Optimal. Leaf size=16 \[ \log \left (-1+x+x^2 \left (9-e^2+x\right )\right ) \]
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Rubi [A] time = 0.03, antiderivative size = 23, normalized size of antiderivative = 1.44, number of steps used = 3, number of rules used = 2, integrand size = 41, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.049, Rules used = {6, 1587} \begin {gather*} \log \left (-x^3-\left (9-e^2\right ) x^2-x+1\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 6
Rule 1587
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-1+\left (-18+2 e^2\right ) x-3 x^2}{1-x-9 x^2+e^2 x^2-x^3} \, dx\\ &=\int \frac {-1+\left (-18+2 e^2\right ) x-3 x^2}{1-x+\left (-9+e^2\right ) x^2-x^3} \, dx\\ &=\log \left (1-x-\left (9-e^2\right ) x^2-x^3\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 20, normalized size = 1.25 \begin {gather*} \log \left (1-x+\left (-9+e^2\right ) x^2-x^3\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.66, size = 19, normalized size = 1.19 \begin {gather*} \log \left (x^{3} - x^{2} e^{2} + 9 \, x^{2} + x - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.31, size = 20, normalized size = 1.25 \begin {gather*} \log \left ({\left | x^{3} - x^{2} e^{2} + 9 \, x^{2} + x - 1 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 18, normalized size = 1.12
method | result | size |
risch | \(\ln \left (x^{3}+\left (-{\mathrm e}^{2}+9\right ) x^{2}+x -1\right )\) | \(18\) |
derivativedivides | \(\ln \left (x^{2} {\mathrm e}^{2}-x^{3}-9 x^{2}-x +1\right )\) | \(23\) |
default | \(\ln \left (x^{2} {\mathrm e}^{2}-x^{3}-9 x^{2}-x +1\right )\) | \(23\) |
norman | \(\ln \left (x^{2} {\mathrm e}^{2}-x^{3}-9 x^{2}-x +1\right )\) | \(23\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.77, size = 19, normalized size = 1.19 \begin {gather*} \log \left (x^{3} - x^{2} e^{2} + 9 \, x^{2} + x - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.00, size = 16, normalized size = 1.00 \begin {gather*} \ln \left (x^3+\left (9-{\mathrm {e}}^2\right )\,x^2+x-1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.29, size = 15, normalized size = 0.94 \begin {gather*} \log {\left (x^{3} + x^{2} \left (9 - e^{2}\right ) + x - 1 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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