Optimal. Leaf size=33 \[ \frac{1}{6} x^6 (A c+b B)+\frac{1}{5} A b x^5+\frac{1}{7} B c x^7 \]
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Rubi [A] time = 0.0441337, antiderivative size = 33, normalized size of antiderivative = 1., 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} \[ \frac{1}{6} x^6 (A c+b B)+\frac{1}{5} A b x^5+\frac{1}{7} B c x^7 \]
Antiderivative was successfully verified.
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Rule 765
Rubi steps
\begin{align*} \int x^3 (A+B x) \left (b x+c x^2\right ) \, dx &=\int \left (A b x^4+(b B+A c) x^5+B c x^6\right ) \, dx\\ &=\frac{1}{5} A b x^5+\frac{1}{6} (b B+A c) x^6+\frac{1}{7} B c x^7\\ \end{align*}
Mathematica [A] time = 0.0053291, size = 33, normalized size = 1. \[ \frac{1}{6} x^6 (A c+b B)+\frac{1}{5} A b x^5+\frac{1}{7} B c x^7 \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 28, normalized size = 0.9 \begin{align*}{\frac{Ab{x}^{5}}{5}}+{\frac{ \left ( Ac+bB \right ){x}^{6}}{6}}+{\frac{Bc{x}^{7}}{7}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.963759, size = 36, normalized size = 1.09 \begin{align*} \frac{1}{7} \, B c x^{7} + \frac{1}{5} \, A b x^{5} + \frac{1}{6} \,{\left (B b + A c\right )} x^{6} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.60246, size = 74, normalized size = 2.24 \begin{align*} \frac{1}{7} x^{7} c B + \frac{1}{6} x^{6} b B + \frac{1}{6} x^{6} c A + \frac{1}{5} x^{5} b A \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.062981, size = 29, normalized size = 0.88 \begin{align*} \frac{A b x^{5}}{5} + \frac{B c x^{7}}{7} + x^{6} \left (\frac{A c}{6} + \frac{B b}{6}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.15303, size = 39, normalized size = 1.18 \begin{align*} \frac{1}{7} \, B c x^{7} + \frac{1}{6} \, B b x^{6} + \frac{1}{6} \, A c x^{6} + \frac{1}{5} \, A b x^{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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