Optimal. Leaf size=29 \[ \left (5+\log \left (\left (-e^{e^x}+2 x-\frac {16 e^{4 x}}{\log (x)}\right )^2\right )\right )^2 \]
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Rubi [B] time = 2.75, antiderivative size = 61, normalized size of antiderivative = 2.10, number of steps used = 4, number of rules used = 3, integrand size = 181, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.017, Rules used = {6688, 12, 6708} \begin {gather*} \log ^2\left (\frac {\left (16 e^{4 x}+\left (e^{e^x}-2 x\right ) \log (x)\right )^2}{\log ^2(x)}\right )+10 \log \left (\frac {\left (16 e^{4 x}+\left (e^{e^x}-2 x\right ) \log (x)\right )^2}{\log ^2(x)}\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6688
Rule 6708
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {4 \left (16 e^{4 x}-64 e^{4 x} x \log (x)-\left (-2+e^{e^x+x}\right ) x \log ^2(x)\right ) \left (-5-\log \left (\frac {\left (16 e^{4 x}+\left (e^{e^x}-2 x\right ) \log (x)\right )^2}{\log ^2(x)}\right )\right )}{x \log (x) \left (16 e^{4 x}+\left (e^{e^x}-2 x\right ) \log (x)\right )} \, dx\\ &=4 \int \frac {\left (16 e^{4 x}-64 e^{4 x} x \log (x)-\left (-2+e^{e^x+x}\right ) x \log ^2(x)\right ) \left (-5-\log \left (\frac {\left (16 e^{4 x}+\left (e^{e^x}-2 x\right ) \log (x)\right )^2}{\log ^2(x)}\right )\right )}{x \log (x) \left (16 e^{4 x}+\left (e^{e^x}-2 x\right ) \log (x)\right )} \, dx\\ &=2 \operatorname {Subst}\left (\int (-5+x) \, dx,x,-\log \left (\frac {\left (16 e^{4 x}+\left (e^{e^x}-2 x\right ) \log (x)\right )^2}{\log ^2(x)}\right )\right )\\ &=10 \log \left (\frac {\left (16 e^{4 x}+\left (e^{e^x}-2 x\right ) \log (x)\right )^2}{\log ^2(x)}\right )+\log ^2\left (\frac {\left (16 e^{4 x}+\left (e^{e^x}-2 x\right ) \log (x)\right )^2}{\log ^2(x)}\right )\\ \end {aligned} \end {gather*}
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Mathematica [B] time = 0.19, size = 59, normalized size = 2.03 \begin {gather*} \log \left (\frac {\left (16 e^{4 x}+\left (e^{e^x}-2 x\right ) \log (x)\right )^2}{\log ^2(x)}\right ) \left (10+\log \left (\frac {\left (16 e^{4 x}+\left (e^{e^x}-2 x\right ) \log (x)\right )^2}{\log ^2(x)}\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.65, size = 159, normalized size = 5.48 \begin {gather*} \log \left (\frac {{\left (4 \, x^{2} e^{\left (2 \, x\right )} \log \relax (x)^{2} - 64 \, x e^{\left (6 \, x\right )} \log \relax (x) + e^{\left (2 \, x + 2 \, e^{x}\right )} \log \relax (x)^{2} - 4 \, {\left (x e^{x} \log \relax (x)^{2} - 8 \, e^{\left (5 \, x\right )} \log \relax (x)\right )} e^{\left (x + e^{x}\right )} + 256 \, e^{\left (10 \, x\right )}\right )} e^{\left (-2 \, x\right )}}{\log \relax (x)^{2}}\right )^{2} + 10 \, \log \left (\frac {{\left (4 \, x^{2} e^{\left (2 \, x\right )} \log \relax (x)^{2} - 64 \, x e^{\left (6 \, x\right )} \log \relax (x) + e^{\left (2 \, x + 2 \, e^{x}\right )} \log \relax (x)^{2} - 4 \, {\left (x e^{x} \log \relax (x)^{2} - 8 \, e^{\left (5 \, x\right )} \log \relax (x)\right )} e^{\left (x + e^{x}\right )} + 256 \, e^{\left (10 \, x\right )}\right )} e^{\left (-2 \, x\right )}}{\log \relax (x)^{2}}\right ) \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*} \int -\frac {4 \, {\left (5 \, x e^{\left (x + e^{x}\right )} \log \relax (x)^{2} + 320 \, x e^{\left (4 \, x\right )} \log \relax (x) - 10 \, x \log \relax (x)^{2} + {\left (x e^{\left (x + e^{x}\right )} \log \relax (x)^{2} + 64 \, x e^{\left (4 \, x\right )} \log \relax (x) - 2 \, x \log \relax (x)^{2} - 16 \, e^{\left (4 \, x\right )}\right )} \log \left (\frac {4 \, x^{2} \log \relax (x)^{2} - 64 \, x e^{\left (4 \, x\right )} \log \relax (x) + e^{\left (2 \, e^{x}\right )} \log \relax (x)^{2} - 4 \, {\left (x \log \relax (x)^{2} - 8 \, e^{\left (4 \, x\right )} \log \relax (x)\right )} e^{\left (e^{x}\right )} + 256 \, e^{\left (8 \, x\right )}}{\log \relax (x)^{2}}\right ) - 80 \, e^{\left (4 \, x\right )}\right )}}{2 \, x^{2} \log \relax (x)^{2} - x e^{\left (e^{x}\right )} \log \relax (x)^{2} - 16 \, x e^{\left (4 \, x\right )} \log \relax (x)}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [F] time = 0.07, size = 0, normalized size = 0.00 \[\int \frac {\left (4 x \,{\mathrm e}^{x} \ln \relax (x )^{2} {\mathrm e}^{{\mathrm e}^{x}}-8 x \ln \relax (x )^{2}+256 x \,{\mathrm e}^{4 x} \ln \relax (x )-64 \,{\mathrm e}^{4 x}\right ) \ln \left (\frac {\ln \relax (x )^{2} {\mathrm e}^{2 \,{\mathrm e}^{x}}+\left (-4 x \ln \relax (x )^{2}+32 \,{\mathrm e}^{4 x} \ln \relax (x )\right ) {\mathrm e}^{{\mathrm e}^{x}}+4 x^{2} \ln \relax (x )^{2}-64 x \,{\mathrm e}^{4 x} \ln \relax (x )+256 \,{\mathrm e}^{8 x}}{\ln \relax (x )^{2}}\right )+20 x \,{\mathrm e}^{x} \ln \relax (x )^{2} {\mathrm e}^{{\mathrm e}^{x}}-40 x \ln \relax (x )^{2}+1280 x \,{\mathrm e}^{4 x} \ln \relax (x )-320 \,{\mathrm e}^{4 x}}{x \ln \relax (x )^{2} {\mathrm e}^{{\mathrm e}^{x}}-2 x^{2} \ln \relax (x )^{2}+16 x \,{\mathrm e}^{4 x} \ln \relax (x )}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} -4 \, \int \frac {5 \, x e^{\left (x + e^{x}\right )} \log \relax (x)^{2} + 320 \, x e^{\left (4 \, x\right )} \log \relax (x) - 10 \, x \log \relax (x)^{2} + {\left (x e^{\left (x + e^{x}\right )} \log \relax (x)^{2} + 64 \, x e^{\left (4 \, x\right )} \log \relax (x) - 2 \, x \log \relax (x)^{2} - 16 \, e^{\left (4 \, x\right )}\right )} \log \left (\frac {4 \, x^{2} \log \relax (x)^{2} - 64 \, x e^{\left (4 \, x\right )} \log \relax (x) + e^{\left (2 \, e^{x}\right )} \log \relax (x)^{2} - 4 \, {\left (x \log \relax (x)^{2} - 8 \, e^{\left (4 \, x\right )} \log \relax (x)\right )} e^{\left (e^{x}\right )} + 256 \, e^{\left (8 \, x\right )}}{\log \relax (x)^{2}}\right ) - 80 \, e^{\left (4 \, x\right )}}{2 \, x^{2} \log \relax (x)^{2} - x e^{\left (e^{x}\right )} \log \relax (x)^{2} - 16 \, x e^{\left (4 \, x\right )} \log \relax (x)}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.33, size = 91, normalized size = 3.14 \begin {gather*} {\ln \left (\frac {256\,{\mathrm {e}}^{8\,x}+{\mathrm {e}}^{2\,{\mathrm {e}}^x}\,{\ln \relax (x)}^2+4\,x^2\,{\ln \relax (x)}^2-{\mathrm {e}}^{{\mathrm {e}}^x}\,\left (4\,x\,{\ln \relax (x)}^2-32\,{\mathrm {e}}^{4\,x}\,\ln \relax (x)\right )-64\,x\,{\mathrm {e}}^{4\,x}\,\ln \relax (x)}{{\ln \relax (x)}^2}\right )}^2+20\,\ln \left (\frac {16\,{\mathrm {e}}^{4\,x}+{\mathrm {e}}^{{\mathrm {e}}^x}\,\ln \relax (x)-2\,x\,\ln \relax (x)}{\ln \relax (x)}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F(-1)] 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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