Optimal. Leaf size=13 \[ \log \left (e^x+2 x+4 (2+x)\right ) \]
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Rubi [A]
time = 0.03, antiderivative size = 9, normalized size of antiderivative = 0.69, number of steps
used = 1, number of rules used = 1, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.062, Rules used = {6816}
\begin {gather*} \log \left (6 x+e^x+8\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 6816
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\log \left (8+e^x+6 x\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 9, normalized size = 0.69 \begin {gather*} \log \left (8+e^x+6 x\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.18, size = 9, normalized size = 0.69
method | result | size |
derivativedivides | \(\ln \left ({\mathrm e}^{x}+6 x +8\right )\) | \(9\) |
default | \(\ln \left ({\mathrm e}^{x}+6 x +8\right )\) | \(9\) |
norman | \(\ln \left ({\mathrm e}^{x}+6 x +8\right )\) | \(9\) |
risch | \(\ln \left ({\mathrm e}^{x}+6 x +8\right )\) | \(9\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.25, size = 8, normalized size = 0.62 \begin {gather*} \log \left (6 \, x + e^{x} + 8\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 8, normalized size = 0.62 \begin {gather*} \log \left (6 \, x + e^{x} + 8\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 8, normalized size = 0.62 \begin {gather*} \log {\left (6 x + e^{x} + 8 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.39, size = 8, normalized size = 0.62 \begin {gather*} \log \left (6 \, x + e^{x} + 8\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.06, size = 8, normalized size = 0.62 \begin {gather*} \ln \left (6\,x+{\mathrm {e}}^x+8\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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