Optimal. Leaf size=24 \[ x (A c+b B)+A b \log (x)+\frac {1}{2} B c x^2 \]
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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 = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {765} \begin {gather*} x (A c+b B)+A b \log (x)+\frac {1}{2} B c x^2 \end {gather*}
Antiderivative was successfully verified.
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Rule 765
Rubi steps
\begin {align*} \int \frac {(A+B x) \left (b x+c x^2\right )}{x^2} \, dx &=\int \left (b B+A c+\frac {A b}{x}+B c x\right ) \, dx\\ &=(b B+A c) x+\frac {1}{2} B c x^2+A b \log (x)\\ \end {align*}
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Mathematica [A] time = 0.01, size = 24, normalized size = 1.00 \begin {gather*} x (A c+b B)+A b \log (x)+\frac {1}{2} B c x^2 \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) \left (b x+c x^2\right )}{x^2} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.39, size = 22, normalized size = 0.92 \begin {gather*} \frac {1}{2} \, B c x^{2} + A b \log \relax (x) + {\left (B b + A c\right )} x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.14, size = 22, normalized size = 0.92 \begin {gather*} \frac {1}{2} \, B c x^{2} + B b x + A c x + A b \log \left ({\left | x \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 22, normalized size = 0.92 \begin {gather*} \frac {B c \,x^{2}}{2}+A b \ln \relax (x )+A c x +B b x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.90, size = 22, normalized size = 0.92 \begin {gather*} \frac {1}{2} \, B c x^{2} + A b \log \relax (x) + {\left (B b + A c\right )} x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 22, normalized size = 0.92 \begin {gather*} x\,\left (A\,c+B\,b\right )+\frac {B\,c\,x^2}{2}+A\,b\,\ln \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 22, normalized size = 0.92 \begin {gather*} A b \log {\relax (x )} + \frac {B c x^{2}}{2} + x \left (A c + B b\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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