Optimal. Leaf size=55 \[ \frac{1}{3} a c x^3+\frac{1}{4} a d x^4+\frac{1}{5} a e x^5+\frac{1}{6} b c x^6+\frac{1}{7} b d x^7+\frac{1}{8} b e x^8 \]
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Rubi [A] time = 0.0554037, antiderivative size = 55, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 21, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.048, Rules used = {1628} \[ \frac{1}{3} a c x^3+\frac{1}{4} a d x^4+\frac{1}{5} a e x^5+\frac{1}{6} b c x^6+\frac{1}{7} b d x^7+\frac{1}{8} b e x^8 \]
Antiderivative was successfully verified.
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Rule 1628
Rubi steps
\begin{align*} \int x^2 \left (c+d x+e x^2\right ) \left (a+b x^3\right ) \, dx &=\int \left (a c x^2+a d x^3+a e x^4+b c x^5+b d x^6+b e x^7\right ) \, dx\\ &=\frac{1}{3} a c x^3+\frac{1}{4} a d x^4+\frac{1}{5} a e x^5+\frac{1}{6} b c x^6+\frac{1}{7} b d x^7+\frac{1}{8} b e x^8\\ \end{align*}
Mathematica [A] time = 0.0032462, size = 55, normalized size = 1. \[ \frac{1}{3} a c x^3+\frac{1}{4} a d x^4+\frac{1}{5} a e x^5+\frac{1}{6} b c x^6+\frac{1}{7} b d x^7+\frac{1}{8} b e x^8 \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 44, normalized size = 0.8 \begin{align*}{\frac{ac{x}^{3}}{3}}+{\frac{ad{x}^{4}}{4}}+{\frac{ae{x}^{5}}{5}}+{\frac{bc{x}^{6}}{6}}+{\frac{bd{x}^{7}}{7}}+{\frac{be{x}^{8}}{8}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.928077, size = 58, normalized size = 1.05 \begin{align*} \frac{1}{8} \, b e x^{8} + \frac{1}{7} \, b d x^{7} + \frac{1}{6} \, b c x^{6} + \frac{1}{5} \, a e x^{5} + \frac{1}{4} \, a d x^{4} + \frac{1}{3} \, a c x^{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.29515, size = 112, normalized size = 2.04 \begin{align*} \frac{1}{8} x^{8} e b + \frac{1}{7} x^{7} d b + \frac{1}{6} x^{6} c b + \frac{1}{5} x^{5} e a + \frac{1}{4} x^{4} d a + \frac{1}{3} x^{3} c a \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.063593, size = 49, normalized size = 0.89 \begin{align*} \frac{a c x^{3}}{3} + \frac{a d x^{4}}{4} + \frac{a e x^{5}}{5} + \frac{b c x^{6}}{6} + \frac{b d x^{7}}{7} + \frac{b e x^{8}}{8} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.06384, size = 61, normalized size = 1.11 \begin{align*} \frac{1}{8} \, b x^{8} e + \frac{1}{7} \, b d x^{7} + \frac{1}{6} \, b c x^{6} + \frac{1}{5} \, a x^{5} e + \frac{1}{4} \, a d x^{4} + \frac{1}{3} \, a c x^{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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