Optimal. Leaf size=24 \[ \log \left (16 e^{-5-x-\frac {3}{2} \left (8+3 x+4 x^2\right )}\right ) \]
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Rubi [A] time = 0.00, antiderivative size = 11, normalized size of antiderivative = 0.46, number of steps used = 1, number of rules used = 1, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {9} \begin {gather*} -\frac {1}{96} (24 x+11)^2 \end {gather*}
Antiderivative was successfully verified.
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Rule 9
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\frac {1}{96} (11+24 x)^2\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 11, normalized size = 0.46 \begin {gather*} -\frac {11 x}{2}-6 x^2 \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.51, size = 9, normalized size = 0.38 \begin {gather*} -6 \, x^{2} - \frac {11}{2} \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.12, size = 9, normalized size = 0.38 \begin {gather*} -6 \, x^{2} - \frac {11}{2} \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 9, normalized size = 0.38
method | result | size |
gosper | \(-\frac {x \left (12 x +11\right )}{2}\) | \(9\) |
default | \(-6 x^{2}-\frac {11}{2} x\) | \(10\) |
norman | \(-6 x^{2}-\frac {11}{2} x\) | \(10\) |
risch | \(-6 x^{2}-\frac {11}{2} x\) | \(10\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 9, normalized size = 0.38 \begin {gather*} -6 \, x^{2} - \frac {11}{2} \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 8, normalized size = 0.33 \begin {gather*} -\frac {x\,\left (12\,x+11\right )}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.05, size = 10, normalized size = 0.42 \begin {gather*} - 6 x^{2} - \frac {11 x}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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