Integrand size = 242, antiderivative size = 35 \[ \int \frac {-54 x-6 e^6 x+162 x^2-108 x^3+e^3 \left (-36 x+54 x^2\right )+2^{60/x} x^{60/x} \left (2 x-6 x^2+4 x^3\right )+2^{20/x} x^{20/x} \left (54 x-162 x^2+108 x^3+e^6 (-40+2 x)+e^3 \left (-120+144 x-36 x^2\right )+\left (40 e^6+e^3 (120-120 x)\right ) \log (2 x)\right )+2^{40/x} x^{40/x} \left (-18 x+54 x^2-36 x^3+e^3 \left (40-44 x+6 x^2\right )+e^3 (-40+40 x) \log (2 x)\right )}{-27+27\ 2^{20/x} x^{20/x}-9\ 2^{40/x} x^{40/x}+2^{60/x} x^{60/x}} \, dx=x^2 \left (1-x+\frac {e^3}{3-2^{20/x} x^{20/x}}\right )^2 \]
\[ \int \frac {-54 x-6 e^6 x+162 x^2-108 x^3+e^3 \left (-36 x+54 x^2\right )+2^{60/x} x^{60/x} \left (2 x-6 x^2+4 x^3\right )+2^{20/x} x^{20/x} \left (54 x-162 x^2+108 x^3+e^6 (-40+2 x)+e^3 \left (-120+144 x-36 x^2\right )+\left (40 e^6+e^3 (120-120 x)\right ) \log (2 x)\right )+2^{40/x} x^{40/x} \left (-18 x+54 x^2-36 x^3+e^3 \left (40-44 x+6 x^2\right )+e^3 (-40+40 x) \log (2 x)\right )}{-27+27\ 2^{20/x} x^{20/x}-9\ 2^{40/x} x^{40/x}+2^{60/x} x^{60/x}} \, dx=\int \frac {-54 x-6 e^6 x+162 x^2-108 x^3+e^3 \left (-36 x+54 x^2\right )+2^{60/x} x^{60/x} \left (2 x-6 x^2+4 x^3\right )+2^{20/x} x^{20/x} \left (54 x-162 x^2+108 x^3+e^6 (-40+2 x)+e^3 \left (-120+144 x-36 x^2\right )+\left (40 e^6+e^3 (120-120 x)\right ) \log (2 x)\right )+2^{40/x} x^{40/x} \left (-18 x+54 x^2-36 x^3+e^3 \left (40-44 x+6 x^2\right )+e^3 (-40+40 x) \log (2 x)\right )}{-27+27\ 2^{20/x} x^{20/x}-9\ 2^{40/x} x^{40/x}+2^{60/x} x^{60/x}} \, dx \]
Integrate[(-54*x - 6*E^6*x + 162*x^2 - 108*x^3 + E^3*(-36*x + 54*x^2) + 2^ (60/x)*x^(60/x)*(2*x - 6*x^2 + 4*x^3) + 2^(20/x)*x^(20/x)*(54*x - 162*x^2 + 108*x^3 + E^6*(-40 + 2*x) + E^3*(-120 + 144*x - 36*x^2) + (40*E^6 + E^3* (120 - 120*x))*Log[2*x]) + 2^(40/x)*x^(40/x)*(-18*x + 54*x^2 - 36*x^3 + E^ 3*(40 - 44*x + 6*x^2) + E^3*(-40 + 40*x)*Log[2*x]))/(-27 + 27*2^(20/x)*x^( 20/x) - 9*2^(40/x)*x^(40/x) + 2^(60/x)*x^(60/x)),x]
Integrate[(-54*x - 6*E^6*x + 162*x^2 - 108*x^3 + E^3*(-36*x + 54*x^2) + 2^ (60/x)*x^(60/x)*(2*x - 6*x^2 + 4*x^3) + 2^(20/x)*x^(20/x)*(54*x - 162*x^2 + 108*x^3 + E^6*(-40 + 2*x) + E^3*(-120 + 144*x - 36*x^2) + (40*E^6 + E^3* (120 - 120*x))*Log[2*x]) + 2^(40/x)*x^(40/x)*(-18*x + 54*x^2 - 36*x^3 + E^ 3*(40 - 44*x + 6*x^2) + E^3*(-40 + 40*x)*Log[2*x]))/(-27 + 27*2^(20/x)*x^( 20/x) - 9*2^(40/x)*x^(40/x) + 2^(60/x)*x^(60/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.
| \(\displaystyle \int \frac {-108 x^3+162 x^2+e^3 \left (54 x^2-36 x\right )+2^{60/x} \left (4 x^3-6 x^2+2 x\right ) x^{60/x}+2^{20/x} x^{20/x} \left (108 x^3-162 x^2+e^3 \left (-36 x^2+144 x-120\right )+54 x+e^6 (2 x-40)+\left (e^3 (120-120 x)+40 e^6\right ) \log (2 x)\right )+2^{40/x} x^{40/x} \left (-36 x^3+54 x^2+e^3 \left (6 x^2-44 x+40\right )-18 x+e^3 (40 x-40) \log (2 x)\right )-6 e^6 x-54 x}{27\ 2^{20/x} x^{20/x}-9\ 2^{40/x} x^{40/x}+2^{60/x} x^{60/x}-27} \, dx\) |
| \(\Big \downarrow \) 6 |
| \(\displaystyle \int \frac {-108 x^3+162 x^2+e^3 \left (54 x^2-36 x\right )+2^{60/x} \left (4 x^3-6 x^2+2 x\right ) x^{60/x}+2^{20/x} x^{20/x} \left (108 x^3-162 x^2+e^3 \left (-36 x^2+144 x-120\right )+54 x+e^6 (2 x-40)+\left (e^3 (120-120 x)+40 e^6\right ) \log (2 x)\right )+2^{40/x} x^{40/x} \left (-36 x^3+54 x^2+e^3 \left (6 x^2-44 x+40\right )-18 x+e^3 (40 x-40) \log (2 x)\right )+\left (-54-6 e^6\right ) x}{27\ 2^{20/x} x^{20/x}-9\ 2^{40/x} x^{40/x}+2^{60/x} x^{60/x}-27}dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {108 x^3-162 x^2-e^3 \left (54 x^2-36 x\right )-2^{60/x} \left (4 x^3-6 x^2+2 x\right ) x^{60/x}-2^{20/x} x^{20/x} \left (108 x^3-162 x^2+e^3 \left (-36 x^2+144 x-120\right )+54 x+e^6 (2 x-40)+\left (e^3 (120-120 x)+40 e^6\right ) \log (2 x)\right )-2^{40/x} x^{40/x} \left (-36 x^3+54 x^2+e^3 \left (6 x^2-44 x+40\right )-18 x+e^3 (40 x-40) \log (2 x)\right )-\left (-54-6 e^6\right ) x}{\left (3-2^{20/x} x^{20/x}\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {120 e^6 (\log (2 x)-1)}{\left (2^{20/x} x^{20/x}-3\right )^3}+\frac {2 e^3 \left (-60 \left (1-\frac {e^3}{60}\right ) x+60 x \log (2 x)-60 \left (1-\frac {e^3}{3}\right ) \log (2 x)+60 \left (1-\frac {e^3}{3}\right )\right )}{\left (3-2^{20/x} x^{20/x}\right )^2}+2 x \left (2 x^2-3 x+1\right )+\frac {2 e^3 \left (3 x^2-22 x+20 x \log (2 x)-20 \log (2 x)+20\right )}{2^{20/x} x^{20/x}-3}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle -120 e^6 \int \frac {1}{\left (2^{20/x} x^{20/x}-3\right )^3}dx+40 e^3 \left (3-e^3\right ) \int \frac {1}{\left (2^{20/x} x^{20/x}-3\right )^2}dx-2 e^3 \left (60-e^3\right ) \int \frac {x}{\left (2^{20/x} x^{20/x}-3\right )^2}dx+40 e^3 \int \frac {1}{2^{20/x} x^{20/x}-3}dx-44 e^3 \int \frac {x}{2^{20/x} x^{20/x}-3}dx-120 e^6 \int \frac {\int \frac {1}{\left (2^{20/x} x^{20/x}-3\right )^3}dx}{x}dx+40 e^3 \left (3-e^3\right ) \int \frac {\int \frac {1}{\left (2^{20/x} x^{20/x}-3\right )^2}dx}{x}dx-120 e^3 \int \frac {\int \frac {x}{\left (2^{20/x} x^{20/x}-3\right )^2}dx}{x}dx+40 e^3 \int \frac {\int \frac {1}{2^{20/x} x^{20/x}-3}dx}{x}dx-40 e^3 \int \frac {\int \frac {x}{2^{20/x} x^{20/x}-3}dx}{x}dx+120 e^6 \log (2 x) \int \frac {1}{\left (2^{20/x} x^{20/x}-3\right )^3}dx-40 e^3 \left (3-e^3\right ) \log (2 x) \int \frac {1}{\left (2^{20/x} x^{20/x}-3\right )^2}dx+120 e^3 \log (2 x) \int \frac {x}{\left (2^{20/x} x^{20/x}-3\right )^2}dx-40 e^3 \log (2 x) \int \frac {1}{2^{20/x} x^{20/x}-3}dx+40 e^3 \log (2 x) \int \frac {x}{2^{20/x} x^{20/x}-3}dx+6 e^3 \int \frac {x^2}{2^{20/x} x^{20/x}-3}dx+x^4-2 x^3+x^2\) |
Int[(-54*x - 6*E^6*x + 162*x^2 - 108*x^3 + E^3*(-36*x + 54*x^2) + 2^(60/x) *x^(60/x)*(2*x - 6*x^2 + 4*x^3) + 2^(20/x)*x^(20/x)*(54*x - 162*x^2 + 108* x^3 + E^6*(-40 + 2*x) + E^3*(-120 + 144*x - 36*x^2) + (40*E^6 + E^3*(120 - 120*x))*Log[2*x]) + 2^(40/x)*x^(40/x)*(-18*x + 54*x^2 - 36*x^3 + E^3*(40 - 44*x + 6*x^2) + E^3*(-40 + 40*x)*Log[2*x]))/(-27 + 27*2^(20/x)*x^(20/x) - 9*2^(40/x)*x^(40/x) + 2^(60/x)*x^(60/x)),x]
3.17.28.3.1 Defintions of rubi rules used
Int[(u_.)*((v_.) + (a_.)*(Fx_) + (b_.)*(Fx_))^(p_.), x_Symbol] :> Int[u*(v + (a + b)*Fx)^p, x] /; FreeQ[{a, b}, x] && !FreeQ[Fx, x]
Leaf count of result is larger than twice the leaf count of optimal. \(61\) vs. \(2(30)=60\).
Time = 0.89 (sec) , antiderivative size = 62, normalized size of antiderivative = 1.77
| method | result | size |
| risch | \(x^{4}-2 x^{3}+x^{2}+\frac {\left (2 \left (2 x \right )^{\frac {20}{x}} x +{\mathrm e}^{3}-6 x -2 \left (2 x \right )^{\frac {20}{x}}+6\right ) x^{2} {\mathrm e}^{3}}{\left (\left (2 x \right )^{\frac {20}{x}}-3\right )^{2}}\) | \(62\) |
| parallelrisch | \(\frac {{\mathrm e}^{\frac {40 \ln \left (2 x \right )}{x}} x^{4}+2 \,{\mathrm e}^{3} {\mathrm e}^{\frac {20 \ln \left (2 x \right )}{x}} x^{3}-6 \,{\mathrm e}^{\frac {20 \ln \left (2 x \right )}{x}} x^{4}-2 \,{\mathrm e}^{\frac {40 \ln \left (2 x \right )}{x}} x^{3}+x^{2} {\mathrm e}^{6}-6 x^{3} {\mathrm e}^{3}-2 \,{\mathrm e}^{3} {\mathrm e}^{\frac {20 \ln \left (2 x \right )}{x}} x^{2}+9 x^{4}+12 \,{\mathrm e}^{\frac {20 \ln \left (2 x \right )}{x}} x^{3}+{\mathrm e}^{\frac {40 \ln \left (2 x \right )}{x}} x^{2}+6 x^{2} {\mathrm e}^{3}-18 x^{3}-6 \,{\mathrm e}^{\frac {20 \ln \left (2 x \right )}{x}} x^{2}+9 x^{2}}{{\mathrm e}^{\frac {40 \ln \left (2 x \right )}{x}}-6 \,{\mathrm e}^{\frac {20 \ln \left (2 x \right )}{x}}+9}\) | \(196\) |
int(((4*x^3-6*x^2+2*x)*exp(20*ln(2*x)/x)^3+((40*x-40)*exp(3)*ln(2*x)+(6*x^ 2-44*x+40)*exp(3)-36*x^3+54*x^2-18*x)*exp(20*ln(2*x)/x)^2+((40*exp(3)^2+(- 120*x+120)*exp(3))*ln(2*x)+(2*x-40)*exp(3)^2+(-36*x^2+144*x-120)*exp(3)+10 8*x^3-162*x^2+54*x)*exp(20*ln(2*x)/x)-6*x*exp(3)^2+(54*x^2-36*x)*exp(3)-10 8*x^3+162*x^2-54*x)/(exp(20*ln(2*x)/x)^3-9*exp(20*ln(2*x)/x)^2+27*exp(20*l n(2*x)/x)-27),x,method=_RETURNVERBOSE)
Leaf count of result is larger than twice the leaf count of optimal. 122 vs. \(2 (25) = 50\).
Time = 0.26 (sec) , antiderivative size = 122, normalized size of antiderivative = 3.49 \[ \int \frac {-54 x-6 e^6 x+162 x^2-108 x^3+e^3 \left (-36 x+54 x^2\right )+2^{60/x} x^{60/x} \left (2 x-6 x^2+4 x^3\right )+2^{20/x} x^{20/x} \left (54 x-162 x^2+108 x^3+e^6 (-40+2 x)+e^3 \left (-120+144 x-36 x^2\right )+\left (40 e^6+e^3 (120-120 x)\right ) \log (2 x)\right )+2^{40/x} x^{40/x} \left (-18 x+54 x^2-36 x^3+e^3 \left (40-44 x+6 x^2\right )+e^3 (-40+40 x) \log (2 x)\right )}{-27+27\ 2^{20/x} x^{20/x}-9\ 2^{40/x} x^{40/x}+2^{60/x} x^{60/x}} \, dx=\frac {9 \, x^{4} - 18 \, x^{3} + x^{2} e^{6} + {\left (x^{4} - 2 \, x^{3} + x^{2}\right )} \left (2 \, x\right )^{\frac {40}{x}} - 2 \, {\left (3 \, x^{4} - 6 \, x^{3} + 3 \, x^{2} - {\left (x^{3} - x^{2}\right )} e^{3}\right )} \left (2 \, x\right )^{\frac {20}{x}} + 9 \, x^{2} - 6 \, {\left (x^{3} - x^{2}\right )} e^{3}}{\left (2 \, x\right )^{\frac {40}{x}} - 6 \, \left (2 \, x\right )^{\frac {20}{x}} + 9} \]
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*ex p(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=\
(9*x^4 - 18*x^3 + x^2*e^6 + (x^4 - 2*x^3 + x^2)*(2*x)^(40/x) - 2*(3*x^4 - 6*x^3 + 3*x^2 - (x^3 - x^2)*e^3)*(2*x)^(20/x) + 9*x^2 - 6*(x^3 - x^2)*e^3) /((2*x)^(40/x) - 6*(2*x)^(20/x) + 9)
Leaf count of result is larger than twice the leaf count of optimal. 85 vs. \(2 (22) = 44\).
Time = 0.19 (sec) , antiderivative size = 85, normalized size of antiderivative = 2.43 \[ \int \frac {-54 x-6 e^6 x+162 x^2-108 x^3+e^3 \left (-36 x+54 x^2\right )+2^{60/x} x^{60/x} \left (2 x-6 x^2+4 x^3\right )+2^{20/x} x^{20/x} \left (54 x-162 x^2+108 x^3+e^6 (-40+2 x)+e^3 \left (-120+144 x-36 x^2\right )+\left (40 e^6+e^3 (120-120 x)\right ) \log (2 x)\right )+2^{40/x} x^{40/x} \left (-18 x+54 x^2-36 x^3+e^3 \left (40-44 x+6 x^2\right )+e^3 (-40+40 x) \log (2 x)\right )}{-27+27\ 2^{20/x} x^{20/x}-9\ 2^{40/x} x^{40/x}+2^{60/x} x^{60/x}} \, dx=x^{4} - 2 x^{3} + x^{2} + \frac {- 6 x^{3} e^{3} + 6 x^{2} e^{3} + x^{2} e^{6} + \left (2 x^{3} e^{3} - 2 x^{2} e^{3}\right ) e^{\frac {20 \log {\left (2 x \right )}}{x}}}{e^{\frac {40 \log {\left (2 x \right )}}{x}} - 6 e^{\frac {20 \log {\left (2 x \right )}}{x}} + 9} \]
integrate(((4*x**3-6*x**2+2*x)*exp(20*ln(2*x)/x)**3+((40*x-40)*exp(3)*ln(2 *x)+(6*x**2-44*x+40)*exp(3)-36*x**3+54*x**2-18*x)*exp(20*ln(2*x)/x)**2+((4 0*exp(3)**2+(-120*x+120)*exp(3))*ln(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*ln(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*ln(2*x)/x)**3-9*exp(20*l n(2*x)/x)**2+27*exp(20*ln(2*x)/x)-27),x)
x**4 - 2*x**3 + x**2 + (-6*x**3*exp(3) + 6*x**2*exp(3) + x**2*exp(6) + (2* x**3*exp(3) - 2*x**2*exp(3))*exp(20*log(2*x)/x))/(exp(40*log(2*x)/x) - 6*e xp(20*log(2*x)/x) + 9)
Leaf count of result is larger than twice the leaf count of optimal. 136 vs. \(2 (25) = 50\).
Time = 0.34 (sec) , antiderivative size = 136, normalized size of antiderivative = 3.89 \[ \int \frac {-54 x-6 e^6 x+162 x^2-108 x^3+e^3 \left (-36 x+54 x^2\right )+2^{60/x} x^{60/x} \left (2 x-6 x^2+4 x^3\right )+2^{20/x} x^{20/x} \left (54 x-162 x^2+108 x^3+e^6 (-40+2 x)+e^3 \left (-120+144 x-36 x^2\right )+\left (40 e^6+e^3 (120-120 x)\right ) \log (2 x)\right )+2^{40/x} x^{40/x} \left (-18 x+54 x^2-36 x^3+e^3 \left (40-44 x+6 x^2\right )+e^3 (-40+40 x) \log (2 x)\right )}{-27+27\ 2^{20/x} x^{20/x}-9\ 2^{40/x} x^{40/x}+2^{60/x} x^{60/x}} \, dx=\frac {9 \, x^{4} - 6 \, x^{3} {\left (e^{3} + 3\right )} + x^{2} {\left (e^{6} + 6 \, e^{3} + 9\right )} + {\left (x^{4} - 2 \, x^{3} + x^{2}\right )} e^{\left (\frac {40 \, \log \left (2\right )}{x} + \frac {40 \, \log \left (x\right )}{x}\right )} - 2 \, {\left (3 \, x^{4} - x^{3} {\left (e^{3} + 6\right )} + x^{2} {\left (e^{3} + 3\right )}\right )} e^{\left (\frac {20 \, \log \left (2\right )}{x} + \frac {20 \, \log \left (x\right )}{x}\right )}}{e^{\left (\frac {40 \, \log \left (2\right )}{x} + \frac {40 \, \log \left (x\right )}{x}\right )} - 6 \, e^{\left (\frac {20 \, \log \left (2\right )}{x} + \frac {20 \, \log \left (x\right )}{x}\right )} + 9} \]
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*ex p(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=\
(9*x^4 - 6*x^3*(e^3 + 3) + x^2*(e^6 + 6*e^3 + 9) + (x^4 - 2*x^3 + x^2)*e^( 40*log(2)/x + 40*log(x)/x) - 2*(3*x^4 - x^3*(e^3 + 6) + x^2*(e^3 + 3))*e^( 20*log(2)/x + 20*log(x)/x))/(e^(40*log(2)/x + 40*log(x)/x) - 6*e^(20*log(2 )/x + 20*log(x)/x) + 9)
Exception generated. \[ \int \frac {-54 x-6 e^6 x+162 x^2-108 x^3+e^3 \left (-36 x+54 x^2\right )+2^{60/x} x^{60/x} \left (2 x-6 x^2+4 x^3\right )+2^{20/x} x^{20/x} \left (54 x-162 x^2+108 x^3+e^6 (-40+2 x)+e^3 \left (-120+144 x-36 x^2\right )+\left (40 e^6+e^3 (120-120 x)\right ) \log (2 x)\right )+2^{40/x} x^{40/x} \left (-18 x+54 x^2-36 x^3+e^3 \left (40-44 x+6 x^2\right )+e^3 (-40+40 x) \log (2 x)\right )}{-27+27\ 2^{20/x} x^{20/x}-9\ 2^{40/x} x^{40/x}+2^{60/x} x^{60/x}} \, dx=\text {Exception raised: TypeError} \]
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*ex p(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=\
Exception raised: TypeError >> an error occurred running a Giac command:IN PUT:sage2:=int(sage0,sageVARx):;OUTPUT:Unable to divide, perhaps due to ro unding error%%%{265420800000,[1,10,15,0]%%%}+%%%{-3981312000000,[1,10,14,0 ]%%%}+%%%
Time = 9.39 (sec) , antiderivative size = 139, normalized size of antiderivative = 3.97 \[ \int \frac {-54 x-6 e^6 x+162 x^2-108 x^3+e^3 \left (-36 x+54 x^2\right )+2^{60/x} x^{60/x} \left (2 x-6 x^2+4 x^3\right )+2^{20/x} x^{20/x} \left (54 x-162 x^2+108 x^3+e^6 (-40+2 x)+e^3 \left (-120+144 x-36 x^2\right )+\left (40 e^6+e^3 (120-120 x)\right ) \log (2 x)\right )+2^{40/x} x^{40/x} \left (-18 x+54 x^2-36 x^3+e^3 \left (40-44 x+6 x^2\right )+e^3 (-40+40 x) \log (2 x)\right )}{-27+27\ 2^{20/x} x^{20/x}-9\ 2^{40/x} x^{40/x}+2^{60/x} x^{60/x}} \, dx=x^2-2\,x^3+x^4-\frac {x^2\,{\mathrm {e}}^6-x^2\,\ln \left (2\,x\right )\,{\mathrm {e}}^6}{\left (\ln \left (2\,x\right )-1\right )\,\left (2^{40/x}\,x^{40/x}-6\,2^{20/x}\,x^{20/x}+9\right )}+\frac {2\,\left (x^2\,{\mathrm {e}}^3-x^3\,{\mathrm {e}}^3-x^2\,\ln \left (2\,x\right )\,{\mathrm {e}}^3+x^3\,\ln \left (2\,x\right )\,{\mathrm {e}}^3\right )}{\left (2^{20/x}\,x^{20/x}-3\right )\,\left (\ln \left (2\,x\right )-1\right )} \]
int(-(54*x + exp(3)*(36*x - 54*x^2) + 6*x*exp(6) - exp((40*log(2*x))/x)*(e xp(3)*(6*x^2 - 44*x + 40) - 18*x + 54*x^2 - 36*x^3 + log(2*x)*exp(3)*(40*x - 40)) - exp((20*log(2*x))/x)*(54*x - exp(3)*(36*x^2 - 144*x + 120) + log (2*x)*(40*exp(6) - exp(3)*(120*x - 120)) - 162*x^2 + 108*x^3 + exp(6)*(2*x - 40)) - 162*x^2 + 108*x^3 - exp((60*log(2*x))/x)*(2*x - 6*x^2 + 4*x^3))/ (27*exp((20*log(2*x))/x) - 9*exp((40*log(2*x))/x) + exp((60*log(2*x))/x) - 27),x)