Optimal. Leaf size=25 \[ \left (-4+e^{-e^{\frac {6 x^2}{\log (2 x)}}+2 x}\right ) x \]
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Rubi [F] time = 4.37, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {-4 \log ^2(2 x)+e^{-e^{\frac {6 x^2}{\log (2 x)}}+2 x} \left ((1+2 x) \log ^2(2 x)+e^{\frac {6 x^2}{\log (2 x)}} \left (6 x^2-12 x^2 \log (2 x)\right )\right )}{\log ^2(2 x)} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-e^{-e^{\frac {6 x^2}{\log (2 x)}}} \left (4 e^{e^{\frac {6 x^2}{\log (2 x)}}}-e^{2 x}-2 e^{2 x} x\right )-\frac {6 e^{-e^{\frac {6 x^2}{\log (2 x)}}+2 x+\frac {6 x^2}{\log (2 x)}} x^2 (-1+2 \log (2 x))}{\log ^2(2 x)}\right ) \, dx\\ &=-\left (6 \int \frac {e^{-e^{\frac {6 x^2}{\log (2 x)}}+2 x+\frac {6 x^2}{\log (2 x)}} x^2 (-1+2 \log (2 x))}{\log ^2(2 x)} \, dx\right )-\int e^{-e^{\frac {6 x^2}{\log (2 x)}}} \left (4 e^{e^{\frac {6 x^2}{\log (2 x)}}}-e^{2 x}-2 e^{2 x} x\right ) \, dx\\ &=-\left (6 \int \left (-\frac {e^{-e^{\frac {6 x^2}{\log (2 x)}}+2 x+\frac {6 x^2}{\log (2 x)}} x^2}{\log ^2(2 x)}+\frac {2 e^{-e^{\frac {6 x^2}{\log (2 x)}}+2 x+\frac {6 x^2}{\log (2 x)}} x^2}{\log (2 x)}\right ) \, dx\right )-\int \left (4-e^{-e^{\frac {6 x^2}{\log (2 x)}}+2 x} (1+2 x)\right ) \, dx\\ &=-4 x+6 \int \frac {e^{-e^{\frac {6 x^2}{\log (2 x)}}+2 x+\frac {6 x^2}{\log (2 x)}} x^2}{\log ^2(2 x)} \, dx-12 \int \frac {e^{-e^{\frac {6 x^2}{\log (2 x)}}+2 x+\frac {6 x^2}{\log (2 x)}} x^2}{\log (2 x)} \, dx+\int e^{-e^{\frac {6 x^2}{\log (2 x)}}+2 x} (1+2 x) \, dx\\ &=-4 x+6 \int \frac {e^{-e^{\frac {6 x^2}{\log (2 x)}}+2 x+\frac {6 x^2}{\log (2 x)}} x^2}{\log ^2(2 x)} \, dx-12 \int \frac {e^{-e^{\frac {6 x^2}{\log (2 x)}}+2 x+\frac {6 x^2}{\log (2 x)}} x^2}{\log (2 x)} \, dx+\int \left (e^{-e^{\frac {6 x^2}{\log (2 x)}}+2 x}+2 e^{-e^{\frac {6 x^2}{\log (2 x)}}+2 x} x\right ) \, dx\\ &=-4 x+2 \int e^{-e^{\frac {6 x^2}{\log (2 x)}}+2 x} x \, dx+6 \int \frac {e^{-e^{\frac {6 x^2}{\log (2 x)}}+2 x+\frac {6 x^2}{\log (2 x)}} x^2}{\log ^2(2 x)} \, dx-12 \int \frac {e^{-e^{\frac {6 x^2}{\log (2 x)}}+2 x+\frac {6 x^2}{\log (2 x)}} x^2}{\log (2 x)} \, dx+\int e^{-e^{\frac {6 x^2}{\log (2 x)}}+2 x} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 1.44, size = 27, normalized size = 1.08 \begin {gather*} -4 x+e^{-e^{\frac {6 x^2}{\log (2 x)}}+2 x} x \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.54, size = 25, normalized size = 1.00 \begin {gather*} x e^{\left (2 \, x - e^{\left (\frac {6 \, x^{2}}{\log \left (2 \, x\right )}\right )}\right )} - 4 \, x \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*} \mathit {undef} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.07, size = 26, normalized size = 1.04
method | result | size |
risch | \(x \,{\mathrm e}^{-{\mathrm e}^{\frac {6 x^{2}}{\ln \left (2 x \right )}}+2 x}-4 x\) | \(26\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.65, size = 26, normalized size = 1.04 \begin {gather*} x e^{\left (2 \, x - e^{\left (\frac {6 \, x^{2}}{\log \relax (2) + \log \relax (x)}\right )}\right )} - 4 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.51, size = 25, normalized size = 1.00 \begin {gather*} x\,{\mathrm {e}}^{2\,x-{\mathrm {e}}^{\frac {6\,x^2}{\ln \left (2\,x\right )}}}-4\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F(-1)] 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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