Optimal. Leaf size=21 \[ \frac{2}{7} a x^{7/2}+\frac{2}{15} c x^{15/2} \]
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Rubi [A] time = 0.0043785, antiderivative size = 21, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077, Rules used = {14} \[ \frac{2}{7} a x^{7/2}+\frac{2}{15} c x^{15/2} \]
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin{align*} \int x^{5/2} \left (a+c x^4\right ) \, dx &=\int \left (a x^{5/2}+c x^{13/2}\right ) \, dx\\ &=\frac{2}{7} a x^{7/2}+\frac{2}{15} c x^{15/2}\\ \end{align*}
Mathematica [A] time = 0.0047318, size = 21, normalized size = 1. \[ \frac{2}{7} a x^{7/2}+\frac{2}{15} c x^{15/2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 16, normalized size = 0.8 \begin{align*}{\frac{14\,c{x}^{4}+30\,a}{105}{x}^{{\frac{7}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.052, size = 18, normalized size = 0.86 \begin{align*} \frac{2}{15} \, c x^{\frac{15}{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 = 1.43881, size = 49, normalized size = 2.33 \begin{align*} \frac{2}{105} \,{\left (7 \, c x^{7} + 15 \, 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 = 7.04226, size = 19, normalized size = 0.9 \begin{align*} \frac{2 a x^{\frac{7}{2}}}{7} + \frac{2 c x^{\frac{15}{2}}}{15} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.09892, size = 18, normalized size = 0.86 \begin{align*} \frac{2}{15} \, c x^{\frac{15}{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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