Optimal. Leaf size=39 \[ \frac{2}{7} x^{7/2} (A c+b B)+\frac{2}{5} A b x^{5/2}+\frac{2}{9} B c x^{9/2} \]
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Rubi [A] time = 0.0152832, 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 = {765} \[ \frac{2}{7} x^{7/2} (A c+b B)+\frac{2}{5} A b x^{5/2}+\frac{2}{9} B c x^{9/2} \]
Antiderivative was successfully verified.
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Rule 765
Rubi steps
\begin{align*} \int \sqrt{x} (A+B x) \left (b x+c x^2\right ) \, dx &=\int \left (A b x^{3/2}+(b B+A c) x^{5/2}+B c x^{7/2}\right ) \, dx\\ &=\frac{2}{5} A b x^{5/2}+\frac{2}{7} (b B+A c) x^{7/2}+\frac{2}{9} B c x^{9/2}\\ \end{align*}
Mathematica [A] time = 0.0112639, size = 33, normalized size = 0.85 \[ \frac{2}{315} x^{5/2} (9 A (7 b+5 c x)+5 B x (9 b+7 c x)) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 28, normalized size = 0.7 \begin{align*}{\frac{70\,Bc{x}^{2}+90\,Acx+90\,bBx+126\,Ab}{315}{x}^{{\frac{5}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.06012, size = 36, normalized size = 0.92 \begin{align*} \frac{2}{9} \, B c x^{\frac{9}{2}} + \frac{2}{5} \, A b x^{\frac{5}{2}} + \frac{2}{7} \,{\left (B b + A c\right )} x^{\frac{7}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.7753, size = 84, normalized size = 2.15 \begin{align*} \frac{2}{315} \,{\left (35 \, B c x^{4} + 63 \, A b x^{2} + 45 \,{\left (B b + A c\right )} x^{3}\right )} \sqrt{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 1.90773, size = 37, normalized size = 0.95 \begin{align*} \frac{2 A b x^{\frac{5}{2}}}{5} + \frac{2 B c x^{\frac{9}{2}}}{9} + \frac{2 x^{\frac{7}{2}} \left (A c + B b\right )}{7} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.12371, size = 39, normalized size = 1. \begin{align*} \frac{2}{9} \, B c x^{\frac{9}{2}} + \frac{2}{7} \, B b x^{\frac{7}{2}} + \frac{2}{7} \, A c x^{\frac{7}{2}} + \frac{2}{5} \, A b x^{\frac{5}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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