Optimal. Leaf size=24 \[ x (a B+A b)+a A \log (x)+\frac{1}{2} b B x^2 \]
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Rubi [A] time = 0.0094834, antiderivative size = 24, 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} \[ x (a B+A b)+a A \log (x)+\frac{1}{2} b B x^2 \]
Antiderivative was successfully verified.
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Rule 76
Rubi steps
\begin{align*} \int \frac{(a+b x) (A+B x)}{x} \, dx &=\int \left (A b+a B+\frac{a A}{x}+b B x\right ) \, dx\\ &=(A b+a B) x+\frac{1}{2} b B x^2+a A \log (x)\\ \end{align*}
Mathematica [A] time = 0.005144, size = 24, normalized size = 1. \[ x (a B+A b)+a A \log (x)+\frac{1}{2} b B x^2 \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 22, normalized size = 0.9 \begin{align*}{\frac{bB{x}^{2}}{2}}+Abx+Bax+aA\ln \left ( x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.13342, size = 30, normalized size = 1.25 \begin{align*} \frac{1}{2} \, B b x^{2} + A a \log \left (x\right ) +{\left (B a + A b\right )} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.85879, size = 57, normalized size = 2.38 \begin{align*} \frac{1}{2} \, B b x^{2} + A a \log \left (x\right ) +{\left (B a + A b\right )} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.279668, size = 22, normalized size = 0.92 \begin{align*} A a \log{\left (x \right )} + \frac{B b x^{2}}{2} + x \left (A b + B a\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.21599, size = 30, normalized size = 1.25 \begin{align*} \frac{1}{2} \, B b x^{2} + B a x + A b x + A a \log \left ({\left | x \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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