Optimal. Leaf size=24 \[ -x+x^4 \log ^2\left (4 \log (5) \log \left ((7+x+e x)^2\right )\right ) \]
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Rubi [F] time = 1.90, 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 {(-7-x-e x) \log \left (49+14 x+x^2+e^2 x^2+e \left (14 x+2 x^2\right )\right )+\left (4 x^4+4 e x^4\right ) \log \left (4 \log (5) \log \left (49+14 x+x^2+e^2 x^2+e \left (14 x+2 x^2\right )\right )\right )+\left (28 x^3+4 x^4+4 e x^4\right ) \log \left (49+14 x+x^2+e^2 x^2+e \left (14 x+2 x^2\right )\right ) \log ^2\left (4 \log (5) \log \left (49+14 x+x^2+e^2 x^2+e \left (14 x+2 x^2\right )\right )\right )}{(7+x+e x) \log \left (49+14 x+x^2+e^2 x^2+e \left (14 x+2 x^2\right )\right )} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {(-7-x-e x) \log \left (49+14 x+x^2+e^2 x^2+e \left (14 x+2 x^2\right )\right )+\left (4 x^4+4 e x^4\right ) \log \left (4 \log (5) \log \left (49+14 x+x^2+e^2 x^2+e \left (14 x+2 x^2\right )\right )\right )+\left (28 x^3+4 x^4+4 e x^4\right ) \log \left (49+14 x+x^2+e^2 x^2+e \left (14 x+2 x^2\right )\right ) \log ^2\left (4 \log (5) \log \left (49+14 x+x^2+e^2 x^2+e \left (14 x+2 x^2\right )\right )\right )}{(7+(1+e) x) \log \left (49+14 x+x^2+e^2 x^2+e \left (14 x+2 x^2\right )\right )} \, dx\\ &=\int \left (-1+\frac {4 (1+e) x^4 \log \left (4 \log (5) \log \left ((7+(1+e) x)^2\right )\right )}{(7+(1+e) x) \log \left ((7+(1+e) x)^2\right )}+4 x^3 \log ^2\left (4 \log (5) \log \left ((7+(1+e) x)^2\right )\right )\right ) \, dx\\ &=-x+4 \int x^3 \log ^2\left (4 \log (5) \log \left ((7+(1+e) x)^2\right )\right ) \, dx+(4 (1+e)) \int \frac {x^4 \log \left (4 \log (5) \log \left ((7+(1+e) x)^2\right )\right )}{(7+(1+e) x) \log \left ((7+(1+e) x)^2\right )} \, dx\\ &=-x+4 \int x^3 \log ^2\left (4 \log (5) \log \left ((7+(1+e) x)^2\right )\right ) \, dx+(4 (1+e)) \int \left (-\frac {343 \log \left (4 \log (5) \log \left ((7+(1+e) x)^2\right )\right )}{(1+e)^4 \log \left ((7+(1+e) x)^2\right )}+\frac {49 x \log \left (4 \log (5) \log \left ((7+(1+e) x)^2\right )\right )}{(1+e)^3 \log \left ((7+(1+e) x)^2\right )}-\frac {7 x^2 \log \left (4 \log (5) \log \left ((7+(1+e) x)^2\right )\right )}{(1+e)^2 \log \left ((7+(1+e) x)^2\right )}+\frac {x^3 \log \left (4 \log (5) \log \left ((7+(1+e) x)^2\right )\right )}{(1+e) \log \left ((7+(1+e) x)^2\right )}+\frac {2401 \log \left (4 \log (5) \log \left ((7+(1+e) x)^2\right )\right )}{(1+e)^4 (7+(1+e) x) \log \left ((7+(1+e) x)^2\right )}\right ) \, dx\\ &=-x+4 \int \frac {x^3 \log \left (4 \log (5) \log \left ((7+(1+e) x)^2\right )\right )}{\log \left ((7+(1+e) x)^2\right )} \, dx+4 \int x^3 \log ^2\left (4 \log (5) \log \left ((7+(1+e) x)^2\right )\right ) \, dx-\frac {1372 \int \frac {\log \left (4 \log (5) \log \left ((7+(1+e) x)^2\right )\right )}{\log \left ((7+(1+e) x)^2\right )} \, dx}{(1+e)^3}+\frac {9604 \int \frac {\log \left (4 \log (5) \log \left ((7+(1+e) x)^2\right )\right )}{(7+(1+e) x) \log \left ((7+(1+e) x)^2\right )} \, dx}{(1+e)^3}+\frac {196 \int \frac {x \log \left (4 \log (5) \log \left ((7+(1+e) x)^2\right )\right )}{\log \left ((7+(1+e) x)^2\right )} \, dx}{(1+e)^2}-\frac {28 \int \frac {x^2 \log \left (4 \log (5) \log \left ((7+(1+e) x)^2\right )\right )}{\log \left ((7+(1+e) x)^2\right )} \, dx}{1+e}\\ &=-x+\frac {2401 \log ^2\left (4 \log (5) \log \left ((7+(1+e) x)^2\right )\right )}{(1+e)^4}+4 \int \frac {x^3 \log \left (4 \log (5) \log \left ((7+(1+e) x)^2\right )\right )}{\log \left ((7+(1+e) x)^2\right )} \, dx+4 \int x^3 \log ^2\left (4 \log (5) \log \left ((7+(1+e) x)^2\right )\right ) \, dx-\frac {1372 \operatorname {Subst}\left (\int \frac {\log \left (4 \log (5) \log \left (x^2\right )\right )}{\log \left (x^2\right )} \, dx,x,7+(1+e) x\right )}{(1+e)^4}+\frac {196 \int \frac {x \log \left (4 \log (5) \log \left ((7+(1+e) x)^2\right )\right )}{\log \left ((7+(1+e) x)^2\right )} \, dx}{(1+e)^2}-\frac {28 \int \frac {x^2 \log \left (4 \log (5) \log \left ((7+(1+e) x)^2\right )\right )}{\log \left ((7+(1+e) x)^2\right )} \, dx}{1+e}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.24, size = 24, normalized size = 1.00 \begin {gather*} -x+x^4 \log ^2\left (4 \log (5) \log \left ((7+x+e x)^2\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.84, size = 41, normalized size = 1.71 \begin {gather*} x^{4} \log \left (4 \, \log \relax (5) \log \left (x^{2} e^{2} + x^{2} + 2 \, {\left (x^{2} + 7 \, x\right )} e + 14 \, x + 49\right )\right )^{2} - x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 4.54, size = 42, normalized size = 1.75 \begin {gather*} x^{4} \log \left (4 \, \log \relax (5) \log \left (x^{2} e^{2} + 2 \, x^{2} e + x^{2} + 14 \, x e + 14 \, x + 49\right )\right )^{2} - x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [F] time = 0.08, size = 0, normalized size = 0.00 \[\int \frac {\left (4 x^{4} {\mathrm e}+4 x^{4}+28 x^{3}\right ) \ln \left (x^{2} {\mathrm e}^{2}+\left (2 x^{2}+14 x \right ) {\mathrm e}+x^{2}+14 x +49\right ) \ln \left (4 \ln \relax (5) \ln \left (x^{2} {\mathrm e}^{2}+\left (2 x^{2}+14 x \right ) {\mathrm e}+x^{2}+14 x +49\right )\right )^{2}+\left (4 x^{4} {\mathrm e}+4 x^{4}\right ) \ln \left (4 \ln \relax (5) \ln \left (x^{2} {\mathrm e}^{2}+\left (2 x^{2}+14 x \right ) {\mathrm e}+x^{2}+14 x +49\right )\right )+\left (-x \,{\mathrm e}-x -7\right ) \ln \left (x^{2} {\mathrm e}^{2}+\left (2 x^{2}+14 x \right ) {\mathrm e}+x^{2}+14 x +49\right )}{\left (x \,{\mathrm e}+x +7\right ) \ln \left (x^{2} {\mathrm e}^{2}+\left (2 x^{2}+14 x \right ) {\mathrm e}+x^{2}+14 x +49\right )}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.98, size = 267, normalized size = 11.12 \begin {gather*} 2 \, x^{4} {\left (3 \, \log \relax (2) + \log \left (\log \relax (5)\right )\right )} \log \left (\log \left (x {\left (e + 1\right )} + 7\right )\right ) + x^{4} \log \left (\log \left (x {\left (e + 1\right )} + 7\right )\right )^{2} + {\left (9 \, \log \relax (2)^{2} + 6 \, \log \relax (2) \log \left (\log \relax (5)\right ) + \log \left (\log \relax (5)\right )^{2}\right )} x^{4} - {\left (\frac {x}{e + 1} - \frac {7 \, \log \left (x {\left (e + 1\right )} + 7\right )}{e^{2} + 2 \, e + 1}\right )} e - \frac {7 \, \log \left (x^{2} e^{2} + 2 \, x^{2} e + x^{2} + 14 \, x e + 14 \, x + 49\right ) \log \left (\log \left (x {\left (e + 1\right )} + 7\right )\right )}{2 \, {\left (e + 1\right )}} - \frac {x}{e + 1} + \frac {7 \, {\left (\frac {{\left (e \log \left (x^{2} e^{2} + 2 \, x^{2} e + x^{2} + 14 \, x e + 14 \, x + 49\right ) + \log \left (x^{2} e^{2} + 2 \, x^{2} e + x^{2} + 14 \, x e + 14 \, x + 49\right )\right )} \log \left (\log \left (x {\left (e + 1\right )} + 7\right )\right )}{e + 1} - 2 \, \log \left (x {\left (e + 1\right )} + 7\right )\right )}}{2 \, {\left (e + 1\right )}} + \frac {7 \, \log \left (x {\left (e + 1\right )} + 7\right )}{e^{2} + 2 \, e + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.26, size = 42, normalized size = 1.75 \begin {gather*} x\,\left (x^3\,{\ln \left (4\,\ln \left (14\,x+\mathrm {e}\,\left (2\,x^2+14\,x\right )+x^2\,{\mathrm {e}}^2+x^2+49\right )\,\ln \relax (5)\right )}^2-1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 1.68, size = 41, normalized size = 1.71 \begin {gather*} x^{4} \log {\left (4 \log {\relax (5 )} \log {\left (x^{2} + x^{2} e^{2} + 14 x + e \left (2 x^{2} + 14 x\right ) + 49 \right )} \right )}^{2} - x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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