Optimal. Leaf size=27 \[ -\frac{A c+b B}{x}-\frac{A b}{2 x^2}+B c \log (x) \]
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Rubi [A] time = 0.0165446, antiderivative size = 27, 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} \[ -\frac{A c+b B}{x}-\frac{A b}{2 x^2}+B c \log (x) \]
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^4} \, dx &=\int \left (\frac{A b}{x^3}+\frac{b B+A c}{x^2}+\frac{B c}{x}\right ) \, dx\\ &=-\frac{A b}{2 x^2}-\frac{b B+A c}{x}+B c \log (x)\\ \end{align*}
Mathematica [A] time = 0.00983, size = 28, normalized size = 1.04 \[ \frac{-A c-b B}{x}-\frac{A b}{2 x^2}+B c \log (x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 28, normalized size = 1. \begin{align*} Bc\ln \left ( x \right ) -{\frac{Ab}{2\,{x}^{2}}}-{\frac{Ac}{x}}-{\frac{bB}{x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.991116, size = 34, normalized size = 1.26 \begin{align*} B c \log \left (x\right ) - \frac{A b + 2 \,{\left (B b + A c\right )} x}{2 \, x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.7421, size = 70, normalized size = 2.59 \begin{align*} \frac{2 \, B c x^{2} \log \left (x\right ) - A b - 2 \,{\left (B b + A c\right )} x}{2 \, x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.399622, size = 26, normalized size = 0.96 \begin{align*} B c \log{\left (x \right )} - \frac{A b + x \left (2 A c + 2 B b\right )}{2 x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.1383, size = 35, normalized size = 1.3 \begin{align*} B c \log \left ({\left | x \right |}\right ) - \frac{A b + 2 \,{\left (B b + A c\right )} x}{2 \, x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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