Optimal. Leaf size=23 \[ \log \left (\left (9+\frac {1}{4} \left (e^5+4 x\right ) \left (x-x^2\right )\right )^2\right ) \]
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Rubi [A]
time = 0.03, antiderivative size = 26, normalized size of antiderivative = 1.13, number of steps
used = 1, number of rules used = 1, integrand size = 44, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.023, Rules used = {1601}
\begin {gather*} 2 \log \left (-4 x^3+4 x^2+e^5 \left (x-x^2\right )+36\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 1601
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=2 \log \left (36+4 x^2-4 x^3+e^5 \left (x-x^2\right )\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 24, normalized size = 1.04 \begin {gather*} 2 \log \left (e^5 (-1+x) x+4 \left (-9-x^2+x^3\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.22, size = 27, normalized size = 1.17
method | result | size |
risch | \(2 \ln \left (-36+4 x^{3}+\left ({\mathrm e}^{5}-4\right ) x^{2}-x \,{\mathrm e}^{5}\right )\) | \(24\) |
default | \(2 \ln \left (x^{2} {\mathrm e}^{5}+4 x^{3}-x \,{\mathrm e}^{5}-4 x^{2}-36\right )\) | \(27\) |
norman | \(2 \ln \left (x^{2} {\mathrm e}^{5}+4 x^{3}-x \,{\mathrm e}^{5}-4 x^{2}-36\right )\) | \(27\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 25, normalized size = 1.09 \begin {gather*} 2 \, \log \left (4 \, x^{3} - 4 \, x^{2} + {\left (x^{2} - x\right )} e^{5} - 36\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 25, normalized size = 1.09 \begin {gather*} 2 \, \log \left (4 \, x^{3} - 4 \, x^{2} + {\left (x^{2} - x\right )} e^{5} - 36\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.22, size = 22, normalized size = 0.96 \begin {gather*} 2 \log {\left (4 x^{3} + x^{2} \left (-4 + e^{5}\right ) - x e^{5} - 36 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.42, size = 26, normalized size = 1.13 \begin {gather*} 2 \, \log \left ({\left | 4 \, x^{3} - 4 \, x^{2} + {\left (x^{2} - x\right )} e^{5} - 36 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 2.14, size = 22, normalized size = 0.96 \begin {gather*} 2\,\ln \left (x^3-\frac {x\,{\mathrm {e}}^5}{4}+\frac {x^2\,\left ({\mathrm {e}}^5-4\right )}{4}-9\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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