Optimal. Leaf size=22 \[ e^4 x \left (-4-\log \left (e^{16/x} x\right )+\log (\log (4))\right ) \]
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Rubi [A] time = 0.05, antiderivative size = 35, normalized size of antiderivative = 1.59, number of steps used = 7, number of rules used = 3, integrand size = 38, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.079, Rules used = {14, 2548, 43} \begin {gather*} e^4 x-e^4 x \log \left (e^{16/x} x\right )-e^4 x (5-\log (\log (4))) \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 43
Rule 2548
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-e^4 \log \left (e^{16/x} x\right )+\frac {e^4 (16-x (5-\log (\log (4))))}{x}\right ) \, dx\\ &=-\left (e^4 \int \log \left (e^{16/x} x\right ) \, dx\right )+e^4 \int \frac {16-x (5-\log (\log (4)))}{x} \, dx\\ &=-e^4 x \log \left (e^{16/x} x\right )+e^4 \int \frac {-16+x}{x} \, dx+e^4 \int \left (-5+\frac {16}{x}+\log (\log (4))\right ) \, dx\\ &=16 e^4 \log (x)-e^4 x \log \left (e^{16/x} x\right )-e^4 x (5-\log (\log (4)))+e^4 \int \left (1-\frac {16}{x}\right ) \, dx\\ &=e^4 x-e^4 x \log \left (e^{16/x} x\right )-e^4 x (5-\log (\log (4)))\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.02, size = 26, normalized size = 1.18 \begin {gather*} e^4 \left (16-x \log \left (e^{16/x} x\right )+x (-4+\log (\log (4)))\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.79, size = 29, normalized size = 1.32 \begin {gather*} -x e^{4} \log \left (x e^{\frac {16}{x}}\right ) + x e^{4} \log \left (2 \, \log \relax (2)\right ) - 4 \, x e^{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.30, size = 26, normalized size = 1.18 \begin {gather*} x e^{4} \log \relax (2) - x e^{4} \log \relax (x) + x e^{4} \log \left (\log \relax (2)\right ) - 4 \, x e^{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.09, size = 34, normalized size = 1.55
method | result | size |
norman | \(\left (-4 \,{\mathrm e}^{4}+{\mathrm e}^{4} \ln \relax (2)+{\mathrm e}^{4} \ln \left (\ln \relax (2)\right )\right ) x -x \,{\mathrm e}^{4} \ln \left (x \,{\mathrm e}^{\frac {16}{x}}\right )\) | \(34\) |
default | \(x \,{\mathrm e}^{4} \ln \left (2 \ln \relax (2)\right )+16 \,{\mathrm e}^{4} \ln \relax (x )-4 x \,{\mathrm e}^{4}-x \,{\mathrm e}^{4} \ln \left (x \,{\mathrm e}^{\frac {16}{x}}\right )+16 \,{\mathrm e}^{4} \ln \left (\frac {16}{x}\right )\) | \(46\) |
risch | \(-x \,{\mathrm e}^{4} \ln \left ({\mathrm e}^{\frac {16}{x}}\right )-x \,{\mathrm e}^{4} \ln \relax (x )+\frac {i x \,{\mathrm e}^{4} \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i {\mathrm e}^{\frac {16}{x}}\right ) \mathrm {csgn}\left (i x \,{\mathrm e}^{\frac {16}{x}}\right )}{2}-\frac {i x \,{\mathrm e}^{4} \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x \,{\mathrm e}^{\frac {16}{x}}\right )^{2}}{2}-\frac {i x \,{\mathrm e}^{4} \pi \,\mathrm {csgn}\left (i {\mathrm e}^{\frac {16}{x}}\right ) \mathrm {csgn}\left (i x \,{\mathrm e}^{\frac {16}{x}}\right )^{2}}{2}+\frac {i x \,{\mathrm e}^{4} \pi \mathrm {csgn}\left (i x \,{\mathrm e}^{\frac {16}{x}}\right )^{3}}{2}+x \,{\mathrm e}^{4} \ln \relax (2)+x \,{\mathrm e}^{4} \ln \left (\ln \relax (2)\right )-4 x \,{\mathrm e}^{4}\) | \(147\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.60, size = 44, normalized size = 2.00 \begin {gather*} -x e^{4} \log \left (x e^{\frac {16}{x}}\right ) + x e^{4} \log \left (2 \, \log \relax (2)\right ) + {\left (x - 16 \, \log \relax (x)\right )} e^{4} - 5 \, x e^{4} + 16 \, e^{4} \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.72, size = 15, normalized size = 0.68 \begin {gather*} x\,{\mathrm {e}}^4\,\left (\ln \relax (2)+\ln \left (\ln \relax (2)\right )-\ln \relax (x)-4\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.33, size = 34, normalized size = 1.55 \begin {gather*} - x e^{4} \log {\left (x e^{\frac {16}{x}} \right )} + x \left (- 4 e^{4} + e^{4} \log {\left (\log {\relax (2 )} \right )} + e^{4} \log {\relax (2 )}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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