Optimal. Leaf size=22 \[ \log (x) (a B+A b)-\frac {a A}{x}+b B x \]
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Rubi [A] time = 0.01, antiderivative size = 22, normalized size of antiderivative = 1.00, 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} \begin {gather*} \log (x) (a B+A b)-\frac {a A}{x}+b B x \end {gather*}
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*}
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Mathematica [A] time = 0.01, size = 22, normalized size = 1.00 \begin {gather*} \log (x) (a B+A b)-\frac {a A}{x}+b B 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) (A+B x)}{x^2} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.26, size = 26, normalized size = 1.18 \begin {gather*} \frac {B b x^{2} + {\left (B a + A b\right )} x \log \relax (x) - A a}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.25, size = 23, normalized size = 1.05 \begin {gather*} B b x + {\left (B a + A b\right )} \log \left ({\left | x \right |}\right ) - \frac {A a}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 23, normalized size = 1.05 \begin {gather*} A b \ln \relax (x )+B a \ln \relax (x )+B b x -\frac {A a}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.10, size = 22, normalized size = 1.00 \begin {gather*} B b x + {\left (B a + A b\right )} \log \relax (x) - \frac {A a}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.30, size = 22, normalized size = 1.00 \begin {gather*} \ln \relax (x)\,\left (A\,b+B\,a\right )+B\,b\,x-\frac {A\,a}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.24, size = 19, normalized size = 0.86 \begin {gather*} - \frac {A a}{x} + B b x + \left (A b + B a\right ) \log {\relax (x )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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