Optimal. Leaf size=75 \[ \frac{1}{6} b^2 x^6 (3 A c+b B)+\frac{1}{5} A b^3 x^5+\frac{1}{8} c^2 x^8 (A c+3 b B)+\frac{3}{7} b c x^7 (A c+b B)+\frac{1}{9} B c^3 x^9 \]
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Rubi [A] time = 0.0573346, antiderivative size = 75, 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} \[ \frac{1}{6} b^2 x^6 (3 A c+b B)+\frac{1}{5} A b^3 x^5+\frac{1}{8} c^2 x^8 (A c+3 b B)+\frac{3}{7} b c x^7 (A c+b B)+\frac{1}{9} B c^3 x^9 \]
Antiderivative was successfully verified.
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Rule 765
Rubi steps
\begin{align*} \int x (A+B x) \left (b x+c x^2\right )^3 \, dx &=\int \left (A b^3 x^4+b^2 (b B+3 A c) x^5+3 b c (b B+A c) x^6+c^2 (3 b B+A c) x^7+B c^3 x^8\right ) \, dx\\ &=\frac{1}{5} A b^3 x^5+\frac{1}{6} b^2 (b B+3 A c) x^6+\frac{3}{7} b c (b B+A c) x^7+\frac{1}{8} c^2 (3 b B+A c) x^8+\frac{1}{9} B c^3 x^9\\ \end{align*}
Mathematica [A] time = 0.0120437, size = 75, normalized size = 1. \[ \frac{1}{6} b^2 x^6 (3 A c+b B)+\frac{1}{5} A b^3 x^5+\frac{1}{8} c^2 x^8 (A c+3 b B)+\frac{3}{7} b c x^7 (A c+b B)+\frac{1}{9} B c^3 x^9 \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 76, normalized size = 1. \begin{align*}{\frac{B{c}^{3}{x}^{9}}{9}}+{\frac{ \left ( A{c}^{3}+3\,Bb{c}^{2} \right ){x}^{8}}{8}}+{\frac{ \left ( 3\,Ab{c}^{2}+3\,B{b}^{2}c \right ){x}^{7}}{7}}+{\frac{ \left ( 3\,A{b}^{2}c+{b}^{3}B \right ){x}^{6}}{6}}+{\frac{A{b}^{3}{x}^{5}}{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.1048, size = 99, normalized size = 1.32 \begin{align*} \frac{1}{9} \, B c^{3} x^{9} + \frac{1}{5} \, A b^{3} x^{5} + \frac{1}{8} \,{\left (3 \, B b c^{2} + A c^{3}\right )} x^{8} + \frac{3}{7} \,{\left (B b^{2} c + A b c^{2}\right )} x^{7} + \frac{1}{6} \,{\left (B b^{3} + 3 \, A b^{2} c\right )} x^{6} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.49758, size = 182, normalized size = 2.43 \begin{align*} \frac{1}{9} x^{9} c^{3} B + \frac{3}{8} x^{8} c^{2} b B + \frac{1}{8} x^{8} c^{3} A + \frac{3}{7} x^{7} c b^{2} B + \frac{3}{7} x^{7} c^{2} b A + \frac{1}{6} x^{6} b^{3} B + \frac{1}{2} x^{6} c b^{2} A + \frac{1}{5} x^{5} b^{3} A \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.140414, size = 82, normalized size = 1.09 \begin{align*} \frac{A b^{3} x^{5}}{5} + \frac{B c^{3} x^{9}}{9} + x^{8} \left (\frac{A c^{3}}{8} + \frac{3 B b c^{2}}{8}\right ) + x^{7} \left (\frac{3 A b c^{2}}{7} + \frac{3 B b^{2} c}{7}\right ) + x^{6} \left (\frac{A b^{2} c}{2} + \frac{B b^{3}}{6}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.15231, size = 104, normalized size = 1.39 \begin{align*} \frac{1}{9} \, B c^{3} x^{9} + \frac{3}{8} \, B b c^{2} x^{8} + \frac{1}{8} \, A c^{3} x^{8} + \frac{3}{7} \, B b^{2} c x^{7} + \frac{3}{7} \, A b c^{2} x^{7} + \frac{1}{6} \, B b^{3} x^{6} + \frac{1}{2} \, A b^{2} c x^{6} + \frac{1}{5} \, A b^{3} x^{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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