Optimal. Leaf size=18 \[ e^{4 e^4-4 x} (4+\log (x))^4 \]
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Rubi [A] time = 0.52, antiderivative size = 29, normalized size of antiderivative = 1.61, number of steps used = 3, number of rules used = 3, integrand size = 86, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.035, Rules used = {6688, 12, 2288} \begin {gather*} \frac {e^{4 e^4-4 x} (\log (x)+4)^3 (4 x+x \log (x))}{x} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2288
Rule 6688
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {4 e^{4 e^4-4 x} (4+\log (x))^3 (1-4 x-x \log (x))}{x} \, dx\\ &=4 \int \frac {e^{4 e^4-4 x} (4+\log (x))^3 (1-4 x-x \log (x))}{x} \, dx\\ &=\frac {e^{4 e^4-4 x} (4+\log (x))^3 (4 x+x \log (x))}{x}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.02, size = 18, normalized size = 1.00 \begin {gather*} e^{4 e^4-4 x} (4+\log (x))^4 \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.65, size = 69, normalized size = 3.83 \begin {gather*} e^{\left (-4 \, x + 4 \, e^{4}\right )} \log \relax (x)^{4} + 16 \, e^{\left (-4 \, x + 4 \, e^{4}\right )} \log \relax (x)^{3} + 96 \, e^{\left (-4 \, x + 4 \, e^{4}\right )} \log \relax (x)^{2} + 256 \, e^{\left (-4 \, x + 4 \, e^{4}\right )} \log \relax (x) + 256 \, e^{\left (-4 \, x + 4 \, e^{4}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.24, size = 69, normalized size = 3.83 \begin {gather*} e^{\left (-4 \, x + 4 \, e^{4}\right )} \log \relax (x)^{4} + 16 \, e^{\left (-4 \, x + 4 \, e^{4}\right )} \log \relax (x)^{3} + 96 \, e^{\left (-4 \, x + 4 \, e^{4}\right )} \log \relax (x)^{2} + 256 \, e^{\left (-4 \, x + 4 \, e^{4}\right )} \log \relax (x) + 256 \, e^{\left (-4 \, x + 4 \, e^{4}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.04, size = 70, normalized size = 3.89
method | result | size |
risch | \(\ln \relax (x )^{4} {\mathrm e}^{4 \,{\mathrm e}^{4}-4 x}+16 \ln \relax (x )^{3} {\mathrm e}^{4 \,{\mathrm e}^{4}-4 x}+96 \ln \relax (x )^{2} {\mathrm e}^{4 \,{\mathrm e}^{4}-4 x}+256 \ln \relax (x ) {\mathrm e}^{4 \,{\mathrm e}^{4}-4 x}+256 \,{\mathrm e}^{4 \,{\mathrm e}^{4}-4 x}\) | \(70\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.45, size = 63, normalized size = 3.50 \begin {gather*} {\left (e^{\left (4 \, e^{4}\right )} \log \relax (x)^{4} + 16 \, e^{\left (4 \, e^{4}\right )} \log \relax (x)^{3} + 96 \, e^{\left (4 \, e^{4}\right )} \log \relax (x)^{2}\right )} e^{\left (-4 \, x\right )} + 256 \, e^{\left (-4 \, x + 4 \, e^{4}\right )} \log \relax (x) + 256 \, e^{\left (-4 \, x + 4 \, e^{4}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 6.06, size = 69, normalized size = 3.83 \begin {gather*} {\mathrm {e}}^{4\,{\mathrm {e}}^4-4\,x}\,{\ln \relax (x)}^4+16\,{\mathrm {e}}^{4\,{\mathrm {e}}^4-4\,x}\,{\ln \relax (x)}^3+96\,{\mathrm {e}}^{4\,{\mathrm {e}}^4-4\,x}\,{\ln \relax (x)}^2+256\,{\mathrm {e}}^{4\,{\mathrm {e}}^4-4\,x}\,\ln \relax (x)+256\,{\mathrm {e}}^{4\,{\mathrm {e}}^4-4\,x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.63, size = 63, normalized size = 3.50 \begin {gather*} \left (e^{4 e^{4}} \log {\relax (x )}^{4} + 16 e^{4 e^{4}} \log {\relax (x )}^{3} + 96 e^{4 e^{4}} \log {\relax (x )}^{2} + 256 e^{4 e^{4}} \log {\relax (x )} + 256 e^{4 e^{4}}\right ) e^{- 4 x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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