Optimal. Leaf size=30 \[ e^{e^{e^{e^x}-e^{2+x^2}} \left (x+(4-\log (x))^2\right )} \]
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Rubi [F]
time = 75.25, 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 {\exp \left (e^{e^x}-e^{2+x^2}+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) \left (-8+x+e^{2+x^2} \left (-32 x^2-2 x^3\right )+\left (2+16 e^{2+x^2} x^2\right ) \log (x)-2 e^{2+x^2} x^2 \log ^2(x)+e^{e^x} \left (e^x \left (16 x+x^2\right )-8 e^x x \log (x)+e^x x \log ^2(x)\right )\right )}{x} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-2 \exp \left (2+e^{e^x}-e^{2+x^2}+x^2+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) x \left (16+x-8 \log (x)+\log ^2(x)\right )+\frac {\exp \left (e^{e^x}-e^{2+x^2}+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) \left (-8+x+16 e^{e^x+x} x+e^{e^x+x} x^2+2 \log (x)-8 e^{e^x+x} x \log (x)+e^{e^x+x} x \log ^2(x)\right )}{x}\right ) \, dx\\ &=-\left (2 \int \exp \left (2+e^{e^x}-e^{2+x^2}+x^2+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) x \left (16+x-8 \log (x)+\log ^2(x)\right ) \, dx\right )+\int \frac {\exp \left (e^{e^x}-e^{2+x^2}+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) \left (-8+x+16 e^{e^x+x} x+e^{e^x+x} x^2+2 \log (x)-8 e^{e^x+x} x \log (x)+e^{e^x+x} x \log ^2(x)\right )}{x} \, dx\\ &=-\left (2 \int \left (\exp \left (2+e^{e^x}-e^{2+x^2}+x^2+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) x (16+x)-8 \exp \left (2+e^{e^x}-e^{2+x^2}+x^2+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) x \log (x)+\exp \left (2+e^{e^x}-e^{2+x^2}+x^2+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) x \log ^2(x)\right ) \, dx\right )+\int \left (\frac {\exp \left (e^{e^x}-e^{2+x^2}+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) (-8+x+2 \log (x))}{x}+\exp \left (e^{e^x}+e^x-e^{2+x^2}+x+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) \, dx\\ &=-\left (2 \int \exp \left (2+e^{e^x}-e^{2+x^2}+x^2+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) x (16+x) \, dx\right )-2 \int \exp \left (2+e^{e^x}-e^{2+x^2}+x^2+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) x \log ^2(x) \, dx+16 \int \exp \left (2+e^{e^x}-e^{2+x^2}+x^2+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) x \log (x) \, dx+\int \frac {\exp \left (e^{e^x}-e^{2+x^2}+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) (-8+x+2 \log (x))}{x} \, dx+\int \exp \left (e^{e^x}+e^x-e^{2+x^2}+x+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) \left (16+x-8 \log (x)+\log ^2(x)\right ) \, dx\\ &=-\left (2 \int \left (16 \exp \left (2+e^{e^x}-e^{2+x^2}+x^2+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) x+\exp \left (2+e^{e^x}-e^{2+x^2}+x^2+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) x^2\right ) \, dx\right )-2 \int \exp \left (2+e^{e^x}-e^{2+x^2}+x^2+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) x \log ^2(x) \, dx+16 \int \exp \left (2+e^{e^x}-e^{2+x^2}+x^2+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) x \log (x) \, dx+\int \left (\frac {\exp \left (e^{e^x}-e^{2+x^2}+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) (-8+x)}{x}+\frac {2 \exp \left (e^{e^x}-e^{2+x^2}+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) \log (x)}{x}\right ) \, dx+\int \left (16 \exp \left (e^{e^x}+e^x-e^{2+x^2}+x+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right )+\exp \left (e^{e^x}+e^x-e^{2+x^2}+x+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) x-8 \exp \left (e^{e^x}+e^x-e^{2+x^2}+x+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) \log (x)+\exp \left (e^{e^x}+e^x-e^{2+x^2}+x+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) \log ^2(x)\right ) \, dx\\ &=-\left (2 \int \exp \left (2+e^{e^x}-e^{2+x^2}+x^2+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) x^2 \, dx\right )+2 \int \frac {\exp \left (e^{e^x}-e^{2+x^2}+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) \log (x)}{x} \, dx-2 \int \exp \left (2+e^{e^x}-e^{2+x^2}+x^2+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) x \log ^2(x) \, dx-8 \int \exp \left (e^{e^x}+e^x-e^{2+x^2}+x+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) \log (x) \, dx+16 \int \exp \left (e^{e^x}+e^x-e^{2+x^2}+x+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) \, dx+16 \int \exp \left (2+e^{e^x}-e^{2+x^2}+x^2+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) x \log (x) \, dx-32 \int \exp \left (2+e^{e^x}-e^{2+x^2}+x^2+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) x \, dx+\int \frac {\exp \left (e^{e^x}-e^{2+x^2}+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) (-8+x)}{x} \, dx+\int \exp \left (e^{e^x}+e^x-e^{2+x^2}+x+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) x \, dx+\int \exp \left (e^{e^x}+e^x-e^{2+x^2}+x+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) \log ^2(x) \, dx\\ &=-\left (2 \int \exp \left (2+e^{e^x}-e^{2+x^2}+x^2+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) x^2 \, dx\right )+2 \int \frac {\exp \left (e^{e^x}-e^{2+x^2}+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) \log (x)}{x} \, dx-2 \int \exp \left (2+e^{e^x}-e^{2+x^2}+x^2+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) x \log ^2(x) \, dx-8 \int \exp \left (e^{e^x}+e^x-e^{2+x^2}+x+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) \log (x) \, dx+16 \int \exp \left (e^{e^x}+e^x-e^{2+x^2}+x+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) \, dx+16 \int \exp \left (2+e^{e^x}-e^{2+x^2}+x^2+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) x \log (x) \, dx-32 \int \exp \left (2+e^{e^x}-e^{2+x^2}+x^2+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) x \, dx+\int \left (\exp \left (e^{e^x}-e^{2+x^2}+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right )-\frac {8 \exp \left (e^{e^x}-e^{2+x^2}+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right )}{x}\right ) \, dx+\int \exp \left (e^{e^x}+e^x-e^{2+x^2}+x+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) x \, dx+\int \exp \left (e^{e^x}+e^x-e^{2+x^2}+x+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) \log ^2(x) \, dx\\ &=-\left (2 \int \exp \left (2+e^{e^x}-e^{2+x^2}+x^2+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) x^2 \, dx\right )+2 \int \frac {\exp \left (e^{e^x}-e^{2+x^2}+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) \log (x)}{x} \, dx-2 \int \exp \left (2+e^{e^x}-e^{2+x^2}+x^2+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) x \log ^2(x) \, dx-8 \int \frac {\exp \left (e^{e^x}-e^{2+x^2}+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right )}{x} \, dx-8 \int \exp \left (e^{e^x}+e^x-e^{2+x^2}+x+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) \log (x) \, dx+16 \int \exp \left (e^{e^x}+e^x-e^{2+x^2}+x+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) \, dx+16 \int \exp \left (2+e^{e^x}-e^{2+x^2}+x^2+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) x \log (x) \, dx-32 \int \exp \left (2+e^{e^x}-e^{2+x^2}+x^2+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) x \, dx+\int \exp \left (e^{e^x}-e^{2+x^2}+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) \, dx+\int \exp \left (e^{e^x}+e^x-e^{2+x^2}+x+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) x \, dx+\int \exp \left (e^{e^x}+e^x-e^{2+x^2}+x+e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )\right ) \log ^2(x) \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.31, size = 31, normalized size = 1.03 \begin {gather*} e^{e^{e^{e^x}-e^{2+x^2}} \left (16+x-8 \log (x)+\log ^2(x)\right )} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.36, size = 27, normalized size = 0.90
method | result | size |
risch | \({\mathrm e}^{\left (\ln \left (x \right )^{2}-8 \ln \left (x \right )+x +16\right ) {\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x}}-{\mathrm e}^{x^{2}+2}}}\) | \(27\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 67 vs.
\(2 (23) = 46\).
time = 0.96, size = 67, normalized size = 2.23 \begin {gather*} e^{\left (e^{\left (-e^{\left (x^{2} + 2\right )} + e^{\left (e^{x}\right )}\right )} \log \left (x\right )^{2} + x e^{\left (-e^{\left (x^{2} + 2\right )} + e^{\left (e^{x}\right )}\right )} - 8 \, e^{\left (-e^{\left (x^{2} + 2\right )} + e^{\left (e^{x}\right )}\right )} \log \left (x\right ) + 16 \, e^{\left (-e^{\left (x^{2} + 2\right )} + e^{\left (e^{x}\right )}\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.39, size = 26, normalized size = 0.87 \begin {gather*} e^{\left ({\left (\log \left (x\right )^{2} + x - 8 \, \log \left (x\right ) + 16\right )} e^{\left (-e^{\left (x^{2} + 2\right )} + e^{\left (e^{x}\right )}\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] Timed out
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 5.39, size = 71, normalized size = 2.37 \begin {gather*} \frac {{\mathrm {e}}^{{\mathrm {e}}^{-{\mathrm {e}}^{x^2}\,{\mathrm {e}}^2}\,{\mathrm {e}}^{{\mathrm {e}}^{{\mathrm {e}}^x}}\,{\ln \left (x\right )}^2}\,{\mathrm {e}}^{x\,{\mathrm {e}}^{-{\mathrm {e}}^{x^2}\,{\mathrm {e}}^2}\,{\mathrm {e}}^{{\mathrm {e}}^{{\mathrm {e}}^x}}}\,{\mathrm {e}}^{16\,{\mathrm {e}}^{-{\mathrm {e}}^{x^2}\,{\mathrm {e}}^2}\,{\mathrm {e}}^{{\mathrm {e}}^{{\mathrm {e}}^x}}}}{x^{8\,{\mathrm {e}}^{-{\mathrm {e}}^{x^2}\,{\mathrm {e}}^2}\,{\mathrm {e}}^{{\mathrm {e}}^{{\mathrm {e}}^x}}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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