Optimal. Leaf size=33 \[ \frac{1}{3} x^3 (a B+A b)+\frac{1}{2} a A x^2+\frac{1}{4} b B x^4 \]
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Rubi [A] time = 0.0189485, antiderivative size = 33, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 12, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.083, Rules used = {76} \[ \frac{1}{3} x^3 (a B+A b)+\frac{1}{2} a A x^2+\frac{1}{4} b B x^4 \]
Antiderivative was successfully verified.
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Rule 76
Rubi steps
\begin{align*} \int x (a+b x) (A+B x) \, dx &=\int \left (a A x+(A b+a B) x^2+b B x^3\right ) \, dx\\ &=\frac{1}{2} a A x^2+\frac{1}{3} (A b+a B) x^3+\frac{1}{4} b B x^4\\ \end{align*}
Mathematica [A] time = 0.0046827, size = 29, normalized size = 0.88 \[ \frac{1}{12} x^2 (a (6 A+4 B x)+b x (4 A+3 B x)) \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 28, normalized size = 0.9 \begin{align*}{\frac{aA{x}^{2}}{2}}+{\frac{ \left ( Ab+Ba \right ){x}^{3}}{3}}+{\frac{bB{x}^{4}}{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.07529, size = 36, normalized size = 1.09 \begin{align*} \frac{1}{4} \, B b x^{4} + \frac{1}{2} \, A a x^{2} + \frac{1}{3} \,{\left (B a + A b\right )} x^{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.64027, size = 74, normalized size = 2.24 \begin{align*} \frac{1}{4} x^{4} b B + \frac{1}{3} x^{3} a B + \frac{1}{3} x^{3} b A + \frac{1}{2} x^{2} a A \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.063705, size = 29, normalized size = 0.88 \begin{align*} \frac{A a x^{2}}{2} + \frac{B b x^{4}}{4} + x^{3} \left (\frac{A b}{3} + \frac{B a}{3}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.21364, size = 39, normalized size = 1.18 \begin{align*} \frac{1}{4} \, B b x^{4} + \frac{1}{3} \, B a x^{3} + \frac{1}{3} \, A b x^{3} + \frac{1}{2} \, A a x^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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