Optimal. Leaf size=22 \[ \log (x) (A c+b B)-\frac{A b}{x}+B c x \]
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Rubi [A] time = 0.0158835, antiderivative size = 22, 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} \[ \log (x) (A c+b B)-\frac{A b}{x}+B c x \]
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^3} \, dx &=\int \left (B c+\frac{A b}{x^2}+\frac{b B+A c}{x}\right ) \, dx\\ &=-\frac{A b}{x}+B c x+(b B+A c) \log (x)\\ \end{align*}
Mathematica [A] time = 0.008849, size = 22, normalized size = 1. \[ \log (x) (A c+b B)-\frac{A b}{x}+B c x \]
Antiderivative was successfully verified.
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Maple [A] time = 0.02, size = 23, normalized size = 1.1 \begin{align*} Bcx+Ac\ln \left ( x \right ) +B\ln \left ( x \right ) b-{\frac{Ab}{x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.965725, size = 30, normalized size = 1.36 \begin{align*} B c x +{\left (B b + A c\right )} \log \left (x\right ) - \frac{A b}{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.77541, size = 57, normalized size = 2.59 \begin{align*} \frac{B c x^{2} +{\left (B b + A c\right )} x \log \left (x\right ) - A b}{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.31423, size = 19, normalized size = 0.86 \begin{align*} - \frac{A b}{x} + B c x + \left (A c + B b\right ) \log{\left (x \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.18852, size = 31, normalized size = 1.41 \begin{align*} B c x +{\left (B b + A c\right )} \log \left ({\left | x \right |}\right ) - \frac{A b}{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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