3.71.31 \(\int \frac {e^{e^{e^{\frac {2+x^2-x^3+(-x+x^2) \log (4 x)}{-x+x^2}} x}+e^{\frac {2+x^2-x^3+(-x+x^2) \log (4 x)}{-x+x^2}} x+\frac {2+x^2-x^3+(-x+x^2) \log (4 x)}{-x+x^2}} (2-2 x-5 x^2+4 x^3-x^4+e^5 (2-2 x-5 x^2+4 x^3-x^4))}{4 x-8 x^2+4 x^3} \, dx\)

Optimal. Leaf size=35 \[ \frac {1}{4} e^{e^{4 e^{-x-\frac {2}{x-x^2}} x^2}} \left (1+e^5\right ) \]

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Rubi [F]  time = 180.00, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \text {\$Aborted} \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^(E^(E^((2 + x^2 - x^3 + (-x + x^2)*Log[4*x])/(-x + x^2))*x) + E^((2 + x^2 - x^3 + (-x + x^2)*Log[4*x])/
(-x + x^2))*x + (2 + x^2 - x^3 + (-x + x^2)*Log[4*x])/(-x + x^2))*(2 - 2*x - 5*x^2 + 4*x^3 - x^4 + E^5*(2 - 2*
x - 5*x^2 + 4*x^3 - x^4)))/(4*x - 8*x^2 + 4*x^3),x]

[Out]

$Aborted

Rubi steps

Aborted

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Mathematica [A]  time = 0.30, size = 36, normalized size = 1.03 \begin {gather*} \frac {1}{4} e^{e^{4 e^{\frac {2}{-1+x}-\frac {2}{x}-x} x^2}} \left (1+e^5\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^(E^(E^((2 + x^2 - x^3 + (-x + x^2)*Log[4*x])/(-x + x^2))*x) + E^((2 + x^2 - x^3 + (-x + x^2)*Log[
4*x])/(-x + x^2))*x + (2 + x^2 - x^3 + (-x + x^2)*Log[4*x])/(-x + x^2))*(2 - 2*x - 5*x^2 + 4*x^3 - x^4 + E^5*(
2 - 2*x - 5*x^2 + 4*x^3 - x^4)))/(4*x - 8*x^2 + 4*x^3),x]

[Out]

(E^E^(4*E^(2/(-1 + x) - 2/x - x)*x^2)*(1 + E^5))/4

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fricas [B]  time = 0.50, size = 206, normalized size = 5.89 \begin {gather*} \frac {1}{4} \, {\left (e^{5} + 1\right )} e^{\left (-x e^{\left (-\frac {x^{3} - x^{2} - {\left (x^{2} - x\right )} \log \left (4 \, x\right ) - 2}{x^{2} - x}\right )} - \frac {x^{3} - x^{2} - {\left (x^{2} - x\right )} e^{\left (x e^{\left (-\frac {x^{3} - x^{2} - {\left (x^{2} - x\right )} \log \left (4 \, x\right ) - 2}{x^{2} - x}\right )}\right )} - {\left (x^{3} - x^{2}\right )} e^{\left (-\frac {x^{3} - x^{2} - {\left (x^{2} - x\right )} \log \left (4 \, x\right ) - 2}{x^{2} - x}\right )} - {\left (x^{2} - x\right )} \log \left (4 \, x\right ) - 2}{x^{2} - x} + \frac {x^{3} - x^{2} - {\left (x^{2} - x\right )} \log \left (4 \, x\right ) - 2}{x^{2} - x}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-x^4+4*x^3-5*x^2-2*x+2)*exp(5)-x^4+4*x^3-5*x^2-2*x+2)*exp(((x^2-x)*log(4*x)-x^3+x^2+2)/(x^2-x))*ex
p(x*exp(((x^2-x)*log(4*x)-x^3+x^2+2)/(x^2-x)))*exp(exp(x*exp(((x^2-x)*log(4*x)-x^3+x^2+2)/(x^2-x))))/(4*x^3-8*
x^2+4*x),x, algorithm="fricas")

[Out]

1/4*(e^5 + 1)*e^(-x*e^(-(x^3 - x^2 - (x^2 - x)*log(4*x) - 2)/(x^2 - x)) - (x^3 - x^2 - (x^2 - x)*e^(x*e^(-(x^3
- x^2 - (x^2 - x)*log(4*x) - 2)/(x^2 - x))) - (x^3 - x^2)*e^(-(x^3 - x^2 - (x^2 - x)*log(4*x) - 2)/(x^2 - x))
- (x^2 - x)*log(4*x) - 2)/(x^2 - x) + (x^3 - x^2 - (x^2 - x)*log(4*x) - 2)/(x^2 - x))

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int -\frac {{\left (x^{4} - 4 \, x^{3} + 5 \, x^{2} + {\left (x^{4} - 4 \, x^{3} + 5 \, x^{2} + 2 \, x - 2\right )} e^{5} + 2 \, x - 2\right )} e^{\left (x e^{\left (-\frac {x^{3} - x^{2} - {\left (x^{2} - x\right )} \log \left (4 \, x\right ) - 2}{x^{2} - x}\right )} - \frac {x^{3} - x^{2} - {\left (x^{2} - x\right )} \log \left (4 \, x\right ) - 2}{x^{2} - x} + e^{\left (x e^{\left (-\frac {x^{3} - x^{2} - {\left (x^{2} - x\right )} \log \left (4 \, x\right ) - 2}{x^{2} - x}\right )}\right )}\right )}}{4 \, {\left (x^{3} - 2 \, x^{2} + x\right )}}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-x^4+4*x^3-5*x^2-2*x+2)*exp(5)-x^4+4*x^3-5*x^2-2*x+2)*exp(((x^2-x)*log(4*x)-x^3+x^2+2)/(x^2-x))*ex
p(x*exp(((x^2-x)*log(4*x)-x^3+x^2+2)/(x^2-x)))*exp(exp(x*exp(((x^2-x)*log(4*x)-x^3+x^2+2)/(x^2-x))))/(4*x^3-8*
x^2+4*x),x, algorithm="giac")

[Out]

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

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maple [B]  time = 0.08, size = 86, normalized size = 2.46

method	result	size
risch	\(\frac {{\mathrm e}^{{\mathrm e}^{x \,{\mathrm e}^{\frac {x^{2} \ln \left (4 x \right )-x^{3}-x \ln \left (4 x \right )+x^{2}+2}{x \left (x -1\right )}}}} {\mathrm e}^{5}}{4}+\frac {{\mathrm e}^{{\mathrm e}^{x \,{\mathrm e}^{\frac {x^{2} \ln \left (4 x \right )-x^{3}-x \ln \left (4 x \right )+x^{2}+2}{x \left (x -1\right )}}}}}{4}\)	\(86\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((-x^4+4*x^3-5*x^2-2*x+2)*exp(5)-x^4+4*x^3-5*x^2-2*x+2)*exp(((x^2-x)*ln(4*x)-x^3+x^2+2)/(x^2-x))*exp(x*exp
(((x^2-x)*ln(4*x)-x^3+x^2+2)/(x^2-x)))*exp(exp(x*exp(((x^2-x)*ln(4*x)-x^3+x^2+2)/(x^2-x))))/(4*x^3-8*x^2+4*x),
x,method=_RETURNVERBOSE)

[Out]

1/4*exp(exp(x*exp((x^2*ln(4*x)-x^3-x*ln(4*x)+x^2+2)/x/(x-1))))*exp(5)+1/4*exp(exp(x*exp((x^2*ln(4*x)-x^3-x*ln(
4*x)+x^2+2)/x/(x-1))))

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maxima [A]  time = 1.37, size = 30, normalized size = 0.86 \begin {gather*} \frac {1}{4} \, {\left (e^{5} + 1\right )} e^{\left (e^{\left (4 \, x^{2} e^{\left (-x + \frac {2}{x - 1} - \frac {2}{x}\right )}\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-x^4+4*x^3-5*x^2-2*x+2)*exp(5)-x^4+4*x^3-5*x^2-2*x+2)*exp(((x^2-x)*log(4*x)-x^3+x^2+2)/(x^2-x))*ex
p(x*exp(((x^2-x)*log(4*x)-x^3+x^2+2)/(x^2-x)))*exp(exp(x*exp(((x^2-x)*log(4*x)-x^3+x^2+2)/(x^2-x))))/(4*x^3-8*
x^2+4*x),x, algorithm="maxima")

[Out]

1/4*(e^5 + 1)*e^(e^(4*x^2*e^(-x + 2/(x - 1) - 2/x)))

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mupad [B]  time = 4.47, size = 83, normalized size = 2.37 \begin {gather*} {\mathrm {e}}^{{\mathrm {e}}^{\frac {4\,x\,x^{\frac {x}{x-x^2}}\,{\mathrm {e}}^{\frac {x^3}{x-x^2}}\,{\mathrm {e}}^{-\frac {x^2}{x-x^2}}\,{\mathrm {e}}^{-\frac {2}{x-x^2}}}{x^{\frac {x^2}{x-x^2}}}}}\,\left (\frac {{\mathrm {e}}^5}{4}+\frac {1}{4}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp((log(4*x)*(x - x^2) - x^2 + x^3 - 2)/(x - x^2))*exp(x*exp((log(4*x)*(x - x^2) - x^2 + x^3 - 2)/(x -
x^2)))*exp(exp(x*exp((log(4*x)*(x - x^2) - x^2 + x^3 - 2)/(x - x^2))))*(2*x + exp(5)*(2*x + 5*x^2 - 4*x^3 + x^
4 - 2) + 5*x^2 - 4*x^3 + x^4 - 2))/(4*x - 8*x^2 + 4*x^3),x)

[Out]

exp(exp((4*x*x^(x/(x - x^2))*exp(x^3/(x - x^2))*exp(-x^2/(x - x^2))*exp(-2/(x - x^2)))/x^(x^2/(x - x^2))))*(ex
p(5)/4 + 1/4)

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sympy [A]  time = 5.89, size = 36, normalized size = 1.03 \begin {gather*} \frac {\left (1 + e^{5}\right ) e^{e^{x e^{\frac {- x^{3} + x^{2} + \left (x^{2} - x\right ) \log {\left (4 x \right )} + 2}{x^{2} - x}}}}}{4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-x**4+4*x**3-5*x**2-2*x+2)*exp(5)-x**4+4*x**3-5*x**2-2*x+2)*exp(((x**2-x)*ln(4*x)-x**3+x**2+2)/(x*
*2-x))*exp(x*exp(((x**2-x)*ln(4*x)-x**3+x**2+2)/(x**2-x)))*exp(exp(x*exp(((x**2-x)*ln(4*x)-x**3+x**2+2)/(x**2-
x))))/(4*x**3-8*x**2+4*x),x)

[Out]

(1 + exp(5))*exp(exp(x*exp((-x**3 + x**2 + (x**2 - x)*log(4*x) + 2)/(x**2 - x))))/4

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