Optimal. Leaf size=38 \[ x (a B+A b)+a A \log (x)+\frac {1}{2} x^2 (A c+b B)+\frac {1}{3} B c x^3 \]
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Rubi [A] time = 0.02, antiderivative size = 38, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 19, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.053, Rules used = {765} \begin {gather*} x (a B+A b)+a A \log (x)+\frac {1}{2} x^2 (A c+b B)+\frac {1}{3} B c x^3 \end {gather*}
Antiderivative was successfully verified.
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Rule 765
Rubi steps
\begin {align*} \int \frac {(A+B x) \left (a+b x+c x^2\right )}{x} \, dx &=\int \left (A b+a B+\frac {a A}{x}+(b B+A c) x+B c x^2\right ) \, dx\\ &=(A b+a B) x+\frac {1}{2} (b B+A c) x^2+\frac {1}{3} B c x^3+a A \log (x)\\ \end {align*}
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Mathematica [A] time = 0.01, size = 38, normalized size = 1.00 \begin {gather*} x (a B+A b)+a A \log (x)+\frac {1}{2} x^2 (A c+b B)+\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+b x+c x^2\right )}{x} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.40, size = 34, normalized size = 0.89 \begin {gather*} \frac {1}{3} \, B c x^{3} + \frac {1}{2} \, {\left (B b + A c\right )} x^{2} + A a \log \relax (x) + {\left (B a + A b\right )} x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 36, normalized size = 0.95 \begin {gather*} \frac {1}{3} \, B c x^{3} + \frac {1}{2} \, B b x^{2} + \frac {1}{2} \, A c x^{2} + B a x + A b 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 = 36, normalized size = 0.95 \begin {gather*} \frac {B c \,x^{3}}{3}+\frac {A c \,x^{2}}{2}+\frac {B b \,x^{2}}{2}+A a \ln \relax (x )+A b x +B a x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.53, size = 34, normalized size = 0.89 \begin {gather*} \frac {1}{3} \, B c x^{3} + \frac {1}{2} \, {\left (B b + A c\right )} x^{2} + A a \log \relax (x) + {\left (B a + A b\right )} x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 35, normalized size = 0.92 \begin {gather*} x\,\left (A\,b+B\,a\right )+x^2\,\left (\frac {A\,c}{2}+\frac {B\,b}{2}\right )+\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 = 0.13, size = 36, normalized size = 0.95 \begin {gather*} A a \log {\relax (x )} + \frac {B c x^{3}}{3} + x^{2} \left (\frac {A c}{2} + \frac {B b}{2}\right ) + x \left (A b + B a\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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