Optimal. Leaf size=21 \[ \log \left (-9+e^x+x+x \left (-1+2 x-x^2\right )^2\right ) \]
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Rubi [A] time = 0.08, antiderivative size = 31, normalized size of antiderivative = 1.48, number of steps used = 1, number of rules used = 1, integrand size = 52, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.019, Rules used = {6684} \begin {gather*} \log \left (-x^5+4 x^4-6 x^3+4 x^2-2 x-e^x+9\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 6684
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\log \left (9-e^x-2 x+4 x^2-6 x^3+4 x^4-x^5\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.22, size = 27, normalized size = 1.29 \begin {gather*} \log \left (-9+e^x+2 x-4 x^2+6 x^3-4 x^4+x^5\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.65, size = 26, normalized size = 1.24 \begin {gather*} \log \left (x^{5} - 4 \, x^{4} + 6 \, x^{3} - 4 \, x^{2} + 2 \, x + e^{x} - 9\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 3.12, size = 26, normalized size = 1.24 \begin {gather*} \log \left (x^{5} - 4 \, x^{4} + 6 \, x^{3} - 4 \, x^{2} + 2 \, x + e^{x} - 9\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 27, normalized size = 1.29
method | result | size |
derivativedivides | \(\ln \left ({\mathrm e}^{x}+x^{5}-4 x^{4}+6 x^{3}-4 x^{2}+2 x -9\right )\) | \(27\) |
default | \(\ln \left ({\mathrm e}^{x}+x^{5}-4 x^{4}+6 x^{3}-4 x^{2}+2 x -9\right )\) | \(27\) |
norman | \(\ln \left ({\mathrm e}^{x}+x^{5}-4 x^{4}+6 x^{3}-4 x^{2}+2 x -9\right )\) | \(27\) |
risch | \(\ln \left ({\mathrm e}^{x}+x^{5}-4 x^{4}+6 x^{3}-4 x^{2}+2 x -9\right )\) | \(27\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.34, size = 26, normalized size = 1.24 \begin {gather*} \log \left (x^{5} - 4 \, x^{4} + 6 \, x^{3} - 4 \, x^{2} + 2 \, x + e^{x} - 9\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.03, size = 26, normalized size = 1.24 \begin {gather*} \ln \left (2\,x+{\mathrm {e}}^x-4\,x^2+6\,x^3-4\,x^4+x^5-9\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.15, size = 27, normalized size = 1.29 \begin {gather*} \log {\left (x^{5} - 4 x^{4} + 6 x^{3} - 4 x^{2} + 2 x + e^{x} - 9 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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