3.2.76 \(\int \frac {e^{3-e^{e^{-\frac {4}{\log (x)}} (x+e^{\frac {4}{\log (x)}} (65536+512 x+x^2))}+e^{-\frac {4}{\log (x)}} (x+e^{\frac {4}{\log (x)}} (65536+512 x+x^2))-\frac {4}{\log (x)}} (-4-\log ^2(x)+e^{\frac {4}{\log (x)}} (-512-2 x) \log ^2(x))}{\log ^2(x)} \, dx\)

Optimal. Leaf size=24 \[ e^{3-e^{e^{-\frac {4}{\log (x)}} x+(256+x)^2}} \]

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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^(3 - E^((x + E^(4/Log[x])*(65536 + 512*x + x^2))/E^(4/Log[x])) + (x + E^(4/Log[x])*(65536 + 512*x + x^2
))/E^(4/Log[x]) - 4/Log[x])*(-4 - Log[x]^2 + E^(4/Log[x])*(-512 - 2*x)*Log[x]^2))/Log[x]^2,x]

[Out]

$Aborted

Rubi steps

Aborted

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Mathematica [A]  time = 12.84, size = 26, normalized size = 1.08 \begin {gather*} e^{3-e^{65536+512 x+e^{-\frac {4}{\log (x)}} x+x^2}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^(3 - E^((x + E^(4/Log[x])*(65536 + 512*x + x^2))/E^(4/Log[x])) + (x + E^(4/Log[x])*(65536 + 512*x
+ x^2))/E^(4/Log[x]) - 4/Log[x])*(-4 - Log[x]^2 + E^(4/Log[x])*(-512 - 2*x)*Log[x]^2))/Log[x]^2,x]

[Out]

E^(3 - E^(65536 + 512*x + x/E^(4/Log[x]) + x^2))

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fricas [B]  time = 1.05, size = 111, normalized size = 4.62 \begin {gather*} e^{\left (-{\left ({\left (x^{2} + 512 \, x + 65536\right )} e^{\frac {4}{\log \relax (x)}} + x\right )} e^{\left (-\frac {4}{\log \relax (x)}\right )} + \frac {{\left ({\left ({\left (x^{2} + 512 \, x + 65539\right )} \log \relax (x) - 4\right )} e^{\frac {4}{\log \relax (x)}} + x \log \relax (x) - e^{\left ({\left ({\left (x^{2} + 512 \, x + 65536\right )} e^{\frac {4}{\log \relax (x)}} + x\right )} e^{\left (-\frac {4}{\log \relax (x)}\right )} + \frac {4}{\log \relax (x)}\right )} \log \relax (x)\right )} e^{\left (-\frac {4}{\log \relax (x)}\right )}}{\log \relax (x)} + \frac {4}{\log \relax (x)}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-2*x-512)*log(x)^2*exp(4/log(x))-log(x)^2-4)*exp(((x^2+512*x+65536)*exp(4/log(x))+x)/exp(4/log(x))
)*exp(-exp(((x^2+512*x+65536)*exp(4/log(x))+x)/exp(4/log(x)))+3)/log(x)^2/exp(4/log(x)),x, algorithm="fricas")

[Out]

e^(-((x^2 + 512*x + 65536)*e^(4/log(x)) + x)*e^(-4/log(x)) + (((x^2 + 512*x + 65539)*log(x) - 4)*e^(4/log(x))
+ x*log(x) - e^(((x^2 + 512*x + 65536)*e^(4/log(x)) + x)*e^(-4/log(x)) + 4/log(x))*log(x))*e^(-4/log(x))/log(x
) + 4/log(x))

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giac [F(-2)]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: TypeError} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-2*x-512)*log(x)^2*exp(4/log(x))-log(x)^2-4)*exp(((x^2+512*x+65536)*exp(4/log(x))+x)/exp(4/log(x))
)*exp(-exp(((x^2+512*x+65536)*exp(4/log(x))+x)/exp(4/log(x)))+3)/log(x)^2/exp(4/log(x)),x, algorithm="giac")

[Out]

Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,sageVARx):;OUTP
UT:int(sage0,sageVARx)  Error: Invalid dimension

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maple [A]  time = 0.03, size = 24, normalized size = 1.00

method	result	size
risch	\({\mathrm e}^{-{\mathrm e}^{x^{2}+512 x +65536+{\mathrm e}^{-\frac {4}{\ln \relax (x )}} x}+3}\)	\(24\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((-2*x-512)*ln(x)^2*exp(4/ln(x))-ln(x)^2-4)*exp(((x^2+512*x+65536)*exp(4/ln(x))+x)/exp(4/ln(x)))*exp(-exp(
((x^2+512*x+65536)*exp(4/ln(x))+x)/exp(4/ln(x)))+3)/ln(x)^2/exp(4/ln(x)),x,method=_RETURNVERBOSE)

[Out]

exp(-exp(x^2+512*x+65536+exp(-4/ln(x))*x)+3)

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maxima [A]  time = 0.81, size = 23, normalized size = 0.96 \begin {gather*} e^{\left (-e^{\left (x^{2} + x e^{\left (-\frac {4}{\log \relax (x)}\right )} + 512 \, x + 65536\right )} + 3\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-2*x-512)*log(x)^2*exp(4/log(x))-log(x)^2-4)*exp(((x^2+512*x+65536)*exp(4/log(x))+x)/exp(4/log(x))
)*exp(-exp(((x^2+512*x+65536)*exp(4/log(x))+x)/exp(4/log(x)))+3)/log(x)^2/exp(4/log(x)),x, algorithm="maxima")

[Out]

e^(-e^(x^2 + x*e^(-4/log(x)) + 512*x + 65536) + 3)

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mupad [B]  time = 0.54, size = 26, normalized size = 1.08 \begin {gather*} {\mathrm {e}}^3\,{\mathrm {e}}^{-{\mathrm {e}}^{512\,x}\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^{x\,{\mathrm {e}}^{-\frac {4}{\ln \relax (x)}}}\,{\mathrm {e}}^{65536}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(-4/log(x))*exp(exp(-4/log(x))*(x + exp(4/log(x))*(512*x + x^2 + 65536)))*exp(3 - exp(exp(-4/log(x))*
(x + exp(4/log(x))*(512*x + x^2 + 65536))))*(log(x)^2 + exp(4/log(x))*log(x)^2*(2*x + 512) + 4))/log(x)^2,x)

[Out]

exp(3)*exp(-exp(512*x)*exp(x^2)*exp(x*exp(-4/log(x)))*exp(65536))

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sympy [A]  time = 16.86, size = 27, normalized size = 1.12 \begin {gather*} e^{3 - e^{\left (x + \left (x^{2} + 512 x + 65536\right ) e^{\frac {4}{\log {\relax (x )}}}\right ) e^{- \frac {4}{\log {\relax (x )}}}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-2*x-512)*ln(x)**2*exp(4/ln(x))-ln(x)**2-4)*exp(((x**2+512*x+65536)*exp(4/ln(x))+x)/exp(4/ln(x)))*
exp(-exp(((x**2+512*x+65536)*exp(4/ln(x))+x)/exp(4/ln(x)))+3)/ln(x)**2/exp(4/ln(x)),x)

[Out]

exp(3 - exp((x + (x**2 + 512*x + 65536)*exp(4/log(x)))*exp(-4/log(x))))

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