Optimal. Leaf size=22 \[ \log (x) (a B+A b)-\frac{a A}{x}+b B x \]
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Rubi [A] time = 0.0126413, antiderivative size = 22, 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} \[ \log (x) (a B+A b)-\frac{a A}{x}+b B x \]
Antiderivative was successfully verified.
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Rule 76
Rubi steps
\begin{align*} \int \frac{(a+b x) (A+B x)}{x^2} \, dx &=\int \left (b B+\frac{a A}{x^2}+\frac{A b+a B}{x}\right ) \, dx\\ &=-\frac{a A}{x}+b B x+(A b+a B) \log (x)\\ \end{align*}
Mathematica [A] time = 0.0098639, size = 22, normalized size = 1. \[ \log (x) (a B+A b)-\frac{a A}{x}+b B x \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 23, normalized size = 1.1 \begin{align*} bBx+A\ln \left ( x \right ) b+B\ln \left ( x \right ) a-{\frac{Aa}{x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.07353, size = 30, normalized size = 1.36 \begin{align*} B b x +{\left (B a + A b\right )} \log \left (x\right ) - \frac{A a}{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.94663, size = 57, normalized size = 2.59 \begin{align*} \frac{B b x^{2} +{\left (B a + A b\right )} x \log \left (x\right ) - A a}{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.344674, size = 19, normalized size = 0.86 \begin{align*} - \frac{A a}{x} + B b x + \left (A b + B a\right ) \log{\left (x \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.20279, size = 31, normalized size = 1.41 \begin{align*} B b x +{\left (B a + A b\right )} \log \left ({\left | x \right |}\right ) - \frac{A a}{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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