Optimal. Leaf size=39 \[ \frac{2}{9} x^{9/2} (a B+A b)+\frac{2}{3} a A x^{3/2}+\frac{2}{15} b B x^{15/2} \]
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Rubi [A] time = 0.0160388, 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} \[ \frac{2}{9} x^{9/2} (a B+A b)+\frac{2}{3} a A x^{3/2}+\frac{2}{15} b B x^{15/2} \]
Antiderivative was successfully verified.
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Rule 448
Rubi steps
\begin{align*} \int \sqrt{x} \left (a+b x^3\right ) \left (A+B x^3\right ) \, dx &=\int \left (a A \sqrt{x}+(A b+a B) x^{7/2}+b B x^{13/2}\right ) \, dx\\ &=\frac{2}{3} a A x^{3/2}+\frac{2}{9} (A b+a B) x^{9/2}+\frac{2}{15} b B x^{15/2}\\ \end{align*}
Mathematica [A] time = 0.0131893, size = 33, normalized size = 0.85 \[ \frac{2}{45} x^{3/2} \left (5 x^3 (a B+A b)+15 a A+3 b B x^6\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 32, normalized size = 0.8 \begin{align*}{\frac{6\,bB{x}^{6}+10\,A{x}^{3}b+10\,B{x}^{3}a+30\,Aa}{45}{x}^{{\frac{3}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.960754, size = 36, normalized size = 0.92 \begin{align*} \frac{2}{15} \, B b x^{\frac{15}{2}} + \frac{2}{9} \,{\left (B a + A b\right )} x^{\frac{9}{2}} + \frac{2}{3} \, A a x^{\frac{3}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.69488, size = 77, normalized size = 1.97 \begin{align*} \frac{2}{45} \,{\left (3 \, B b x^{7} + 5 \,{\left (B a + A b\right )} x^{4} + 15 \, A a x\right )} \sqrt{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 2.52409, size = 46, normalized size = 1.18 \begin{align*} \frac{2 A a x^{\frac{3}{2}}}{3} + \frac{2 A b x^{\frac{9}{2}}}{9} + \frac{2 B a x^{\frac{9}{2}}}{9} + \frac{2 B b x^{\frac{15}{2}}}{15} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.09066, size = 39, normalized size = 1. \begin{align*} \frac{2}{15} \, B b x^{\frac{15}{2}} + \frac{2}{9} \, B a x^{\frac{9}{2}} + \frac{2}{9} \, A b x^{\frac{9}{2}} + \frac{2}{3} \, A a x^{\frac{3}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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