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 = 0.01, antiderivative size = 24, 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} \[ x (a B+A b)+a A \log (x)+\frac {1}{2} b B x^2 \]
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*}
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Mathematica [A] time = 0.01, size = 24, normalized size = 1.00 \[ x (a B+A b)+a A \log (x)+\frac {1}{2} b B x^2 \]
Antiderivative was successfully verified.
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fricas [A] time = 0.62, size = 22, normalized size = 0.92 \[ \frac {1}{2} \, B b x^{2} + A a \log \relax (x) + {\left (B a + A b\right )} x \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.28, size = 22, normalized size = 0.92 \[ \frac {1}{2} \, B b x^{2} + B a x + A b x + A a \log \left ({\left | x \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 22, normalized size = 0.92 \[ \frac {B b \,x^{2}}{2}+A a \ln \relax (x )+A b x +B a x \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.10, size = 22, normalized size = 0.92 \[ \frac {1}{2} \, B b x^{2} + A a \log \relax (x) + {\left (B a + A b\right )} x \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.29, size = 22, normalized size = 0.92 \[ x\,\left (A\,b+B\,a\right )+\frac {B\,b\,x^2}{2}+A\,a\,\ln \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.14, size = 22, normalized size = 0.92 \[ A a \log {\relax (x )} + \frac {B b x^{2}}{2} + x \left (A b + B a\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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