Optimal. Leaf size=23 \[ \log \left (3+\frac {1}{3} \left (e^x+\frac {7 x}{4}+\frac {x^2}{2}\right )\right ) \]
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Rubi [A] time = 0.04, antiderivative size = 16, normalized size of antiderivative = 0.70, number of steps used = 1, number of rules used = 1, integrand size = 28, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.036, Rules used = {6684} \begin {gather*} \log \left (2 x^2+7 x+4 e^x+36\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 6684
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\log \left (36+4 e^x+7 x+2 x^2\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.10, size = 16, normalized size = 0.70 \begin {gather*} \log \left (36+4 e^x+7 x+2 x^2\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.97, size = 15, normalized size = 0.65 \begin {gather*} \log \left (2 \, x^{2} + 7 \, x + 4 \, e^{x} + 36\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.23, size = 15, normalized size = 0.65 \begin {gather*} \log \left (2 \, x^{2} + 7 \, x + 4 \, e^{x} + 36\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 14, normalized size = 0.61
method | result | size |
risch | \(\ln \left (\frac {x^{2}}{2}+\frac {7 x}{4}+{\mathrm e}^{x}+9\right )\) | \(14\) |
derivativedivides | \(\ln \left (4 \,{\mathrm e}^{x}+2 x^{2}+7 x +36\right )\) | \(16\) |
default | \(\ln \left (4 \,{\mathrm e}^{x}+2 x^{2}+7 x +36\right )\) | \(16\) |
norman | \(\ln \left (4 \,{\mathrm e}^{x}+2 x^{2}+7 x +36\right )\) | \(16\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 15, normalized size = 0.65 \begin {gather*} \log \left (2 \, x^{2} + 7 \, x + 4 \, e^{x} + 36\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.20, size = 13, normalized size = 0.57 \begin {gather*} \ln \left (\frac {7\,x}{2}+2\,{\mathrm {e}}^x+x^2+18\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.13, size = 15, normalized size = 0.65 \begin {gather*} \log {\left (\frac {x^{2}}{2} + \frac {7 x}{4} + e^{x} + 9 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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