3.80.3 \(\int \frac {-1+e^{e^{e^{7+x^2}}}-\log (x)+2 e^{7+e^{7+x^2}+x^2} x^2 \log (x)+(-e^{e^{e^{7+x^2}}}+\log (x)) \log (e^{-e^{e^{7+x^2}}} (e^{e^{e^{7+x^2}}} x-x \log (x)))}{e^{e^{e^{7+x^2}}} x^2-x^2 \log (x)} \, dx\)

Optimal. Leaf size=26 \[ \frac {\log \left (x \left (1-e^{-e^{e^{7+x^2}}} \log (x)\right )\right )}{x} \]

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Rubi [F]  time = 1.82, 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*} \int \frac {-1+e^{e^{e^{7+x^2}}}-\log (x)+2 e^{7+e^{7+x^2}+x^2} x^2 \log (x)+\left (-e^{e^{e^{7+x^2}}}+\log (x)\right ) \log \left (e^{-e^{e^{7+x^2}}} \left (e^{e^{e^{7+x^2}}} x-x \log (x)\right )\right )}{e^{e^{e^{7+x^2}}} x^2-x^2 \log (x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-1 + E^E^E^(7 + x^2) - Log[x] + 2*E^(7 + E^(7 + x^2) + x^2)*x^2*Log[x] + (-E^E^E^(7 + x^2) + Log[x])*Log[
(E^E^E^(7 + x^2)*x - x*Log[x])/E^E^E^(7 + x^2)])/(E^E^E^(7 + x^2)*x^2 - x^2*Log[x]),x]

[Out]

-x^(-1) - Defer[Int][1/(x^2*(E^E^E^(7 + x^2) - Log[x])), x] + 2*Defer[Int][(E^(7 + E^(7 + x^2) + x^2)*Log[x])/
(E^E^E^(7 + x^2) - Log[x]), x] - Defer[Int][Log[x - (x*Log[x])/E^E^E^(7 + x^2)]/x^2, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {2 e^{7+e^{7+x^2}+x^2} \log (x)}{e^{e^{e^{7+x^2}}}-\log (x)}-\frac {1-e^{e^{e^{7+x^2}}}+\log (x)+e^{e^{e^{7+x^2}}} \log \left (x-e^{-e^{e^{7+x^2}}} x \log (x)\right )-\log (x) \log \left (x-e^{-e^{e^{7+x^2}}} x \log (x)\right )}{x^2 \left (e^{e^{e^{7+x^2}}}-\log (x)\right )}\right ) \, dx\\ &=2 \int \frac {e^{7+e^{7+x^2}+x^2} \log (x)}{e^{e^{e^{7+x^2}}}-\log (x)} \, dx-\int \frac {1-e^{e^{e^{7+x^2}}}+\log (x)+e^{e^{e^{7+x^2}}} \log \left (x-e^{-e^{e^{7+x^2}}} x \log (x)\right )-\log (x) \log \left (x-e^{-e^{e^{7+x^2}}} x \log (x)\right )}{x^2 \left (e^{e^{e^{7+x^2}}}-\log (x)\right )} \, dx\\ &=2 \int \frac {e^{7+e^{7+x^2}+x^2} \log (x)}{e^{e^{e^{7+x^2}}}-\log (x)} \, dx-\int \left (\frac {1}{x^2 \left (e^{e^{e^{7+x^2}}}-\log (x)\right )}+\frac {-1+\log \left (x-e^{-e^{e^{7+x^2}}} x \log (x)\right )}{x^2}\right ) \, dx\\ &=2 \int \frac {e^{7+e^{7+x^2}+x^2} \log (x)}{e^{e^{e^{7+x^2}}}-\log (x)} \, dx-\int \frac {1}{x^2 \left (e^{e^{e^{7+x^2}}}-\log (x)\right )} \, dx-\int \frac {-1+\log \left (x-e^{-e^{e^{7+x^2}}} x \log (x)\right )}{x^2} \, dx\\ &=2 \int \frac {e^{7+e^{7+x^2}+x^2} \log (x)}{e^{e^{e^{7+x^2}}}-\log (x)} \, dx-\int \frac {1}{x^2 \left (e^{e^{e^{7+x^2}}}-\log (x)\right )} \, dx-\int \left (-\frac {1}{x^2}+\frac {\log \left (x-e^{-e^{e^{7+x^2}}} x \log (x)\right )}{x^2}\right ) \, dx\\ &=-\frac {1}{x}+2 \int \frac {e^{7+e^{7+x^2}+x^2} \log (x)}{e^{e^{e^{7+x^2}}}-\log (x)} \, dx-\int \frac {1}{x^2 \left (e^{e^{e^{7+x^2}}}-\log (x)\right )} \, dx-\int \frac {\log \left (x-e^{-e^{e^{7+x^2}}} x \log (x)\right )}{x^2} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.19, size = 25, normalized size = 0.96 \begin {gather*} \frac {\log \left (x-e^{-e^{e^{7+x^2}}} x \log (x)\right )}{x} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-1 + E^E^E^(7 + x^2) - Log[x] + 2*E^(7 + E^(7 + x^2) + x^2)*x^2*Log[x] + (-E^E^E^(7 + x^2) + Log[x]
)*Log[(E^E^E^(7 + x^2)*x - x*Log[x])/E^E^E^(7 + x^2)])/(E^E^E^(7 + x^2)*x^2 - x^2*Log[x]),x]

[Out]

Log[x - (x*Log[x])/E^E^E^(7 + x^2)]/x

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fricas [A]  time = 1.12, size = 32, normalized size = 1.23 \begin {gather*} \frac {\log \left ({\left (x e^{\left (e^{\left (e^{\left (x^{2} + 7\right )}\right )}\right )} - x \log \relax (x)\right )} e^{\left (-e^{\left (e^{\left (x^{2} + 7\right )}\right )}\right )}\right )}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-exp(exp(exp(x^2+7)))+log(x))*log((x*exp(exp(exp(x^2+7)))-x*log(x))/exp(exp(exp(x^2+7))))+exp(exp(
exp(x^2+7)))+2*x^2*exp(x^2+7)*log(x)*exp(exp(x^2+7))-log(x)-1)/(x^2*exp(exp(exp(x^2+7)))-x^2*log(x)),x, algori
thm="fricas")

[Out]

log((x*e^(e^(e^(x^2 + 7))) - x*log(x))*e^(-e^(e^(x^2 + 7))))/x

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {2 \, x^{2} e^{\left (x^{2} + e^{\left (x^{2} + 7\right )} + 7\right )} \log \relax (x) - {\left (e^{\left (e^{\left (e^{\left (x^{2} + 7\right )}\right )}\right )} - \log \relax (x)\right )} \log \left ({\left (x e^{\left (e^{\left (e^{\left (x^{2} + 7\right )}\right )}\right )} - x \log \relax (x)\right )} e^{\left (-e^{\left (e^{\left (x^{2} + 7\right )}\right )}\right )}\right ) + e^{\left (e^{\left (e^{\left (x^{2} + 7\right )}\right )}\right )} - \log \relax (x) - 1}{x^{2} e^{\left (e^{\left (e^{\left (x^{2} + 7\right )}\right )}\right )} - x^{2} \log \relax (x)}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-exp(exp(exp(x^2+7)))+log(x))*log((x*exp(exp(exp(x^2+7)))-x*log(x))/exp(exp(exp(x^2+7))))+exp(exp(
exp(x^2+7)))+2*x^2*exp(x^2+7)*log(x)*exp(exp(x^2+7))-log(x)-1)/(x^2*exp(exp(exp(x^2+7)))-x^2*log(x)),x, algori
thm="giac")

[Out]

integrate((2*x^2*e^(x^2 + e^(x^2 + 7) + 7)*log(x) - (e^(e^(e^(x^2 + 7))) - log(x))*log((x*e^(e^(e^(x^2 + 7)))
- x*log(x))*e^(-e^(e^(x^2 + 7)))) + e^(e^(e^(x^2 + 7))) - log(x) - 1)/(x^2*e^(e^(e^(x^2 + 7))) - x^2*log(x)),
x)

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maple [C]  time = 0.22, size = 470, normalized size = 18.08

method	result	size
risch	\(-\frac {\ln \left ({\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x^{2}+7}}}\right )}{x}+\frac {-i \pi \,\mathrm {csgn}\left (i \left (-{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x^{2}+7}}}+\ln \relax (x )\right )\right ) \mathrm {csgn}\left (i {\mathrm e}^{-{\mathrm e}^{{\mathrm e}^{x^{2}+7}}}\right ) \mathrm {csgn}\left (i {\mathrm e}^{-{\mathrm e}^{{\mathrm e}^{x^{2}+7}}} \left (-{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x^{2}+7}}}+\ln \relax (x )\right )\right )+i \pi \,\mathrm {csgn}\left (i \left (-{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x^{2}+7}}}+\ln \relax (x )\right )\right ) \mathrm {csgn}\left (i {\mathrm e}^{-{\mathrm e}^{{\mathrm e}^{x^{2}+7}}} \left (-{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x^{2}+7}}}+\ln \relax (x )\right )\right )^{2}+i \pi \,\mathrm {csgn}\left (i {\mathrm e}^{-{\mathrm e}^{{\mathrm e}^{x^{2}+7}}}\right ) \mathrm {csgn}\left (i {\mathrm e}^{-{\mathrm e}^{{\mathrm e}^{x^{2}+7}}} \left (-{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x^{2}+7}}}+\ln \relax (x )\right )\right )^{2}-i \pi \mathrm {csgn}\left (i {\mathrm e}^{-{\mathrm e}^{{\mathrm e}^{x^{2}+7}}} \left (-{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x^{2}+7}}}+\ln \relax (x )\right )\right )^{3}+i \pi \,\mathrm {csgn}\left (i {\mathrm e}^{-{\mathrm e}^{{\mathrm e}^{x^{2}+7}}} \left (-{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x^{2}+7}}}+\ln \relax (x )\right )\right ) \mathrm {csgn}\left (i x \left (-{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x^{2}+7}}}+\ln \relax (x )\right ) {\mathrm e}^{-{\mathrm e}^{{\mathrm e}^{x^{2}+7}}}\right )^{2}-i \pi \,\mathrm {csgn}\left (i {\mathrm e}^{-{\mathrm e}^{{\mathrm e}^{x^{2}+7}}} \left (-{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x^{2}+7}}}+\ln \relax (x )\right )\right ) \mathrm {csgn}\left (i x \left (-{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x^{2}+7}}}+\ln \relax (x )\right ) {\mathrm e}^{-{\mathrm e}^{{\mathrm e}^{x^{2}+7}}}\right ) \mathrm {csgn}\left (i x \right )+i \pi \mathrm {csgn}\left (i x \left (-{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x^{2}+7}}}+\ln \relax (x )\right ) {\mathrm e}^{-{\mathrm e}^{{\mathrm e}^{x^{2}+7}}}\right )^{3}-2 i \pi \mathrm {csgn}\left (i x \left (-{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x^{2}+7}}}+\ln \relax (x )\right ) {\mathrm e}^{-{\mathrm e}^{{\mathrm e}^{x^{2}+7}}}\right )^{2}+i \pi \mathrm {csgn}\left (i x \left (-{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x^{2}+7}}}+\ln \relax (x )\right ) {\mathrm e}^{-{\mathrm e}^{{\mathrm e}^{x^{2}+7}}}\right )^{2} \mathrm {csgn}\left (i x \right )+2 i \pi +2 \ln \relax (x )+2 \ln \left (-{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x^{2}+7}}}+\ln \relax (x )\right )}{2 x}\)	\(470\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((-exp(exp(exp(x^2+7)))+ln(x))*ln((x*exp(exp(exp(x^2+7)))-x*ln(x))/exp(exp(exp(x^2+7))))+exp(exp(exp(x^2+7
)))+2*x^2*exp(x^2+7)*ln(x)*exp(exp(x^2+7))-ln(x)-1)/(x^2*exp(exp(exp(x^2+7)))-x^2*ln(x)),x,method=_RETURNVERBO
SE)

[Out]

-1/x*ln(exp(exp(exp(x^2+7))))+1/2*(-I*Pi*csgn(I*(-exp(exp(exp(x^2+7)))+ln(x)))*csgn(I*exp(-exp(exp(x^2+7))))*c
sgn(I*exp(-exp(exp(x^2+7)))*(-exp(exp(exp(x^2+7)))+ln(x)))+I*Pi*csgn(I*(-exp(exp(exp(x^2+7)))+ln(x)))*csgn(I*e
xp(-exp(exp(x^2+7)))*(-exp(exp(exp(x^2+7)))+ln(x)))^2+I*Pi*csgn(I*exp(-exp(exp(x^2+7))))*csgn(I*exp(-exp(exp(x
^2+7)))*(-exp(exp(exp(x^2+7)))+ln(x)))^2-I*Pi*csgn(I*exp(-exp(exp(x^2+7)))*(-exp(exp(exp(x^2+7)))+ln(x)))^3+I*
Pi*csgn(I*exp(-exp(exp(x^2+7)))*(-exp(exp(exp(x^2+7)))+ln(x)))*csgn(I*x*(-exp(exp(exp(x^2+7)))+ln(x))*exp(-exp
(exp(x^2+7))))^2-I*Pi*csgn(I*exp(-exp(exp(x^2+7)))*(-exp(exp(exp(x^2+7)))+ln(x)))*csgn(I*x*(-exp(exp(exp(x^2+7
)))+ln(x))*exp(-exp(exp(x^2+7))))*csgn(I*x)+I*Pi*csgn(I*x*(-exp(exp(exp(x^2+7)))+ln(x))*exp(-exp(exp(x^2+7))))
^3-2*I*Pi*csgn(I*x*(-exp(exp(exp(x^2+7)))+ln(x))*exp(-exp(exp(x^2+7))))^2+I*Pi*csgn(I*x*(-exp(exp(exp(x^2+7)))
+ln(x))*exp(-exp(exp(x^2+7))))^2*csgn(I*x)+2*I*Pi+2*ln(x)+2*ln(-exp(exp(exp(x^2+7)))+ln(x)))/x

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maxima [A]  time = 0.44, size = 33, normalized size = 1.27 \begin {gather*} -\frac {e^{\left (e^{\left (x^{2} + 7\right )}\right )} - \log \relax (x) - \log \left (e^{\left (e^{\left (e^{\left (x^{2} + 7\right )}\right )}\right )} - \log \relax (x)\right )}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-exp(exp(exp(x^2+7)))+log(x))*log((x*exp(exp(exp(x^2+7)))-x*log(x))/exp(exp(exp(x^2+7))))+exp(exp(
exp(x^2+7)))+2*x^2*exp(x^2+7)*log(x)*exp(exp(x^2+7))-log(x)-1)/(x^2*exp(exp(exp(x^2+7)))-x^2*log(x)),x, algori
thm="maxima")

[Out]

-(e^(e^(x^2 + 7)) - log(x) - log(e^(e^(e^(x^2 + 7))) - log(x)))/x

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mupad [B]  time = 5.42, size = 23, normalized size = 0.88 \begin {gather*} \frac {\ln \left (x-x\,{\mathrm {e}}^{-{\mathrm {e}}^{{\mathrm {e}}^{x^2}\,{\mathrm {e}}^7}}\,\ln \relax (x)\right )}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((log(x) - exp(exp(exp(x^2 + 7))) + log(exp(-exp(exp(x^2 + 7)))*(x*exp(exp(exp(x^2 + 7))) - x*log(x)))*(exp
(exp(exp(x^2 + 7))) - log(x)) - 2*x^2*exp(exp(x^2 + 7))*exp(x^2 + 7)*log(x) + 1)/(x^2*log(x) - x^2*exp(exp(exp
(x^2 + 7)))),x)

[Out]

log(x - x*exp(-exp(exp(x^2)*exp(7)))*log(x))/x

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sympy [A]  time = 77.90, size = 29, normalized size = 1.12 \begin {gather*} \frac {\log {\left (\left (x e^{e^{e^{x^{2} + 7}}} - x \log {\relax (x )}\right ) e^{- e^{e^{x^{2} + 7}}} \right )}}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-exp(exp(exp(x**2+7)))+ln(x))*ln((x*exp(exp(exp(x**2+7)))-x*ln(x))/exp(exp(exp(x**2+7))))+exp(exp(
exp(x**2+7)))+2*x**2*exp(x**2+7)*ln(x)*exp(exp(x**2+7))-ln(x)-1)/(x**2*exp(exp(exp(x**2+7)))-x**2*ln(x)),x)

[Out]

log((x*exp(exp(exp(x**2 + 7))) - x*log(x))*exp(-exp(exp(x**2 + 7))))/x

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