Optimal. Leaf size=33 \[ \frac{1}{5} x^5 (a B+A b)+\frac{1}{3} a A x^3+\frac{1}{7} b B x^7 \]
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Rubi [A] time = 0.0195923, antiderivative size = 33, 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 = {448} \[ \frac{1}{5} x^5 (a B+A b)+\frac{1}{3} a A x^3+\frac{1}{7} b B x^7 \]
Antiderivative was successfully verified.
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Rule 448
Rubi steps
\begin{align*} \int x^2 \left (a+b x^2\right ) \left (A+B x^2\right ) \, dx &=\int \left (a A x^2+(A b+a B) x^4+b B x^6\right ) \, dx\\ &=\frac{1}{3} a A x^3+\frac{1}{5} (A b+a B) x^5+\frac{1}{7} b B x^7\\ \end{align*}
Mathematica [A] time = 0.0055308, size = 33, normalized size = 1. \[ \frac{1}{5} x^5 (a B+A b)+\frac{1}{3} a A x^3+\frac{1}{7} b B x^7 \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 28, normalized size = 0.9 \begin{align*}{\frac{aA{x}^{3}}{3}}+{\frac{ \left ( Ab+Ba \right ){x}^{5}}{5}}+{\frac{bB{x}^{7}}{7}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.991062, size = 36, normalized size = 1.09 \begin{align*} \frac{1}{7} \, B b x^{7} + \frac{1}{5} \,{\left (B a + A b\right )} x^{5} + \frac{1}{3} \, A a x^{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.24705, size = 74, normalized size = 2.24 \begin{align*} \frac{1}{7} x^{7} b B + \frac{1}{5} x^{5} a B + \frac{1}{5} x^{5} 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 = 0.057648, size = 29, normalized size = 0.88 \begin{align*} \frac{A a x^{3}}{3} + \frac{B b x^{7}}{7} + x^{5} \left (\frac{A b}{5} + \frac{B a}{5}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.12168, size = 39, normalized size = 1.18 \begin{align*} \frac{1}{7} \, B b x^{7} + \frac{1}{5} \, B a x^{5} + \frac{1}{5} \, A b x^{5} + \frac{1}{3} \, A a x^{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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