Optimal. Leaf size=37 \[ \frac{2}{7} x^{7/2} (a B+A b)+2 a A \sqrt{x}+\frac{2}{13} b B x^{13/2} \]
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Rubi [A] time = 0.0148383, antiderivative size = 37, 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} \[ \frac{2}{7} x^{7/2} (a B+A b)+2 a A \sqrt{x}+\frac{2}{13} b B x^{13/2} \]
Antiderivative was successfully verified.
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Rule 448
Rubi steps
\begin{align*} \int \frac{\left (a+b x^3\right ) \left (A+B x^3\right )}{\sqrt{x}} \, dx &=\int \left (\frac{a A}{\sqrt{x}}+(A b+a B) x^{5/2}+b B x^{11/2}\right ) \, dx\\ &=2 a A \sqrt{x}+\frac{2}{7} (A b+a B) x^{7/2}+\frac{2}{13} b B x^{13/2}\\ \end{align*}
Mathematica [A] time = 0.0134174, size = 33, normalized size = 0.89 \[ \frac{2}{91} \sqrt{x} \left (13 x^3 (a B+A b)+91 a A+7 b B x^6\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 32, normalized size = 0.9 \begin{align*}{\frac{14\,bB{x}^{6}+26\,A{x}^{3}b+26\,B{x}^{3}a+182\,Aa}{91}\sqrt{x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.947247, size = 36, normalized size = 0.97 \begin{align*} \frac{2}{13} \, B b x^{\frac{13}{2}} + \frac{2}{7} \,{\left (B a + A b\right )} x^{\frac{7}{2}} + 2 \, A a \sqrt{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.70982, size = 76, normalized size = 2.05 \begin{align*} \frac{2}{91} \,{\left (7 \, B b x^{6} + 13 \,{\left (B a + A b\right )} x^{3} + 91 \, A a\right )} \sqrt{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 2.07037, size = 44, normalized size = 1.19 \begin{align*} 2 A a \sqrt{x} + \frac{2 A b x^{\frac{7}{2}}}{7} + \frac{2 B a x^{\frac{7}{2}}}{7} + \frac{2 B b x^{\frac{13}{2}}}{13} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.10385, size = 39, normalized size = 1.05 \begin{align*} \frac{2}{13} \, B b x^{\frac{13}{2}} + \frac{2}{7} \, B a x^{\frac{7}{2}} + \frac{2}{7} \, A b x^{\frac{7}{2}} + 2 \, A a \sqrt{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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