Optimal. Leaf size=30 \[ e^3-\frac {1}{2} \log \left (e^{\frac {4 \left (x+x^2\right )}{\log (4)}}-x-\log (2)\right ) \]
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Rubi [A]
time = 0.07, antiderivative size = 32, normalized size of antiderivative = 1.07, number of steps
used = 1, number of rules used = 1, integrand size = 60, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.017, Rules used = {6816}
\begin {gather*} -\frac {1}{2} \log \left (e^{\frac {4 x^2}{\log (4)}+\frac {4 x}{\log (4)}}-x-\log (2)\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 6816
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\frac {1}{2} \log \left (e^{\frac {4 x}{\log (4)}+\frac {4 x^2}{\log (4)}}-x-\log (2)\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.08, size = 32, normalized size = 1.07 \begin {gather*} -\frac {1}{2} \log \left (e^{\frac {4 x}{\log (4)}+\frac {4 x^2}{\log (4)}}-x-\log (2)\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.18, size = 23, normalized size = 0.77
method | result | size |
risch | \(-\frac {\ln \left ({\mathrm e}^{\frac {2 \left (x +1\right ) x}{\ln \left (2\right )}}-\ln \left (2\right )-x \right )}{2}\) | \(23\) |
norman | \(-\frac {\ln \left (-{\mathrm e}^{\frac {4 x^{2}+4 x}{2 \ln \left (2\right )}}+\ln \left (2\right )+x \right )}{2}\) | \(26\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 27, normalized size = 0.90 \begin {gather*} -\frac {1}{2} \, \log \left ({\left (x + \log \left (2\right )\right )} \log \left (2\right ) - e^{\left (\frac {2 \, {\left (x^{2} + x\right )}}{\log \left (2\right )}\right )} \log \left (2\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.33, size = 23, normalized size = 0.77 \begin {gather*} -\frac {1}{2} \, \log \left (-x + e^{\left (\frac {2 \, {\left (x^{2} + x\right )}}{\log \left (2\right )}\right )} - \log \left (2\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.10, size = 22, normalized size = 0.73 \begin {gather*} - \frac {\log {\left (- x + e^{\frac {2 x^{2} + 2 x}{\log {\left (2 \right )}}} - \log {\left (2 \right )} \right )}}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.42, size = 21, normalized size = 0.70 \begin {gather*} -\frac {1}{2} \, \log \left (x - e^{\left (\frac {2 \, {\left (x^{2} + x\right )}}{\log \left (2\right )}\right )} + \log \left (2\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.29, size = 20, normalized size = 0.67 \begin {gather*} -\frac {\ln \left (x+\ln \left (2\right )-{\mathrm {e}}^{\frac {2\,x\,\left (x+1\right )}{\ln \left (2\right )}}\right )}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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