Optimal. Leaf size=22 \[ \log (x) (A c+b B)-\frac {A b}{x}+B c x \]
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Rubi [A] time = 0.02, antiderivative size = 22, normalized size of antiderivative = 1.00, 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} \begin {gather*} \log (x) (A c+b B)-\frac {A b}{x}+B c x \end {gather*}
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*}
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Mathematica [A] time = 0.01, size = 22, normalized size = 1.00 \begin {gather*} \log (x) (A c+b B)-\frac {A b}{x}+B c x \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {(A+B x) \left (b x+c x^2\right )}{x^3} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.39, size = 26, normalized size = 1.18 \begin {gather*} \frac {B c x^{2} + {\left (B b + A c\right )} x \log \relax (x) - A b}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 23, normalized size = 1.05 \begin {gather*} B c x + {\left (B b + A c\right )} \log \left ({\left | x \right |}\right ) - \frac {A b}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 23, normalized size = 1.05 \begin {gather*} A c \ln \relax (x )+B b \ln \relax (x )+B c x -\frac {A b}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.87, size = 22, normalized size = 1.00 \begin {gather*} B c x + {\left (B b + A c\right )} \log \relax (x) - \frac {A b}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 22, normalized size = 1.00 \begin {gather*} \ln \relax (x)\,\left (A\,c+B\,b\right )+B\,c\,x-\frac {A\,b}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.15, size = 19, normalized size = 0.86 \begin {gather*} - \frac {A b}{x} + B c x + \left (A c + B b\right ) \log {\relax (x )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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