Optimal. Leaf size=10 \[ \log \left (a x+b x^2\right ) \]
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Rubi [A] time = 0.0039895, antiderivative size = 10, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.056, Rules used = {628} \[ \log \left (a x+b x^2\right ) \]
Antiderivative was successfully verified.
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Rule 628
Rubi steps
\begin{align*} \int \frac{a+2 b x}{a x+b x^2} \, dx &=\log \left (a x+b x^2\right )\\ \end{align*}
Mathematica [A] time = 0.0039173, size = 9, normalized size = 0.9 \[ \log (a+b x)+\log (x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.043, size = 9, normalized size = 0.9 \begin{align*} \ln \left ( x \left ( bx+a \right ) \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.11328, size = 14, normalized size = 1.4 \begin{align*} \log \left (b x^{2} + a x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.55282, size = 24, normalized size = 2.4 \begin{align*} \log \left (b x^{2} + a x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.981668, size = 8, normalized size = 0.8 \begin{align*} \log{\left (a x + b x^{2} \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.33478, size = 15, normalized size = 1.5 \begin{align*} \log \left ({\left | b x + a \right |}\right ) + \log \left ({\left | x \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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