Optimal. Leaf size=9 \[ \log \left (x^2+5 x+4\right ) \]
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Rubi [A] time = 0.0030123, antiderivative size = 9, normalized size of antiderivative = 1., 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} \[ \log \left (x^2+5 x+4\right ) \]
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*}
Mathematica [A] time = 0.0022838, size = 9, normalized size = 1. \[ \log \left (x^2+5 x+4\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 10, normalized size = 1.1 \begin{align*} \ln \left ({x}^{2}+5\,x+4 \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.11543, size = 12, normalized size = 1.33 \begin{align*} \log \left (x^{2} + 5 \, x + 4\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.55628, size = 27, normalized size = 3. \begin{align*} \log \left (x^{2} + 5 \, x + 4\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.186435, size = 8, normalized size = 0.89 \begin{align*} \log{\left (x^{2} + 5 x + 4 \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.27087, size = 15, normalized size = 1.67 \begin{align*} \log \left ({\left | x + 4 \right |}\right ) + \log \left ({\left | x + 1 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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