Optimal. Leaf size=47 \[ \frac{1}{4} x^4 (a B+A b)+\frac{1}{3} a A x^3+\frac{1}{5} x^5 (A c+b B)+\frac{1}{6} B c x^6 \]
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Rubi [A] time = 0.04975, antiderivative size = 47, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.053, Rules used = {765} \[ \frac{1}{4} x^4 (a B+A b)+\frac{1}{3} a A x^3+\frac{1}{5} x^5 (A c+b B)+\frac{1}{6} B c x^6 \]
Antiderivative was successfully verified.
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Rule 765
Rubi steps
\begin{align*} \int x^2 (A+B x) \left (a+b x+c x^2\right ) \, dx &=\int \left (a A x^2+(A b+a B) x^3+(b B+A c) x^4+B c x^5\right ) \, dx\\ &=\frac{1}{3} a A x^3+\frac{1}{4} (A b+a B) x^4+\frac{1}{5} (b B+A c) x^5+\frac{1}{6} B c x^6\\ \end{align*}
Mathematica [A] time = 0.0136169, size = 47, normalized size = 1. \[ \frac{1}{4} x^4 (a B+A b)+\frac{1}{3} a A x^3+\frac{1}{5} x^5 (A c+b B)+\frac{1}{6} B c x^6 \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 40, normalized size = 0.9 \begin{align*}{\frac{aA{x}^{3}}{3}}+{\frac{ \left ( Ab+aB \right ){x}^{4}}{4}}+{\frac{ \left ( Ac+bB \right ){x}^{5}}{5}}+{\frac{Bc{x}^{6}}{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.07806, size = 53, normalized size = 1.13 \begin{align*} \frac{1}{6} \, B c x^{6} + \frac{1}{5} \,{\left (B b + A c\right )} x^{5} + \frac{1}{3} \, A a x^{3} + \frac{1}{4} \,{\left (B a + A b\right )} x^{4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.14623, size = 112, normalized size = 2.38 \begin{align*} \frac{1}{6} x^{6} c B + \frac{1}{5} x^{5} b B + \frac{1}{5} x^{5} c A + \frac{1}{4} x^{4} a B + \frac{1}{4} x^{4} b A + \frac{1}{3} x^{3} a A \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.07567, size = 42, normalized size = 0.89 \begin{align*} \frac{A a x^{3}}{3} + \frac{B c x^{6}}{6} + x^{5} \left (\frac{A c}{5} + \frac{B b}{5}\right ) + x^{4} \left (\frac{A b}{4} + \frac{B a}{4}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.26294, size = 58, normalized size = 1.23 \begin{align*} \frac{1}{6} \, B c x^{6} + \frac{1}{5} \, B b x^{5} + \frac{1}{5} \, A c x^{5} + \frac{1}{4} \, B a x^{4} + \frac{1}{4} \, A b x^{4} + \frac{1}{3} \, A a x^{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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