Optimal. Leaf size=30 \[ \frac{a^2 x^7}{7}+\frac{1}{4} a b x^8+\frac{b^2 x^9}{9} \]
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Rubi [A] time = 0.0314118, antiderivative size = 30, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.118, Rules used = {1584, 43} \[ \frac{a^2 x^7}{7}+\frac{1}{4} a b x^8+\frac{b^2 x^9}{9} \]
Antiderivative was successfully verified.
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Rule 1584
Rule 43
Rubi steps
\begin{align*} \int x^2 \left (a x^2+b x^3\right )^2 \, dx &=\int x^6 (a+b x)^2 \, dx\\ &=\int \left (a^2 x^6+2 a b x^7+b^2 x^8\right ) \, dx\\ &=\frac{a^2 x^7}{7}+\frac{1}{4} a b x^8+\frac{b^2 x^9}{9}\\ \end{align*}
Mathematica [A] time = 0.0023497, size = 30, normalized size = 1. \[ \frac{a^2 x^7}{7}+\frac{1}{4} a b x^8+\frac{b^2 x^9}{9} \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 25, normalized size = 0.8 \begin{align*}{\frac{{a}^{2}{x}^{7}}{7}}+{\frac{ab{x}^{8}}{4}}+{\frac{{b}^{2}{x}^{9}}{9}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.986406, size = 32, normalized size = 1.07 \begin{align*} \frac{1}{9} \, b^{2} x^{9} + \frac{1}{4} \, a b x^{8} + \frac{1}{7} \, a^{2} x^{7} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0.574869, size = 55, normalized size = 1.83 \begin{align*} \frac{1}{9} x^{9} b^{2} + \frac{1}{4} x^{8} b a + \frac{1}{7} x^{7} a^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.122817, size = 24, normalized size = 0.8 \begin{align*} \frac{a^{2} x^{7}}{7} + \frac{a b x^{8}}{4} + \frac{b^{2} x^{9}}{9} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.1433, size = 32, normalized size = 1.07 \begin{align*} \frac{1}{9} \, b^{2} x^{9} + \frac{1}{4} \, a b x^{8} + \frac{1}{7} \, a^{2} x^{7} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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