Optimal. Leaf size=39 \[ \frac{2}{15} x^{15/2} (a B+A b)+\frac{2}{9} a A x^{9/2}+\frac{2}{21} b B x^{21/2} \]
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Rubi [A] time = 0.0154295, antiderivative size = 39, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05, Rules used = {448} \[ \frac{2}{15} x^{15/2} (a B+A b)+\frac{2}{9} a A x^{9/2}+\frac{2}{21} b B x^{21/2} \]
Antiderivative was successfully verified.
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Rule 448
Rubi steps
\begin{align*} \int x^{7/2} \left (a+b x^3\right ) \left (A+B x^3\right ) \, dx &=\int \left (a A x^{7/2}+(A b+a B) x^{13/2}+b B x^{19/2}\right ) \, dx\\ &=\frac{2}{9} a A x^{9/2}+\frac{2}{15} (A b+a B) x^{15/2}+\frac{2}{21} b B x^{21/2}\\ \end{align*}
Mathematica [A] time = 0.0150327, size = 33, normalized size = 0.85 \[ \frac{2}{315} x^{9/2} \left (21 x^3 (a B+A b)+35 a A+15 b B x^6\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 32, normalized size = 0.8 \begin{align*}{\frac{30\,bB{x}^{6}+42\,A{x}^{3}b+42\,B{x}^{3}a+70\,Aa}{315}{x}^{{\frac{9}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.956209, size = 36, normalized size = 0.92 \begin{align*} \frac{2}{21} \, B b x^{\frac{21}{2}} + \frac{2}{15} \,{\left (B a + A b\right )} x^{\frac{15}{2}} + \frac{2}{9} \, A a x^{\frac{9}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.50193, size = 85, normalized size = 2.18 \begin{align*} \frac{2}{315} \,{\left (15 \, B b x^{10} + 21 \,{\left (B a + A b\right )} x^{7} + 35 \, A a x^{4}\right )} \sqrt{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 35.8397, size = 46, normalized size = 1.18 \begin{align*} \frac{2 A a x^{\frac{9}{2}}}{9} + \frac{2 A b x^{\frac{15}{2}}}{15} + \frac{2 B a x^{\frac{15}{2}}}{15} + \frac{2 B b x^{\frac{21}{2}}}{21} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.11723, size = 39, normalized size = 1. \begin{align*} \frac{2}{21} \, B b x^{\frac{21}{2}} + \frac{2}{15} \, B a x^{\frac{15}{2}} + \frac{2}{15} \, A b x^{\frac{15}{2}} + \frac{2}{9} \, A a x^{\frac{9}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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