40}{x}}}{x^{4}} - \frac {6 \, \left (2 \, x\right )^{\frac {20}{x}}}{x^{4}} + \frac {9}{x^{4}}\right )}} + \frac {9}{\frac {\left (2 \, x\right )^{\frac {40}{x}}}{x^{4}} - \frac {6 \, \left (2 \, x\right )^{\frac {20}{x}}}{x^{4}} + \frac {9}{x^{4}}} - \frac {2 \, \left (2 \, x\right )^{\frac {20}{x}} e^{3}}{x^{2} {\left (\frac {\left (2 \, x\right )^{\frac {40}{x}}}{x^{4}} - \frac {6 \, \left (2 \, x\right )^{\frac {20}{x}}}{x^{4}} + \frac {9}{x^{4}}\right )}} - \frac {6 \, e^{3}}{x {\left (\frac {\left (2 \, x\right )^{\frac {40}{x}}}{x^{4}} - \frac {6 \, \left (2 \, x\right )^{\frac {20}{x}}}{x^{4}} + \frac {9}{x^{4}}\right )}} + \frac {\left (2 \, x\right )^{\frac {40}{x}}}{x^{2} {\left (\frac {\left (2 \, x\right )^{\frac {40}{x}}}{x^{4}} - \frac {6 \, \left (2 \, x\right )^{\frac {20}{x}}}{x^{4}} + \frac {9}{x^{4}}\right )}} - \frac {6 \, \left (2 \, x\right )^{\frac {20}{x}}}{x^{2} {\left (\frac {\left (2 \, x\right )^{\frac {40}{x}}}{x^{4}} - \frac {6 \, \left (2 \, x\right )^{\frac {20}{x}}}{x^{4}} + \frac {9}{x^{4}}\right )}} - \frac {18}{x {\left (\frac {\left (2 \, x\right )^{\frac {40}{x}}}{x^{4}} - \frac {6 \, \left (2 \, x\right )^{\frac {20}{x}}}{x^{4}} + \frac {9}{x^{4}}\right )}} + \frac {e^{6}}{x^{2} {\left (\frac {\left (2 \, x\right )^{\frac {40}{x}}}{x^{4}} - \frac {6 \, \left (2 \, x\right )^{\frac {20}{x}}}{x^{4}} + \frac {9}{x^{4}}\right )}} + \frac {6 \, e^{3}}{x^{2} {\left (\frac {\left (2 \, x\right )^{\frac {40}{x}}}{x^{4}} - \frac {6 \, \left (2 \, x\right )^{\frac {20}{x}}}{x^{4}} + \frac {9}{x^{4}}\right )}} + \frac {9}{x^{2} {\left (\frac {\left (2 \, x\right )^{\frac {40}{x}}}{x^{4}} - \frac {6 \, \left (2 \, x\right )^{\frac {20}{x}}}{x^{4}} + \frac {9}{x^{4}}\right )}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Exception raised: TypeError} \]________________________________________________________________________________________