Optimal. Leaf size=30 \[ \frac{a^2 x^3}{3}+\frac{2}{5} a b x^5+\frac{b^2 x^7}{7} \]
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Rubi [A] time = 0.0095821, antiderivative size = 30, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077, Rules used = {270} \[ \frac{a^2 x^3}{3}+\frac{2}{5} a b x^5+\frac{b^2 x^7}{7} \]
Antiderivative was successfully verified.
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Rule 270
Rubi steps
\begin{align*} \int x^2 \left (a+b x^2\right )^2 \, dx &=\int \left (a^2 x^2+2 a b x^4+b^2 x^6\right ) \, dx\\ &=\frac{a^2 x^3}{3}+\frac{2}{5} a b x^5+\frac{b^2 x^7}{7}\\ \end{align*}
Mathematica [A] time = 0.0006403, size = 30, normalized size = 1. \[ \frac{a^2 x^3}{3}+\frac{2}{5} a b x^5+\frac{b^2 x^7}{7} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 25, normalized size = 0.8 \begin{align*}{\frac{{a}^{2}{x}^{3}}{3}}+{\frac{2\,ab{x}^{5}}{5}}+{\frac{{b}^{2}{x}^{7}}{7}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.86725, size = 32, normalized size = 1.07 \begin{align*} \frac{1}{7} \, b^{2} x^{7} + \frac{2}{5} \, a b x^{5} + \frac{1}{3} \, a^{2} x^{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.28939, size = 55, normalized size = 1.83 \begin{align*} \frac{1}{7} x^{7} b^{2} + \frac{2}{5} x^{5} b a + \frac{1}{3} x^{3} a^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.058723, size = 26, normalized size = 0.87 \begin{align*} \frac{a^{2} x^{3}}{3} + \frac{2 a b x^{5}}{5} + \frac{b^{2} x^{7}}{7} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.26912, size = 32, normalized size = 1.07 \begin{align*} \frac{1}{7} \, b^{2} x^{7} + \frac{2}{5} \, a b x^{5} + \frac{1}{3} \, a^{2} x^{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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