Optimal. Leaf size=9 \[ \log \left (x^2+5 x+4\right ) \]
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Rubi [A] time = 0.00, antiderivative size = 9, normalized size of antiderivative = 1.00, 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 = {628} \begin {gather*} \log \left (x^2+5 x+4\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 628
Rubi steps
\begin {align*} \int \frac {5+2 x}{4+5 x+x^2} \, dx &=\log \left (4+5 x+x^2\right )\\ \end {align*}
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Mathematica [A] time = 0.00, size = 9, normalized size = 1.00 \begin {gather*} \log \left (x^2+5 x+4\right ) \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {5+2 x}{4+5 x+x^2} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.38, size = 9, normalized size = 1.00 \begin {gather*} \log \left (x^{2} + 5 \, x + 4\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.19, size = 10, normalized size = 1.11 \begin {gather*} \log \left ({\left | x^{2} + 5 \, x + 4 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 10, normalized size = 1.11 \begin {gather*} \ln \left (x^{2}+5 x +4\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.49, size = 9, normalized size = 1.00 \begin {gather*} \log \left (x^{2} + 5 \, x + 4\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 = 1.00 \begin {gather*} \ln \left (x^2+5\,x+4\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 8, normalized size = 0.89 \begin {gather*} \log {\left (x^{2} + 5 x + 4 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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