Optimal. Leaf size=13 \[ \log \left (\frac {1}{3+x-(16+x)^2}\right ) \]
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Rubi [A]
time = 0.00, antiderivative size = 11, normalized size of antiderivative = 0.85, 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+31 x+253\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 642
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\log \left (253+31 x+x^2\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 11, normalized size = 0.85 \begin {gather*} -\log \left (253+31 x+x^2\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 1.31, size = 12, normalized size = 0.92
method | result | size |
default | \(-\ln \left (x^{2}+31 x +253\right )\) | \(12\) |
norman | \(-\ln \left (x^{2}+31 x +253\right )\) | \(12\) |
risch | \(-\ln \left (x^{2}+31 x +253\right )\) | \(12\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 11, normalized size = 0.85 \begin {gather*} -\log \left (x^{2} + 31 \, x + 253\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.29, size = 11, normalized size = 0.85 \begin {gather*} -\log \left (x^{2} + 31 \, x + 253\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 10, normalized size = 0.77 \begin {gather*} - \log {\left (x^{2} + 31 x + 253 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 11, normalized size = 0.85 \begin {gather*} -\log \left (x^{2} + 31 \, x + 253\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.04, size = 11, normalized size = 0.85 \begin {gather*} -\ln \left (x^2+31\,x+253\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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