Optimal. Leaf size=20 \[ \log \left (8-\frac {1}{2} e^{-3-x} x (1+2 x)\right ) \]
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Rubi [F] time = 0.26, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {-1-3 x+2 x^2}{16 e^{3+x}-x-2 x^2} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-\frac {1}{16 e^{3+x}-x-2 x^2}+\frac {3 x}{-16 e^{3+x}+x+2 x^2}-\frac {2 x^2}{-16 e^{3+x}+x+2 x^2}\right ) \, dx\\ &=-\left (2 \int \frac {x^2}{-16 e^{3+x}+x+2 x^2} \, dx\right )+3 \int \frac {x}{-16 e^{3+x}+x+2 x^2} \, dx-\int \frac {1}{16 e^{3+x}-x-2 x^2} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.09, size = 21, normalized size = 1.05 \begin {gather*} -x+\log \left (16 e^{3+x}-x-2 x^2\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.50, size = 20, normalized size = 1.00 \begin {gather*} -x + \log \left (-2 \, x^{2} - x + 16 \, e^{\left (x + 3\right )}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.19, size = 18, normalized size = 0.90 \begin {gather*} -x + \log \left (2 \, x^{2} + x - 16 \, e^{\left (x + 3\right )}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 19, normalized size = 0.95
method | result | size |
risch | \(-x +\ln \left ({\mathrm e}^{x}-\frac {\left (2 x +1\right ) x \,{\mathrm e}^{-3}}{16}\right )\) | \(19\) |
norman | \(-x +\ln \left (16 \,{\mathrm e}^{x} {\mathrm e}^{3}-2 x^{2}-x \right )\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.50, size = 22, normalized size = 1.10 \begin {gather*} -x + \log \left (-\frac {1}{16} \, {\left (2 \, x^{2} + x - 16 \, e^{\left (x + 3\right )}\right )} e^{\left (-3\right )}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.09, size = 18, normalized size = 0.90 \begin {gather*} \ln \left (x-16\,{\mathrm {e}}^{x+3}+2\,x^2\right )-x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.15, size = 19, normalized size = 0.95 \begin {gather*} - x + \log {\left (\frac {- 2 x^{2} - x}{16 e^{3}} + e^{x} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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