Optimal. Leaf size=55 \[ \frac{2}{5} x^{5/2} (a B+A b)+\frac{2}{3} a A x^{3/2}+\frac{2}{7} x^{7/2} (A c+b B)+\frac{2}{9} B c x^{9/2} \]
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Rubi [A] time = 0.0242031, antiderivative size = 55, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 21, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.048, Rules used = {765} \[ \frac{2}{5} x^{5/2} (a B+A b)+\frac{2}{3} a A x^{3/2}+\frac{2}{7} x^{7/2} (A c+b B)+\frac{2}{9} B c x^{9/2} \]
Antiderivative was successfully verified.
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Rule 765
Rubi steps
\begin{align*} \int \sqrt{x} (A+B x) \left (a+b x+c x^2\right ) \, dx &=\int \left (a A \sqrt{x}+(A b+a B) x^{3/2}+(b B+A c) x^{5/2}+B c x^{7/2}\right ) \, dx\\ &=\frac{2}{3} a A x^{3/2}+\frac{2}{5} (A b+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 = 0.0456567, size = 47, normalized size = 0.85 \[ \frac{2}{315} x^{3/2} (21 a (5 A+3 B x)+x (9 A (7 b+5 c x)+5 B x (9 b+7 c x))) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 42, normalized size = 0.8 \begin{align*}{\frac{70\,Bc{x}^{3}+90\,Ac{x}^{2}+90\,Bb{x}^{2}+126\,Abx+126\,aBx+210\,aA}{315}{x}^{{\frac{3}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.986449, size = 53, normalized size = 0.96 \begin{align*} \frac{2}{9} \, B c x^{\frac{9}{2}} + \frac{2}{7} \,{\left (B b + A c\right )} x^{\frac{7}{2}} + \frac{2}{3} \, A a x^{\frac{3}{2}} + \frac{2}{5} \,{\left (B a + A b\right )} x^{\frac{5}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.22996, size = 111, normalized size = 2.02 \begin{align*} \frac{2}{315} \,{\left (35 \, B c x^{4} + 45 \,{\left (B b + A c\right )} x^{3} + 105 \, A a x + 63 \,{\left (B a + A b\right )} x^{2}\right )} \sqrt{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 3.3018, size = 53, normalized size = 0.96 \begin{align*} \frac{2 A a x^{\frac{3}{2}}}{3} + \frac{2 B c x^{\frac{9}{2}}}{9} + \frac{2 x^{\frac{7}{2}} \left (A c + B b\right )}{7} + \frac{2 x^{\frac{5}{2}} \left (A b + B a\right )}{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.14287, size = 58, normalized size = 1.05 \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} \, B a x^{\frac{5}{2}} + \frac{2}{5} \, A b x^{\frac{5}{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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