Optimal. Leaf size=20 \[ \frac{4 \left (x^{5/2}+x\right )^{3/2}}{9 x^{3/2}} \]
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Rubi [A] time = 0.003314, antiderivative size = 20, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091, Rules used = {2000} \[ \frac{4 \left (x^{5/2}+x\right )^{3/2}}{9 x^{3/2}} \]
Antiderivative was successfully verified.
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Rule 2000
Rubi steps
\begin{align*} \int \sqrt{x+x^{5/2}} \, dx &=\frac{4 \left (x+x^{5/2}\right )^{3/2}}{9 x^{3/2}}\\ \end{align*}
Mathematica [A] time = 0.0099119, size = 20, normalized size = 1. \[ \frac{4 \left (x^{5/2}+x\right )^{3/2}}{9 x^{3/2}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.009, size = 18, normalized size = 0.9 \begin{align*}{\frac{4}{9}\sqrt{x+{x}^{{\frac{5}{2}}}} \left ( 1+{x}^{{\frac{3}{2}}} \right ){\frac{1}{\sqrt{x}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \sqrt{x^{\frac{5}{2}} + x}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.1921, size = 55, normalized size = 2.75 \begin{align*} \frac{4 \, \sqrt{x^{\frac{5}{2}} + x}{\left (x^{2} + \sqrt{x}\right )}}{9 \, x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \sqrt{x^{\frac{5}{2}} + x}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.27574, size = 15, normalized size = 0.75 \begin{align*} \frac{4}{9} \,{\left (x^{\frac{3}{2}} + 1\right )}^{\frac{3}{2}} - \frac{4}{9} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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