Optimal. Leaf size=24 \[ \log \left (20 \log \left (4+\frac {e^x-\frac {e^5}{8 x}}{x^2}\right )\right ) \]
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Rubi [A] time = 0.16, antiderivative size = 24, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 69, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.014, Rules used = {6684} \begin {gather*} \log \left (\log \left (-\frac {-32 x^3-8 e^x x+e^5}{8 x^3}\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 6684
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\log \left (\log \left (-\frac {e^5-8 e^x x-32 x^3}{8 x^3}\right )\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.43, size = 21, normalized size = 0.88 \begin {gather*} \log \left (\log \left (4-\frac {e^5}{8 x^3}+\frac {e^x}{x^2}\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.60, size = 22, normalized size = 0.92 \begin {gather*} \log \left (\log \left (\frac {32 \, x^{3} + 8 \, x e^{x} - e^{5}}{8 \, x^{3}}\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.23, size = 22, normalized size = 0.92 \begin {gather*} \log \left (\log \left (\frac {32 \, x^{3} + 8 \, x e^{x} - e^{5}}{8 \, x^{3}}\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.29, size = 23, normalized size = 0.96
method | result | size |
norman | \(\ln \left (\ln \left (\frac {8 \,{\mathrm e}^{x} x -{\mathrm e}^{5}+32 x^{3}}{8 x^{3}}\right )\right )\) | \(23\) |
risch | \(\ln \left (\ln \left (-32 x^{3}-8 \,{\mathrm e}^{x} x +{\mathrm e}^{5}\right )+\frac {i \left (\pi \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )-2 \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}+\pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right ) \mathrm {csgn}\left (i x^{3}\right )-\pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{3}\right )^{2}+\pi \mathrm {csgn}\left (i x^{2}\right )^{3}-\pi \,\mathrm {csgn}\left (i x^{2}\right ) \mathrm {csgn}\left (i x^{3}\right )^{2}+\pi \mathrm {csgn}\left (i x^{3}\right )^{3}-\pi \,\mathrm {csgn}\left (\frac {i}{x^{3}}\right ) \mathrm {csgn}\left (i \left (-32 x^{3}-8 \,{\mathrm e}^{x} x +{\mathrm e}^{5}\right )\right ) \mathrm {csgn}\left (\frac {i \left (-32 x^{3}-8 \,{\mathrm e}^{x} x +{\mathrm e}^{5}\right )}{x^{3}}\right )+\pi \,\mathrm {csgn}\left (\frac {i}{x^{3}}\right ) \mathrm {csgn}\left (\frac {i \left (-32 x^{3}-8 \,{\mathrm e}^{x} x +{\mathrm e}^{5}\right )}{x^{3}}\right )^{2}-2 \pi \mathrm {csgn}\left (\frac {i \left (-32 x^{3}-8 \,{\mathrm e}^{x} x +{\mathrm e}^{5}\right )}{x^{3}}\right )^{2}+\pi \,\mathrm {csgn}\left (i \left (-32 x^{3}-8 \,{\mathrm e}^{x} x +{\mathrm e}^{5}\right )\right ) \mathrm {csgn}\left (\frac {i \left (-32 x^{3}-8 \,{\mathrm e}^{x} x +{\mathrm e}^{5}\right )}{x^{3}}\right )^{2}+\pi \mathrm {csgn}\left (\frac {i \left (-32 x^{3}-8 \,{\mathrm e}^{x} x +{\mathrm e}^{5}\right )}{x^{3}}\right )^{3}+6 i \ln \relax (x )+6 i \ln \relax (2)+2 \pi \right )}{2}\right )\) | \(314\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.51, size = 26, normalized size = 1.08 \begin {gather*} \log \left (-3 \, \log \relax (2) + \log \left (32 \, x^{3} + 8 \, x e^{x} - e^{5}\right ) - 3 \, \log \relax (x)\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.29, size = 22, normalized size = 0.92 \begin {gather*} \ln \left (\ln \left (\frac {8\,x\,{\mathrm {e}}^x-{\mathrm {e}}^5+32\,x^3}{8\,x^3}\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.40, size = 20, normalized size = 0.83 \begin {gather*} \log {\left (\log {\left (\frac {4 x^{3} + x e^{x} - \frac {e^{5}}{8}}{x^{3}} \right )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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