Optimal. Leaf size=19 \[ \frac {1}{2 \log \left (2 \left (x+\log \left (e^x x^2\right )\right )\right )} \]
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Rubi [A]
time = 0.04, antiderivative size = 21, normalized size of antiderivative = 1.11, number of steps
used = 1, number of rules used = 1, integrand size = 39, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.026, Rules used = {6818}
\begin {gather*} \frac {1}{2 \log \left (2 \log \left (e^x x^2\right )+2 x\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 6818
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{2 \log \left (2 x+2 \log \left (e^x x^2\right )\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 19, normalized size = 1.00 \begin {gather*} \frac {1}{2 \log \left (2 \left (x+\log \left (e^x x^2\right )\right )\right )} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.44, size = 18, normalized size = 0.95
method | result | size |
default | \(\frac {1}{2 \ln \left (2\right )+2 \ln \left (\ln \left ({\mathrm e}^{x} x^{2}\right )+x \right )}\) | \(18\) |
risch | \(\frac {1}{2 \ln \left (4 \ln \left (x \right )+2 \ln \left ({\mathrm e}^{x}\right )-i \pi \,\mathrm {csgn}\left (i x^{2}\right ) \left (-\mathrm {csgn}\left (i x^{2}\right )+\mathrm {csgn}\left (i x \right )\right )^{2}-i \pi \,\mathrm {csgn}\left (i x^{2} {\mathrm e}^{x}\right ) \left (-\mathrm {csgn}\left (i x^{2} {\mathrm e}^{x}\right )+\mathrm {csgn}\left (i x^{2}\right )\right ) \left (-\mathrm {csgn}\left (i x^{2} {\mathrm e}^{x}\right )+\mathrm {csgn}\left (i {\mathrm e}^{x}\right )\right )+2 x \right )}\) | \(97\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.50, size = 14, normalized size = 0.74 \begin {gather*} \frac {1}{2 \, {\left (2 \, \log \left (2\right ) + \log \left (x + \log \left (x\right )\right )\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 18, normalized size = 0.95 \begin {gather*} \frac {1}{2 \, \log \left (2 \, x + 2 \, \log \left (x^{2} e^{x}\right )\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.15, size = 17, normalized size = 0.89 \begin {gather*} \frac {1}{2 \log {\left (2 x + 2 \log {\left (x^{2} e^{x} \right )} \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 15, normalized size = 0.79 \begin {gather*} \frac {1}{2 \, \log \left (4 \, x + 2 \, \log \left (x^{2}\right )\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.21, size = 13, normalized size = 0.68 \begin {gather*} \frac {1}{2\,\ln \left (4\,x+\ln \left (x^4\right )\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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