Optimal. Leaf size=28 \[ a A \log (x)+a B x+\frac {1}{2} A c x^2+\frac {1}{3} B c x^3 \]
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Rubi [A] time = 0.01, antiderivative size = 28, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.062, Rules used = {766} \begin {gather*} a A \log (x)+a B x+\frac {1}{2} A c x^2+\frac {1}{3} B c x^3 \end {gather*}
Antiderivative was successfully verified.
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Rule 766
Rubi steps
\begin {align*} \int \frac {(A+B x) \left (a+c x^2\right )}{x} \, dx &=\int \left (a B+\frac {a A}{x}+A c x+B c x^2\right ) \, dx\\ &=a B x+\frac {1}{2} A c x^2+\frac {1}{3} B c x^3+a A \log (x)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 28, normalized size = 1.00 \begin {gather*} a A \log (x)+a B x+\frac {1}{2} A c x^2+\frac {1}{3} B c x^3 \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 (a+c x^2\right )}{x} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.39, size = 24, normalized size = 0.86 \begin {gather*} \frac {1}{3} \, B c x^{3} + \frac {1}{2} \, A c x^{2} + B a x + A a \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 25, normalized size = 0.89 \begin {gather*} \frac {1}{3} \, B c x^{3} + \frac {1}{2} \, A c x^{2} + B a x + A a \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 = 25, normalized size = 0.89 \begin {gather*} \frac {B c \,x^{3}}{3}+\frac {A c \,x^{2}}{2}+A a \ln \relax (x )+B a x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.57, size = 24, normalized size = 0.86 \begin {gather*} \frac {1}{3} \, B c x^{3} + \frac {1}{2} \, A c x^{2} + B a x + A a \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 24, normalized size = 0.86 \begin {gather*} B\,a\,x+\frac {A\,c\,x^2}{2}+\frac {B\,c\,x^3}{3}+A\,a\,\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 = 27, normalized size = 0.96 \begin {gather*} A a \log {\relax (x )} + \frac {A c x^{2}}{2} + B a x + \frac {B c x^{3}}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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