Optimal. Leaf size=25 \[ e^{-1-e^x+x+x^2+x \left (4 x+\log \left (\log ^2(\log (x))\right )\right )} \]
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Rubi [A]
time = 0.56, antiderivative size = 23, normalized size of antiderivative = 0.92, number of steps
used = 1, number of rules used = 1, integrand size = 63, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.016, Rules used = {6838}
\begin {gather*} e^{5 x^2+x-e^x-1} \log ^2(\log (x))^x \end {gather*}
Antiderivative was successfully verified.
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Rule 6838
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=e^{-1-e^x+x+5 x^2} \log ^2(\log (x))^x\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.19, size = 23, normalized size = 0.92 \begin {gather*} e^{-1-e^x+x+5 x^2} \log ^2(\log (x))^x \end {gather*}
Antiderivative was successfully verified.
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Maple [C] Result contains higher order function than in optimal. Order 9 vs. order
3.
time = 1.34, size = 84, normalized size = 3.36
method | result | size |
risch | \(\ln \left (\ln \left (x \right )\right )^{2 x} {\mathrm e}^{-1-\frac {i x \pi \mathrm {csgn}\left (i \ln \left (\ln \left (x \right )\right )^{2}\right )^{3}}{2}+i x \pi \mathrm {csgn}\left (i \ln \left (\ln \left (x \right )\right )^{2}\right )^{2} \mathrm {csgn}\left (i \ln \left (\ln \left (x \right )\right )\right )-\frac {i x \pi \,\mathrm {csgn}\left (i \ln \left (\ln \left (x \right )\right )^{2}\right ) \mathrm {csgn}\left (i \ln \left (\ln \left (x \right )\right )\right )^{2}}{2}-{\mathrm e}^{x}+5 x^{2}+x}\) | \(84\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.36, size = 20, normalized size = 0.80 \begin {gather*} e^{\left (5 \, x^{2} + 2 \, x \log \left (\log \left (\log \left (x\right )\right )\right ) + x - e^{x} - 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.41, size = 21, normalized size = 0.84 \begin {gather*} e^{\left (5 \, x^{2} + x \log \left (\log \left (\log \left (x\right )\right )^{2}\right ) + x - e^{x} - 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 2.58, size = 22, normalized size = 0.88 \begin {gather*} e^{5 x^{2} + x \log {\left (\log {\left (\log {\left (x \right )} \right )}^{2} \right )} + x - e^{x} - 1} \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*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.84, size = 23, normalized size = 0.92 \begin {gather*} {\mathrm {e}}^{-1}\,{\mathrm {e}}^{5\,x^2}\,{\mathrm {e}}^{-{\mathrm {e}}^x}\,{\mathrm {e}}^x\,{\left ({\ln \left (\ln \left (x\right )\right )}^2\right )}^x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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