Optimal. Leaf size=21 \[ \frac{2}{7} a x^{7/2}+\frac{2}{9} b x^{9/2} \]
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Rubi [A] time = 0.0040576, antiderivative size = 21, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091, Rules used = {43} \[ \frac{2}{7} a x^{7/2}+\frac{2}{9} b x^{9/2} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int x^{5/2} (a+b x) \, dx &=\int \left (a x^{5/2}+b x^{7/2}\right ) \, dx\\ &=\frac{2}{7} a x^{7/2}+\frac{2}{9} b x^{9/2}\\ \end{align*}
Mathematica [A] time = 0.0051564, size = 17, normalized size = 0.81 \[ \frac{2}{63} x^{7/2} (9 a+7 b x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 14, normalized size = 0.7 \begin{align*}{\frac{14\,bx+18\,a}{63}{x}^{{\frac{7}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.997184, size = 18, normalized size = 0.86 \begin{align*} \frac{2}{9} \, b x^{\frac{9}{2}} + \frac{2}{7} \, a x^{\frac{7}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.50522, size = 46, normalized size = 2.19 \begin{align*} \frac{2}{63} \,{\left (7 \, b x^{4} + 9 \, a x^{3}\right )} \sqrt{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 2.3505, size = 19, normalized size = 0.9 \begin{align*} \frac{2 a x^{\frac{7}{2}}}{7} + \frac{2 b x^{\frac{9}{2}}}{9} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.26386, size = 18, normalized size = 0.86 \begin{align*} \frac{2}{9} \, b x^{\frac{9}{2}} + \frac{2}{7} \, a x^{\frac{7}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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