Optimal. Leaf size=18 \[ \log \left (2-(-5+x) \left (2-e^3+2 x\right )\right ) \]
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Rubi [A] time = 0.01, antiderivative size = 21, normalized size of antiderivative = 1.17, 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 = {1587} \begin {gather*} \log \left (-2 x^2+8 x-e^3 (5-x)+12\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 1587
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\log \left (12-e^3 (5-x)+8 x-2 x^2\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 18, normalized size = 1.00 \begin {gather*} \log \left (12+e^3 (-5+x)+8 x-2 x^2\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.46, size = 18, normalized size = 1.00 \begin {gather*} \log \left (2 \, x^{2} - {\left (x - 5\right )} e^{3} - 8 \, x - 12\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.19, size = 21, normalized size = 1.17 \begin {gather*} \log \left ({\left | 2 \, x^{2} - x e^{3} - 8 \, x + 5 \, e^{3} - 12 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.21, size = 18, normalized size = 1.00
method | result | size |
derivativedivides | \(\ln \left (\left (x -5\right ) {\mathrm e}^{3}-2 x^{2}+8 x +12\right )\) | \(18\) |
default | \(\ln \left (x \,{\mathrm e}^{3}-2 x^{2}-5 \,{\mathrm e}^{3}+8 x +12\right )\) | \(20\) |
norman | \(\ln \left (x \,{\mathrm e}^{3}-2 x^{2}-5 \,{\mathrm e}^{3}+8 x +12\right )\) | \(20\) |
risch | \(\ln \left (2 x^{2}+x \left (-8-{\mathrm e}^{3}\right )+5 \,{\mathrm e}^{3}-12\right )\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 18, normalized size = 1.00 \begin {gather*} \log \left (2 \, x^{2} - {\left (x - 5\right )} e^{3} - 8 \, x - 12\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.15, size = 17, normalized size = 0.94 \begin {gather*} \ln \left (\frac {5\,{\mathrm {e}}^3}{2}-\frac {x\,\left ({\mathrm {e}}^3+8\right )}{2}+x^2-6\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.21, size = 20, normalized size = 1.11 \begin {gather*} \log {\left (2 x^{2} + x \left (- e^{3} - 8\right ) - 12 + 5 e^{3} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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