Optimal. Leaf size=13 \[ \log \left (a-b x-c x^2\right ) \]
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Rubi [A] time = 0.0047574, antiderivative size = 13, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 21, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.048, 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 = 0.0045095, size = 12, normalized size = 0.92 \[ \log (x (b+c x)-a) \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 14, 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 = 1.18616, size = 18, normalized size = 1.38 \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 = 0.950366, size = 30, normalized size = 2.31 \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 = 0.393052, size = 10, normalized size = 0.77 \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 = 1.12131, size = 18, normalized size = 1.38 \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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