Optimal. Leaf size=10 \[ \log \left (-1+(-3-x)^2\right ) \]
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Rubi [A]
time = 0.00, antiderivative size = 9, normalized size of antiderivative = 0.90, number of steps
used = 1, number of rules used = 1, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.062, Rules used = {642}
\begin {gather*} \log \left (x^2+6 x+8\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 642
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\log \left (8+6 x+x^2\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 9, normalized size = 0.90 \begin {gather*} \log \left (8+6 x+x^2\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 1.63, size = 10, normalized size = 1.00
method | result | size |
derivativedivides | \(\ln \left (x^{2}+6 x +8\right )\) | \(10\) |
default | \(\ln \left (x^{2}+6 x +8\right )\) | \(10\) |
norman | \(\ln \left (2+x \right )+\ln \left (4+x \right )\) | \(10\) |
risch | \(\ln \left (x^{2}+6 x +8\right )\) | \(10\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 9, normalized size = 0.90 \begin {gather*} \log \left (x^{2} + 6 \, x + 8\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 9, normalized size = 0.90 \begin {gather*} \log \left (x^{2} + 6 \, x + 8\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.02, size = 8, normalized size = 0.80 \begin {gather*} \log {\left (x^{2} + 6 x + 8 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.43, size = 10, normalized size = 1.00 \begin {gather*} \log \left ({\left | x^{2} + 6 \, x + 8 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.04, size = 9, normalized size = 0.90 \begin {gather*} \ln \left (x^2+6\,x+8\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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