Optimal. Leaf size=33 \[ \frac {1}{3} x^3 (A c+b B)+\frac {1}{2} A b x^2+\frac {1}{4} B c x^4 \]
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Rubi [A] time = 0.02, antiderivative size = 33, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {631} \begin {gather*} \frac {1}{3} x^3 (A c+b B)+\frac {1}{2} A b x^2+\frac {1}{4} B c x^4 \end {gather*}
Antiderivative was successfully verified.
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Rule 631
Rubi steps
\begin {align*} \int (A+B x) \left (b x+c x^2\right ) \, dx &=\int \left (A b x+(b B+A c) x^2+B c x^3\right ) \, dx\\ &=\frac {1}{2} A b x^2+\frac {1}{3} (b B+A c) x^3+\frac {1}{4} B c x^4\\ \end {align*}
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Mathematica [A] time = 0.00, size = 29, normalized size = 0.88 \begin {gather*} \frac {1}{12} x^2 (A (6 b+4 c x)+B x (4 b+3 c 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 (A+B x) \left (b x+c x^2\right ) \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.35, size = 29, normalized size = 0.88 \begin {gather*} \frac {1}{4} x^{4} c B + \frac {1}{3} x^{3} b B + \frac {1}{3} x^{3} c A + \frac {1}{2} x^{2} b A \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.14, size = 29, normalized size = 0.88 \begin {gather*} \frac {1}{4} \, B c x^{4} + \frac {1}{3} \, B b x^{3} + \frac {1}{3} \, A c x^{3} + \frac {1}{2} \, A b x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 28, normalized size = 0.85 \begin {gather*} \frac {B c \,x^{4}}{4}+\frac {A b \,x^{2}}{2}+\frac {\left (A c +b B \right ) x^{3}}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.89, size = 27, normalized size = 0.82 \begin {gather*} \frac {1}{4} \, B c x^{4} + \frac {1}{2} \, A b x^{2} + \frac {1}{3} \, {\left (B b + A c\right )} x^{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 28, normalized size = 0.85 \begin {gather*} \frac {B\,c\,x^4}{4}+\left (\frac {A\,c}{3}+\frac {B\,b}{3}\right )\,x^3+\frac {A\,b\,x^2}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.06, size = 29, normalized size = 0.88 \begin {gather*} \frac {A b x^{2}}{2} + \frac {B c x^{4}}{4} + x^{3} \left (\frac {A c}{3} + \frac {B b}{3}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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