Optimal. Leaf size=11 \[ \log \left (a+b x+c x^2\right ) \]
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Rubi [A] time = 0.0040946, antiderivative size = 11, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.053, Rules used = {628} \[ \log \left (a+b x+c x^2\right ) \]
Antiderivative was successfully verified.
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Rule 628
Rubi steps
\begin{align*} \int \frac{b+2 c x}{a+b x+c x^2} \, dx &=\log \left (a+b x+c x^2\right )\\ \end{align*}
Mathematica [A] time = 0.0029445, size = 10, normalized size = 0.91 \[ \log (a+x (b+c x)) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 12, normalized size = 1.1 \begin{align*} \ln \left ( c{x}^{2}+bx+a \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.13787, size = 15, normalized size = 1.36 \begin{align*} \log \left (c x^{2} + b x + a\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0.979356, size = 30, normalized size = 2.73 \begin{align*} \log \left (c x^{2} + b x + a\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.297273, size = 10, normalized size = 0.91 \begin{align*} \log{\left (a + b x + c x^{2} \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.09568, size = 15, normalized size = 1.36 \begin{align*} \log \left (c x^{2} + b x + a\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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