Optimal. Leaf size=29 \[ \left (e^{e^x+x \left (4+e^x-\log \left (x^2 \log (2)\right )\right )}-\log (3)\right )^2 \]
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Rubi [B] time = 0.59, antiderivative size = 63, normalized size of antiderivative = 2.17, number of steps used = 3, number of rules used = 1, integrand size = 101, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.010, Rules used = {6706} \begin {gather*} e^{2 e^x x+8 x+2 e^x} \left (x^2\right )^{-2 x} \log ^{-2 x}(2)-e^{e^x x+4 x+e^x} \left (x^2\right )^{-x} \log (9) \log ^{-x}(2) \end {gather*}
Antiderivative was successfully verified.
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Rule 6706
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int e^{2 e^x+8 x+2 e^x x-2 x \log \left (x^2 \log (2)\right )} \left (4+e^x (4+2 x)-2 \log \left (x^2 \log (2)\right )\right ) \, dx+\int e^{e^x+4 x+e^x x-x \log \left (x^2 \log (2)\right )} \left (-4 \log (3)+e^x (-4-2 x) \log (3)+2 \log (3) \log \left (x^2 \log (2)\right )\right ) \, dx\\ &=e^{2 e^x+8 x+2 e^x x} \left (x^2\right )^{-2 x} \log ^{-2 x}(2)-e^{e^x+4 x+e^x x} \left (x^2\right )^{-x} \log ^{-x}(2) \log (9)\\ \end {aligned} \end {gather*}
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Mathematica [F] time = 5.80, size = 0, normalized size = 0.00 \begin {gather*} \int \left (e^{2 e^x+8 x+2 e^x x-2 x \log \left (x^2 \log (2)\right )} \left (4+e^x (4+2 x)-2 \log \left (x^2 \log (2)\right )\right )+e^{e^x+4 x+e^x x-x \log \left (x^2 \log (2)\right )} \left (-4 \log (3)+e^x (-4-2 x) \log (3)+2 \log (3) \log \left (x^2 \log (2)\right )\right )\right ) \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.79, size = 48, normalized size = 1.66 \begin {gather*} -2 \, e^{\left ({\left (x + 1\right )} e^{x} - x \log \left (x^{2} \log \relax (2)\right ) + 4 \, x\right )} \log \relax (3) + e^{\left (2 \, {\left (x + 1\right )} e^{x} - 2 \, x \log \left (x^{2} \log \relax (2)\right ) + 8 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.97, size = 50, normalized size = 1.72 \begin {gather*} -2 \, e^{\left (x e^{x} - x \log \left (x^{2} \log \relax (2)\right ) + 4 \, x + e^{x}\right )} \log \relax (3) + e^{\left (2 \, x e^{x} - 2 \, x \log \left (x^{2} \log \relax (2)\right ) + 8 \, x + 2 \, e^{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 1.77, size = 51, normalized size = 1.76
method | result | size |
default | \(-2 \ln \relax (3) {\mathrm e}^{-x \ln \left (x^{2} \ln \relax (2)\right )+{\mathrm e}^{x} x +4 x +{\mathrm e}^{x}}+{\mathrm e}^{-2 x \ln \left (x^{2} \ln \relax (2)\right )+2 \,{\mathrm e}^{x} x +8 x +2 \,{\mathrm e}^{x}}\) | \(51\) |
risch | \({\mathrm e}^{-4 x \ln \relax (x )+2 \,{\mathrm e}^{x} x -2 x \ln \left (\ln \relax (2)\right )+2 \,{\mathrm e}^{x}+8 x} {\mathrm e}^{i \pi x \mathrm {csgn}\left (i x^{2}\right )^{3}} {\mathrm e}^{-2 i \pi x \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}} {\mathrm e}^{i \pi x \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )}-2 \ln \relax (3) {\mathrm e}^{-2 x \ln \relax (x )+{\mathrm e}^{x} x -x \ln \left (\ln \relax (2)\right )+4 x +{\mathrm e}^{x}} {\mathrm e}^{\frac {i \pi x \mathrm {csgn}\left (i x^{2}\right )^{3}}{2}} {\mathrm e}^{-i \pi x \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}} {\mathrm e}^{\frac {i \pi x \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )}{2}}\) | \(164\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.70, size = 52, normalized size = 1.79 \begin {gather*} -2 \, e^{\left (x e^{x} - 2 \, x \log \relax (x) - x \log \left (\log \relax (2)\right ) + 4 \, x + e^{x}\right )} \log \relax (3) + e^{\left (2 \, x e^{x} - 4 \, x \log \relax (x) - 2 \, x \log \left (\log \relax (2)\right ) + 8 \, x + 2 \, e^{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.66, size = 59, normalized size = 2.03 \begin {gather*} -\frac {{\mathrm {e}}^{x\,{\mathrm {e}}^x}\,{\mathrm {e}}^{4\,x}\,{\mathrm {e}}^{{\mathrm {e}}^x}\,\left (2\,{\ln \relax (2)}^x\,\ln \relax (3)\,{\left (x^2\right )}^x-{\mathrm {e}}^{x\,{\mathrm {e}}^x}\,{\mathrm {e}}^{4\,x}\,{\mathrm {e}}^{{\mathrm {e}}^x}\right )}{{\ln \relax (2)}^{2\,x}\,{\left (x^2\right )}^{2\,x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 3.58, size = 60, normalized size = 2.07 \begin {gather*} - 2 e^{x e^{x} - x \log {\left (x^{2} \log {\relax (2 )} \right )} + 4 x} e^{e^{x}} \log {\relax (3 )} + e^{2 x e^{x} - 2 x \log {\left (x^{2} \log {\relax (2 )} \right )} + 8 x} e^{2 e^{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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