Optimal. Leaf size=55 \[ \frac{1}{6} A b^2 x^6+\frac{1}{8} c x^8 (A c+2 b B)+\frac{1}{7} b x^7 (2 A c+b B)+\frac{1}{9} B c^2 x^9 \]
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Rubi [A] time = 0.0616889, antiderivative size = 55, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05, Rules used = {765} \[ \frac{1}{6} A b^2 x^6+\frac{1}{8} c x^8 (A c+2 b B)+\frac{1}{7} b x^7 (2 A c+b B)+\frac{1}{9} B c^2 x^9 \]
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 )^2 \, dx &=\int \left (A b^2 x^5+b (b B+2 A c) x^6+c (2 b B+A c) x^7+B c^2 x^8\right ) \, dx\\ &=\frac{1}{6} A b^2 x^6+\frac{1}{7} b (b B+2 A c) x^7+\frac{1}{8} c (2 b B+A c) x^8+\frac{1}{9} B c^2 x^9\\ \end{align*}
Mathematica [A] time = 0.0097525, size = 55, normalized size = 1. \[ \frac{1}{6} A b^2 x^6+\frac{1}{8} c x^8 (A c+2 b B)+\frac{1}{7} b x^7 (2 A c+b B)+\frac{1}{9} B c^2 x^9 \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 52, normalized size = 1. \begin{align*}{\frac{B{c}^{2}{x}^{9}}{9}}+{\frac{ \left ( A{c}^{2}+2\,Bbc \right ){x}^{8}}{8}}+{\frac{ \left ( 2\,Abc+{b}^{2}B \right ){x}^{7}}{7}}+{\frac{A{b}^{2}{x}^{6}}{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.06708, size = 69, normalized size = 1.25 \begin{align*} \frac{1}{9} \, B c^{2} x^{9} + \frac{1}{6} \, A b^{2} x^{6} + \frac{1}{8} \,{\left (2 \, B b c + A c^{2}\right )} x^{8} + \frac{1}{7} \,{\left (B b^{2} + 2 \, A b c\right )} x^{7} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.60969, size = 128, normalized size = 2.33 \begin{align*} \frac{1}{9} x^{9} c^{2} B + \frac{1}{4} x^{8} c b B + \frac{1}{8} x^{8} c^{2} A + \frac{1}{7} x^{7} b^{2} B + \frac{2}{7} x^{7} c b A + \frac{1}{6} x^{6} b^{2} A \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.070848, size = 54, normalized size = 0.98 \begin{align*} \frac{A b^{2} x^{6}}{6} + \frac{B c^{2} x^{9}}{9} + x^{8} \left (\frac{A c^{2}}{8} + \frac{B b c}{4}\right ) + x^{7} \left (\frac{2 A b c}{7} + \frac{B b^{2}}{7}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.14127, size = 72, normalized size = 1.31 \begin{align*} \frac{1}{9} \, B c^{2} x^{9} + \frac{1}{4} \, B b c x^{8} + \frac{1}{8} \, A c^{2} x^{8} + \frac{1}{7} \, B b^{2} x^{7} + \frac{2}{7} \, A b c x^{7} + \frac{1}{6} \, A b^{2} x^{6} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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