Optimal. Leaf size=21 \[ \frac{2}{5} a x^{5/2}+\frac{2}{7} b x^{7/2} \]
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Rubi [A] time = 0.0036704, 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} \[ \frac{2}{5} a x^{5/2}+\frac{2}{7} b x^{7/2} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int x^{3/2} (a+b x) \, dx &=\int \left (a x^{3/2}+b x^{5/2}\right ) \, dx\\ &=\frac{2}{5} a x^{5/2}+\frac{2}{7} b x^{7/2}\\ \end{align*}
Mathematica [A] time = 0.0041991, size = 17, normalized size = 0.81 \[ \frac{2}{35} x^{5/2} (7 a+5 b x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 14, normalized size = 0.7 \begin{align*}{\frac{10\,bx+14\,a}{35}{x}^{{\frac{5}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.05742, size = 18, normalized size = 0.86 \begin{align*} \frac{2}{7} \, b x^{\frac{7}{2}} + \frac{2}{5} \, a x^{\frac{5}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.59495, size = 46, normalized size = 2.19 \begin{align*} \frac{2}{35} \,{\left (5 \, b x^{3} + 7 \, a x^{2}\right )} \sqrt{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.846176, size = 19, normalized size = 0.9 \begin{align*} \frac{2 a x^{\frac{5}{2}}}{5} + \frac{2 b x^{\frac{7}{2}}}{7} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.18716, size = 18, normalized size = 0.86 \begin{align*} \frac{2}{7} \, b x^{\frac{7}{2}} + \frac{2}{5} \, a x^{\frac{5}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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