\(\int \frac {e^{e^{\frac {18+18 x-18 \log ^2(2)+(1-x-x^2+x^3+(-1+2 x-x^2) \log ^2(2)) \log (\frac {x}{2})}{1-2 x+x^2}}+\frac {18+18 x-18 \log ^2(2)+(1-x-x^2+x^3+(-1+2 x-x^2) \log ^2(2)) \log (\frac {x}{2})}{1-2 x+x^2}} (-1-52 x-18 x^2-2 x^3+x^4+(1+33 x+3 x^2-x^3) \log ^2(2)+(-x+3 x^2-3 x^3+x^4) \log (\frac {x}{2}))}{-x+3 x^2-3 x^3+x^4} \, dx\) [6569]

Optimal result

Integrand size = 201, antiderivative size = 30 \[ \int \frac {e^{e^{\frac {18+18 x-18 \log ^2(2)+\left (1-x-x^2+x^3+\left (-1+2 x-x^2\right ) \log ^2(2)\right ) \log \left (\frac {x}{2}\right )}{1-2 x+x^2}}+\frac {18+18 x-18 \log ^2(2)+\left (1-x-x^2+x^3+\left (-1+2 x-x^2\right ) \log ^2(2)\right ) \log \left (\frac {x}{2}\right )}{1-2 x+x^2}} \left (-1-52 x-18 x^2-2 x^3+x^4+\left (1+33 x+3 x^2-x^3\right ) \log ^2(2)+\left (-x+3 x^2-3 x^3+x^4\right ) \log \left (\frac {x}{2}\right )\right )}{-x+3 x^2-3 x^3+x^4} \, dx=e^{e^{\left (1+x-\log ^2(2)\right ) \left (\frac {18}{(1-x)^2}+\log \left (\frac {x}{2}\right )\right )}} \]

[Out]

exp(exp((x+1-ln(2)^2)*(18/(1-x)^2+ln(1/2*x))))

Rubi [F(-1)]

Timed out. \[ \int \frac {e^{e^{\frac {18+18 x-18 \log ^2(2)+\left (1-x-x^2+x^3+\left (-1+2 x-x^2\right ) \log ^2(2)\right ) \log \left (\frac {x}{2}\right )}{1-2 x+x^2}}+\frac {18+18 x-18 \log ^2(2)+\left (1-x-x^2+x^3+\left (-1+2 x-x^2\right ) \log ^2(2)\right ) \log \left (\frac {x}{2}\right )}{1-2 x+x^2}} \left (-1-52 x-18 x^2-2 x^3+x^4+\left (1+33 x+3 x^2-x^3\right ) \log ^2(2)+\left (-x+3 x^2-3 x^3+x^4\right ) \log \left (\frac {x}{2}\right )\right )}{-x+3 x^2-3 x^3+x^4} \, dx=\text {\$Aborted} \]

[In]

Int[(E^(E^((18 + 18*x - 18*Log[2]^2 + (1 - x - x^2 + x^3 + (-1 + 2*x - x^2)*Log[2]^2)*Log[x/2])/(1 - 2*x + x^2
)) + (18 + 18*x - 18*Log[2]^2 + (1 - x - x^2 + x^3 + (-1 + 2*x - x^2)*Log[2]^2)*Log[x/2])/(1 - 2*x + x^2))*(-1
- 52*x - 18*x^2 - 2*x^3 + x^4 + (1 + 33*x + 3*x^2 - x^3)*Log[2]^2 + (-x + 3*x^2 - 3*x^3 + x^4)*Log[x/2]))/(-x
+ 3*x^2 - 3*x^3 + x^4),x]

[Out]

$Aborted

Rubi steps Aborted

Mathematica [F]

\[ \int \frac {e^{e^{\frac {18+18 x-18 \log ^2(2)+\left (1-x-x^2+x^3+\left (-1+2 x-x^2\right ) \log ^2(2)\right ) \log \left (\frac {x}{2}\right )}{1-2 x+x^2}}+\frac {18+18 x-18 \log ^2(2)+\left (1-x-x^2+x^3+\left (-1+2 x-x^2\right ) \log ^2(2)\right ) \log \left (\frac {x}{2}\right )}{1-2 x+x^2}} \left (-1-52 x-18 x^2-2 x^3+x^4+\left (1+33 x+3 x^2-x^3\right ) \log ^2(2)+\left (-x+3 x^2-3 x^3+x^4\right ) \log \left (\frac {x}{2}\right )\right )}{-x+3 x^2-3 x^3+x^4} \, dx=\int \frac {e^{e^{\frac {18+18 x-18 \log ^2(2)+\left (1-x-x^2+x^3+\left (-1+2 x-x^2\right ) \log ^2(2)\right ) \log \left (\frac {x}{2}\right )}{1-2 x+x^2}}+\frac {18+18 x-18 \log ^2(2)+\left (1-x-x^2+x^3+\left (-1+2 x-x^2\right ) \log ^2(2)\right ) \log \left (\frac {x}{2}\right )}{1-2 x+x^2}} \left (-1-52 x-18 x^2-2 x^3+x^4+\left (1+33 x+3 x^2-x^3\right ) \log ^2(2)+\left (-x+3 x^2-3 x^3+x^4\right ) \log \left (\frac {x}{2}\right )\right )}{-x+3 x^2-3 x^3+x^4} \, dx \]

[In]

Integrate[(E^(E^((18 + 18*x - 18*Log[2]^2 + (1 - x - x^2 + x^3 + (-1 + 2*x - x^2)*Log[2]^2)*Log[x/2])/(1 - 2*x
+ x^2)) + (18 + 18*x - 18*Log[2]^2 + (1 - x - x^2 + x^3 + (-1 + 2*x - x^2)*Log[2]^2)*Log[x/2])/(1 - 2*x + x^2
))*(-1 - 52*x - 18*x^2 - 2*x^3 + x^4 + (1 + 33*x + 3*x^2 - x^3)*Log[2]^2 + (-x + 3*x^2 - 3*x^3 + x^4)*Log[x/2]
))/(-x + 3*x^2 - 3*x^3 + x^4),x]

[Out]

Integrate[(E^(E^((18 + 18*x - 18*Log[2]^2 + (1 - x - x^2 + x^3 + (-1 + 2*x - x^2)*Log[2]^2)*Log[x/2])/(1 - 2*x
+ x^2)) + (18 + 18*x - 18*Log[2]^2 + (1 - x - x^2 + x^3 + (-1 + 2*x - x^2)*Log[2]^2)*Log[x/2])/(1 - 2*x + x^2
))*(-1 - 52*x - 18*x^2 - 2*x^3 + x^4 + (1 + 33*x + 3*x^2 - x^3)*Log[2]^2 + (-x + 3*x^2 - 3*x^3 + x^4)*Log[x/2]
))/(-x + 3*x^2 - 3*x^3 + x^4), x]

Maple [A] (verified)

Time = 122.07 (sec) , antiderivative size = 40, normalized size of antiderivative = 1.33

method	result	size
risch	\({\mathrm e}^{{\mathrm e}^{-\frac {\left (\ln \left (2\right )^{2}-x -1\right ) \left (x^{2} \ln \left (\frac {x}{2}\right )-2 x \ln \left (\frac {x}{2}\right )+\ln \left (\frac {x}{2}\right )+18\right )}{\left (-1+x \right )^{2}}}}\)	\(40\)
parallelrisch	\({\mathrm e}^{{\mathrm e}^{\frac {\left (\left (-x^{2}+2 x -1\right ) \ln \left (2\right )^{2}+x^{3}-x^{2}-x +1\right ) \ln \left (\frac {x}{2}\right )-18 \ln \left (2\right )^{2}+18 x +18}{x^{2}-2 x +1}}}\)	\(58\)

[In]

int(((x^4-3*x^3+3*x^2-x)*ln(1/2*x)+(-x^3+3*x^2+33*x+1)*ln(2)^2+x^4-2*x^3-18*x^2-52*x-1)*exp((((-x^2+2*x-1)*ln(
2)^2+x^3-x^2-x+1)*ln(1/2*x)-18*ln(2)^2+18*x+18)/(x^2-2*x+1))*exp(exp((((-x^2+2*x-1)*ln(2)^2+x^3-x^2-x+1)*ln(1/
2*x)-18*ln(2)^2+18*x+18)/(x^2-2*x+1)))/(x^4-3*x^3+3*x^2-x),x,method=_RETURNVERBOSE)

[Out]

exp(exp(-(ln(2)^2-x-1)*(x^2*ln(1/2*x)-2*x*ln(1/2*x)+ln(1/2*x)+18)/(-1+x)^2))

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 177 vs. \(2 (25) = 50\).

Time = 0.28 (sec) , antiderivative size = 177, normalized size of antiderivative = 5.90 \[ \int \frac {e^{e^{\frac {18+18 x-18 \log ^2(2)+\left (1-x-x^2+x^3+\left (-1+2 x-x^2\right ) \log ^2(2)\right ) \log \left (\frac {x}{2}\right )}{1-2 x+x^2}}+\frac {18+18 x-18 \log ^2(2)+\left (1-x-x^2+x^3+\left (-1+2 x-x^2\right ) \log ^2(2)\right ) \log \left (\frac {x}{2}\right )}{1-2 x+x^2}} \left (-1-52 x-18 x^2-2 x^3+x^4+\left (1+33 x+3 x^2-x^3\right ) \log ^2(2)+\left (-x+3 x^2-3 x^3+x^4\right ) \log \left (\frac {x}{2}\right )\right )}{-x+3 x^2-3 x^3+x^4} \, dx=e^{\left (\frac {{\left (x^{2} - 2 \, x + 1\right )} e^{\left (-\frac {18 \, \log \left (2\right )^{2} - {\left (x^{3} - {\left (x^{2} - 2 \, x + 1\right )} \log \left (2\right )^{2} - x^{2} - x + 1\right )} \log \left (\frac {1}{2} \, x\right ) - 18 \, x - 18}{x^{2} - 2 \, x + 1}\right )} - 18 \, \log \left (2\right )^{2} + {\left (x^{3} - {\left (x^{2} - 2 \, x + 1\right )} \log \left (2\right )^{2} - x^{2} - x + 1\right )} \log \left (\frac {1}{2} \, x\right ) + 18 \, x + 18}{x^{2} - 2 \, x + 1} + \frac {18 \, \log \left (2\right )^{2} - {\left (x^{3} - {\left (x^{2} - 2 \, x + 1\right )} \log \left (2\right )^{2} - x^{2} - x + 1\right )} \log \left (\frac {1}{2} \, x\right ) - 18 \, x - 18}{x^{2} - 2 \, x + 1}\right )} \]

[In]

integrate(((x^4-3*x^3+3*x^2-x)*log(1/2*x)+(-x^3+3*x^2+33*x+1)*log(2)^2+x^4-2*x^3-18*x^2-52*x-1)*exp((((-x^2+2*
x-1)*log(2)^2+x^3-x^2-x+1)*log(1/2*x)-18*log(2)^2+18*x+18)/(x^2-2*x+1))*exp(exp((((-x^2+2*x-1)*log(2)^2+x^3-x^
2-x+1)*log(1/2*x)-18*log(2)^2+18*x+18)/(x^2-2*x+1)))/(x^4-3*x^3+3*x^2-x),x, algorithm="fricas")

[Out]

e^(((x^2 - 2*x + 1)*e^(-(18*log(2)^2 - (x^3 - (x^2 - 2*x + 1)*log(2)^2 - x^2 - x + 1)*log(1/2*x) - 18*x - 18)/
(x^2 - 2*x + 1)) - 18*log(2)^2 + (x^3 - (x^2 - 2*x + 1)*log(2)^2 - x^2 - x + 1)*log(1/2*x) + 18*x + 18)/(x^2 -
2*x + 1) + (18*log(2)^2 - (x^3 - (x^2 - 2*x + 1)*log(2)^2 - x^2 - x + 1)*log(1/2*x) - 18*x - 18)/(x^2 - 2*x +
1))

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 51 vs. \(2 (22) = 44\).

Time = 2.62 (sec) , antiderivative size = 51, normalized size of antiderivative = 1.70 \[ \int \frac {e^{e^{\frac {18+18 x-18 \log ^2(2)+\left (1-x-x^2+x^3+\left (-1+2 x-x^2\right ) \log ^2(2)\right ) \log \left (\frac {x}{2}\right )}{1-2 x+x^2}}+\frac {18+18 x-18 \log ^2(2)+\left (1-x-x^2+x^3+\left (-1+2 x-x^2\right ) \log ^2(2)\right ) \log \left (\frac {x}{2}\right )}{1-2 x+x^2}} \left (-1-52 x-18 x^2-2 x^3+x^4+\left (1+33 x+3 x^2-x^3\right ) \log ^2(2)+\left (-x+3 x^2-3 x^3+x^4\right ) \log \left (\frac {x}{2}\right )\right )}{-x+3 x^2-3 x^3+x^4} \, dx=e^{e^{\frac {18 x + \left (x^{3} - x^{2} - x + \left (- x^{2} + 2 x - 1\right ) \log {\left (2 \right )}^{2} + 1\right ) \log {\left (\frac {x}{2} \right )} - 18 \log {\left (2 \right )}^{2} + 18}{x^{2} - 2 x + 1}}} \]

[In]

integrate(((x**4-3*x**3+3*x**2-x)*ln(1/2*x)+(-x**3+3*x**2+33*x+1)*ln(2)**2+x**4-2*x**3-18*x**2-52*x-1)*exp((((
-x**2+2*x-1)*ln(2)**2+x**3-x**2-x+1)*ln(1/2*x)-18*ln(2)**2+18*x+18)/(x**2-2*x+1))*exp(exp((((-x**2+2*x-1)*ln(2
)**2+x**3-x**2-x+1)*ln(1/2*x)-18*ln(2)**2+18*x+18)/(x**2-2*x+1)))/(x**4-3*x**3+3*x**2-x),x)

[Out]

exp(exp((18*x + (x**3 - x**2 - x + (-x**2 + 2*x - 1)*log(2)**2 + 1)*log(x/2) - 18*log(2)**2 + 18)/(x**2 - 2*x
+ 1)))

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 62 vs. \(2 (25) = 50\).

Time = 2.43 (sec) , antiderivative size = 62, normalized size of antiderivative = 2.07 \[ \int \frac {e^{e^{\frac {18+18 x-18 \log ^2(2)+\left (1-x-x^2+x^3+\left (-1+2 x-x^2\right ) \log ^2(2)\right ) \log \left (\frac {x}{2}\right )}{1-2 x+x^2}}+\frac {18+18 x-18 \log ^2(2)+\left (1-x-x^2+x^3+\left (-1+2 x-x^2\right ) \log ^2(2)\right ) \log \left (\frac {x}{2}\right )}{1-2 x+x^2}} \left (-1-52 x-18 x^2-2 x^3+x^4+\left (1+33 x+3 x^2-x^3\right ) \log ^2(2)+\left (-x+3 x^2-3 x^3+x^4\right ) \log \left (\frac {x}{2}\right )\right )}{-x+3 x^2-3 x^3+x^4} \, dx=e^{\left (\frac {1}{2} \, x e^{\left (\log \left (2\right )^{3} - \log \left (2\right )^{2} \log \left (x\right ) - x \log \left (2\right ) + x \log \left (x\right ) - \frac {18 \, \log \left (2\right )^{2}}{x^{2} - 2 \, x + 1} + \frac {36}{x^{2} - 2 \, x + 1} + \frac {18}{x - 1}\right )}\right )} \]

[In]

integrate(((x^4-3*x^3+3*x^2-x)*log(1/2*x)+(-x^3+3*x^2+33*x+1)*log(2)^2+x^4-2*x^3-18*x^2-52*x-1)*exp((((-x^2+2*
x-1)*log(2)^2+x^3-x^2-x+1)*log(1/2*x)-18*log(2)^2+18*x+18)/(x^2-2*x+1))*exp(exp((((-x^2+2*x-1)*log(2)^2+x^3-x^
2-x+1)*log(1/2*x)-18*log(2)^2+18*x+18)/(x^2-2*x+1)))/(x^4-3*x^3+3*x^2-x),x, algorithm="maxima")

[Out]

e^(1/2*x*e^(log(2)^3 - log(2)^2*log(x) - x*log(2) + x*log(x) - 18*log(2)^2/(x^2 - 2*x + 1) + 36/(x^2 - 2*x + 1
) + 18/(x - 1)))

Giac [F]

\[ \int \frac {e^{e^{\frac {18+18 x-18 \log ^2(2)+\left (1-x-x^2+x^3+\left (-1+2 x-x^2\right ) \log ^2(2)\right ) \log \left (\frac {x}{2}\right )}{1-2 x+x^2}}+\frac {18+18 x-18 \log ^2(2)+\left (1-x-x^2+x^3+\left (-1+2 x-x^2\right ) \log ^2(2)\right ) \log \left (\frac {x}{2}\right )}{1-2 x+x^2}} \left (-1-52 x-18 x^2-2 x^3+x^4+\left (1+33 x+3 x^2-x^3\right ) \log ^2(2)+\left (-x+3 x^2-3 x^3+x^4\right ) \log \left (\frac {x}{2}\right )\right )}{-x+3 x^2-3 x^3+x^4} \, dx=\int { \frac {{\left (x^{4} - 2 \, x^{3} - {\left (x^{3} - 3 \, x^{2} - 33 \, x - 1\right )} \log \left (2\right )^{2} - 18 \, x^{2} + {\left (x^{4} - 3 \, x^{3} + 3 \, x^{2} - x\right )} \log \left (\frac {1}{2} \, x\right ) - 52 \, x - 1\right )} e^{\left (-\frac {18 \, \log \left (2\right )^{2} - {\left (x^{3} - {\left (x^{2} - 2 \, x + 1\right )} \log \left (2\right )^{2} - x^{2} - x + 1\right )} \log \left (\frac {1}{2} \, x\right ) - 18 \, x - 18}{x^{2} - 2 \, x + 1} + e^{\left (-\frac {18 \, \log \left (2\right )^{2} - {\left (x^{3} - {\left (x^{2} - 2 \, x + 1\right )} \log \left (2\right )^{2} - x^{2} - x + 1\right )} \log \left (\frac {1}{2} \, x\right ) - 18 \, x - 18}{x^{2} - 2 \, x + 1}\right )}\right )}}{x^{4} - 3 \, x^{3} + 3 \, x^{2} - x} \,d x } \]

[In]

integrate(((x^4-3*x^3+3*x^2-x)*log(1/2*x)+(-x^3+3*x^2+33*x+1)*log(2)^2+x^4-2*x^3-18*x^2-52*x-1)*exp((((-x^2+2*
x-1)*log(2)^2+x^3-x^2-x+1)*log(1/2*x)-18*log(2)^2+18*x+18)/(x^2-2*x+1))*exp(exp((((-x^2+2*x-1)*log(2)^2+x^3-x^
2-x+1)*log(1/2*x)-18*log(2)^2+18*x+18)/(x^2-2*x+1)))/(x^4-3*x^3+3*x^2-x),x, algorithm="giac")

[Out]

integrate((x^4 - 2*x^3 - (x^3 - 3*x^2 - 33*x - 1)*log(2)^2 - 18*x^2 + (x^4 - 3*x^3 + 3*x^2 - x)*log(1/2*x) - 5
2*x - 1)*e^(-(18*log(2)^2 - (x^3 - (x^2 - 2*x + 1)*log(2)^2 - x^2 - x + 1)*log(1/2*x) - 18*x - 18)/(x^2 - 2*x
+ 1) + e^(-(18*log(2)^2 - (x^3 - (x^2 - 2*x + 1)*log(2)^2 - x^2 - x + 1)*log(1/2*x) - 18*x - 18)/(x^2 - 2*x +
1)))/(x^4 - 3*x^3 + 3*x^2 - x), x)

Mupad [B] (verification not implemented)

Time = 13.99 (sec) , antiderivative size = 159, normalized size of antiderivative = 5.30 \[ \int \frac {e^{e^{\frac {18+18 x-18 \log ^2(2)+\left (1-x-x^2+x^3+\left (-1+2 x-x^2\right ) \log ^2(2)\right ) \log \left (\frac {x}{2}\right )}{1-2 x+x^2}}+\frac {18+18 x-18 \log ^2(2)+\left (1-x-x^2+x^3+\left (-1+2 x-x^2\right ) \log ^2(2)\right ) \log \left (\frac {x}{2}\right )}{1-2 x+x^2}} \left (-1-52 x-18 x^2-2 x^3+x^4+\left (1+33 x+3 x^2-x^3\right ) \log ^2(2)+\left (-x+3 x^2-3 x^3+x^4\right ) \log \left (\frac {x}{2}\right )\right )}{-x+3 x^2-3 x^3+x^4} \, dx={\mathrm {e}}^{{\left (\frac {1}{2}\right )}^{x+1}\,x^{\frac {x^2}{x-1}-\frac {x+x^2\,{\ln \left (2\right )}^2-2\,x\,{\ln \left (2\right )}^2+{\ln \left (2\right )}^2}{x^2-2\,x+1}+\frac {1}{x^2-2\,x+1}}\,{\mathrm {e}}^{\frac {18}{x^2-2\,x+1}}\,{\mathrm {e}}^{-\frac {2\,x\,{\ln \left (2\right )}^3}{x^2-2\,x+1}}\,{\mathrm {e}}^{\frac {18\,x}{x^2-2\,x+1}}\,{\mathrm {e}}^{\frac {x^2\,{\ln \left (2\right )}^3}{x^2-2\,x+1}}\,{\mathrm {e}}^{\frac {{\ln \left (2\right )}^3}{x^2-2\,x+1}}\,{\mathrm {e}}^{-\frac {18\,{\ln \left (2\right )}^2}{x^2-2\,x+1}}} \]

[In]

int((exp((18*x - log(x/2)*(x + log(2)^2*(x^2 - 2*x + 1) + x^2 - x^3 - 1) - 18*log(2)^2 + 18)/(x^2 - 2*x + 1))*
exp(exp((18*x - log(x/2)*(x + log(2)^2*(x^2 - 2*x + 1) + x^2 - x^3 - 1) - 18*log(2)^2 + 18)/(x^2 - 2*x + 1)))*
(52*x + log(x/2)*(x - 3*x^2 + 3*x^3 - x^4) - log(2)^2*(33*x + 3*x^2 - x^3 + 1) + 18*x^2 + 2*x^3 - x^4 + 1))/(x
- 3*x^2 + 3*x^3 - x^4),x)

[Out]

exp((1/2)^(x + 1)*x^(x^2/(x - 1) - (x + x^2*log(2)^2 - 2*x*log(2)^2 + log(2)^2)/(x^2 - 2*x + 1) + 1/(x^2 - 2*x
+ 1))*exp(18/(x^2 - 2*x + 1))*exp(-(2*x*log(2)^3)/(x^2 - 2*x + 1))*exp((18*x)/(x^2 - 2*x + 1))*exp((x^2*log(2
)^3)/(x^2 - 2*x + 1))*exp(log(2)^3/(x^2 - 2*x + 1))*exp(-(18*log(2)^2)/(x^2 - 2*x + 1)))