Optimal. Leaf size=28 \[ \frac {1}{2} e^{e^{-4+e^{\frac {e^x}{4}+2 x}}+\log ^2(x)} \]
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Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(71\) vs. \(2(28)=56\).
time = 0.29, antiderivative size = 71, normalized size of antiderivative = 2.54, number of steps
used = 2, number of rules used = 2, integrand size = 79, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.025, Rules used = {12, 2326}
\begin {gather*} \frac {\left (e^x x+8 x\right ) \exp \left (e^{e^{\frac {1}{4} \left (8 x+e^x\right )}-4}+\frac {1}{4} \left (-8 x-e^x\right )+\frac {1}{4} \left (8 x+e^x\right )+\log ^2(x)\right )}{2 \left (e^x+8\right ) x} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2326
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{8} \int \frac {e^{e^{-4+e^{\frac {1}{4} \left (e^x+8 x\right )}}} \left (\exp \left (-4+e^{\frac {1}{4} \left (e^x+8 x\right )}+\frac {1}{4} \left (e^x+8 x\right )+\log ^2(x)\right ) \left (8 x+e^x x\right )+8 e^{\log ^2(x)} \log (x)\right )}{x} \, dx\\ &=\frac {\exp \left (e^{-4+e^{\frac {1}{4} \left (e^x+8 x\right )}}+\frac {1}{4} \left (-e^x-8 x\right )+\frac {1}{4} \left (e^x+8 x\right )+\log ^2(x)\right ) \left (8 x+e^x x\right )}{2 \left (8+e^x\right ) x}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.26, size = 28, normalized size = 1.00 \begin {gather*} \frac {1}{2} e^{e^{-4+e^{\frac {e^x}{4}+2 x}}+\log ^2(x)} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.14, size = 21, normalized size = 0.75
method | result | size |
risch | \(\frac {{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{\frac {{\mathrm e}^{x}}{4}+2 x}-4}+\ln \left (x \right )^{2}}}{2}\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.70, size = 20, normalized size = 0.71 \begin {gather*} \frac {1}{2} \, e^{\left (\log \left (x\right )^{2} + e^{\left (e^{\left (2 \, x + \frac {1}{4} \, e^{x}\right )} - 4\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 20, normalized size = 0.71 \begin {gather*} \frac {1}{2} \, e^{\left (\log \left (x\right )^{2} + e^{\left (e^{\left (2 \, x + \frac {1}{4} \, e^{x}\right )} - 4\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] Timed out
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \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 = 3.11, size = 22, normalized size = 0.79 \begin {gather*} \frac {{\mathrm {e}}^{{\ln \left (x\right )}^2}\,{\mathrm {e}}^{{\mathrm {e}}^{-4}\,{\mathrm {e}}^{{\mathrm {e}}^{2\,x}\,{\mathrm {e}}^{\frac {{\mathrm {e}}^x}{4}}}}}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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