Optimal. Leaf size=13 \[ d \log \left (a+b x+c x^2\right ) \]
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Rubi [A] time = 0.0048115, antiderivative size = 13, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.045, Rules used = {628} \[ d \log \left (a+b x+c x^2\right ) \]
Antiderivative was successfully verified.
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Rule 628
Rubi steps
\begin{align*} \int \frac{b d+2 c d x}{a+b x+c x^2} \, dx &=d \log \left (a+b x+c x^2\right )\\ \end{align*}
Mathematica [A] time = 0.002052, size = 12, normalized size = 0.92 \[ d \log (a+x (b+c x)) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.04, size = 14, normalized size = 1.1 \begin{align*} d\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 = 1.29871, size = 18, normalized size = 1.38 \begin{align*} d \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 = 1.7289, size = 32, normalized size = 2.46 \begin{align*} d \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 = 0.333279, size = 12, normalized size = 0.92 \begin{align*} d \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 = 1.22793, size = 18, normalized size = 1.38 \begin{align*} d \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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