Optimal. Leaf size=24 \[ x (A c+b B)+A b \log (x)+\frac{1}{2} B c x^2 \]
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Rubi [A] time = 0.0127155, antiderivative size = 24, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.056, Rules used = {765} \[ x (A c+b B)+A b \log (x)+\frac{1}{2} B c x^2 \]
Antiderivative was successfully verified.
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Rule 765
Rubi steps
\begin{align*} \int \frac{(A+B x) \left (b x+c x^2\right )}{x^2} \, dx &=\int \left (b B+A c+\frac{A b}{x}+B c x\right ) \, dx\\ &=(b B+A c) x+\frac{1}{2} B c x^2+A b \log (x)\\ \end{align*}
Mathematica [A] time = 0.005294, size = 24, normalized size = 1. \[ x (A c+b B)+A b \log (x)+\frac{1}{2} B c x^2 \]
Antiderivative was successfully verified.
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Maple [A] time = 0.007, size = 22, normalized size = 0.9 \begin{align*}{\frac{Bc{x}^{2}}{2}}+Acx+bBx+Ab\ln \left ( x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.967713, size = 30, normalized size = 1.25 \begin{align*} \frac{1}{2} \, B c x^{2} + A b \log \left (x\right ) +{\left (B b + A c\right )} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.75176, size = 57, normalized size = 2.38 \begin{align*} \frac{1}{2} \, B c x^{2} + A b \log \left (x\right ) +{\left (B b + A c\right )} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.29136, size = 22, normalized size = 0.92 \begin{align*} A b \log{\left (x \right )} + \frac{B c x^{2}}{2} + x \left (A c + B b\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.14413, size = 30, normalized size = 1.25 \begin{align*} \frac{1}{2} \, B c x^{2} + B b x + A c x + A b \log \left ({\left | x \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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