Optimal. Leaf size=27 \[ -\frac{a B+A b}{x}-\frac{a A}{2 x^2}+b B \log (x) \]
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Rubi [A] time = 0.013042, antiderivative size = 27, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 14, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.071, Rules used = {76} \[ -\frac{a B+A b}{x}-\frac{a A}{2 x^2}+b B \log (x) \]
Antiderivative was successfully verified.
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Rule 76
Rubi steps
\begin{align*} \int \frac{(a+b x) (A+B x)}{x^3} \, dx &=\int \left (\frac{a A}{x^3}+\frac{A b+a B}{x^2}+\frac{b B}{x}\right ) \, dx\\ &=-\frac{a A}{2 x^2}-\frac{A b+a B}{x}+b B \log (x)\\ \end{align*}
Mathematica [A] time = 0.0105576, size = 28, normalized size = 1.04 \[ \frac{-a B-A b}{x}-\frac{a A}{2 x^2}+b B \log (x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 28, normalized size = 1. \begin{align*} bB\ln \left ( x \right ) -{\frac{Aa}{2\,{x}^{2}}}-{\frac{Ab}{x}}-{\frac{Ba}{x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.15508, size = 34, normalized size = 1.26 \begin{align*} B b \log \left (x\right ) - \frac{A a + 2 \,{\left (B a + A b\right )} x}{2 \, x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.9138, size = 70, normalized size = 2.59 \begin{align*} \frac{2 \, B b x^{2} \log \left (x\right ) - A a - 2 \,{\left (B a + A b\right )} x}{2 \, x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.42327, size = 26, normalized size = 0.96 \begin{align*} B b \log{\left (x \right )} - \frac{A a + x \left (2 A b + 2 B a\right )}{2 x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.2282, size = 35, normalized size = 1.3 \begin{align*} B b \log \left ({\left | x \right |}\right ) - \frac{A a + 2 \,{\left (B a + A b\right )} x}{2 \, x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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