Optimal. Leaf size=26 \[ \frac {13}{6 \left (-x+\log \left (\log \left (-3+e^{x/2}+e^{x^2}\right )\right )\right )} \]
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Rubi [A]
time = 0.66, antiderivative size = 26, normalized size of antiderivative = 1.00, number of steps
used = 3, number of rules used = 3, integrand size = 206, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.015, Rules used = {6820, 12,
6818} \begin {gather*} -\frac {13}{6 \left (x-\log \left (\log \left (e^{x^2}+e^{x/2}-3\right )\right )\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6818
Rule 6820
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {13 \left (e^{x/2}+4 e^{x^2} x-2 \left (-3+e^{x/2}+e^{x^2}\right ) \log \left (-3+e^{x/2}+e^{x^2}\right )\right )}{12 \left (3-e^{x/2}-e^{x^2}\right ) \log \left (-3+e^{x/2}+e^{x^2}\right ) \left (x-\log \left (\log \left (-3+e^{x/2}+e^{x^2}\right )\right )\right )^2} \, dx\\ &=\frac {13}{12} \int \frac {e^{x/2}+4 e^{x^2} x-2 \left (-3+e^{x/2}+e^{x^2}\right ) \log \left (-3+e^{x/2}+e^{x^2}\right )}{\left (3-e^{x/2}-e^{x^2}\right ) \log \left (-3+e^{x/2}+e^{x^2}\right ) \left (x-\log \left (\log \left (-3+e^{x/2}+e^{x^2}\right )\right )\right )^2} \, dx\\ &=-\frac {13}{6 \left (x-\log \left (\log \left (-3+e^{x/2}+e^{x^2}\right )\right )\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.09, size = 26, normalized size = 1.00 \begin {gather*} \frac {13}{6 \left (-x+\log \left (\log \left (-3+e^{x/2}+e^{x^2}\right )\right )\right )} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.28, size = 21, normalized size = 0.81
method | result | size |
risch | \(-\frac {13}{6 \left (x -\ln \left (\ln \left ({\mathrm e}^{x^{2}}+{\mathrm e}^{\frac {x}{2}}-3\right )\right )\right )}\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.37, size = 20, normalized size = 0.77 \begin {gather*} -\frac {13}{6 \, {\left (x - \log \left (\log \left (e^{\left (x^{2}\right )} + e^{\left (\frac {1}{2} \, x\right )} - 3\right )\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 = 0.77 \begin {gather*} -\frac {13}{6 \, {\left (x - \log \left (\log \left (e^{\left (x^{2}\right )} + e^{\left (\frac {1}{2} \, x\right )} - 3\right )\right )\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 7.95, size = 20, normalized size = 0.77 \begin {gather*} \frac {13}{- 6 x + 6 \log {\left (\log {\left (e^{\frac {x}{2}} + e^{x^{2}} - 3 \right )} \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.21, size = 20, normalized size = 0.77 \begin {gather*} -\frac {13}{6 \, {\left (x - \log \left (\log \left (e^{\left (x^{2}\right )} + e^{\left (\frac {1}{2} \, x\right )} - 3\right )\right )\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 5.76, size = 22, normalized size = 0.85 \begin {gather*} -\frac {13}{6\,\left (x-\ln \left (\ln \left ({\mathrm {e}}^{x/2}+{\mathrm {e}}^{x^2}-3\right )\right )\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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