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 = 0.00, antiderivative size = 20, normalized size of antiderivative = 1.00, 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} \begin {gather*} \frac {4 \left (x^{5/2}+x\right )^{3/2}}{9 x^{3/2}} \end {gather*}
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*}
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Mathematica [A] time = 0.01, size = 20, normalized size = 1.00 \begin {gather*} \frac {4 \left (x^{5/2}+x\right )^{3/2}}{9 x^{3/2}} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.04, size = 20, normalized size = 1.00 \begin {gather*} \frac {4 \left (x^{5/2}+x\right )^{3/2}}{9 x^{3/2}} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.43, size = 19, normalized size = 0.95 \begin {gather*} \frac {4 \, \sqrt {x^{\frac {5}{2}} + x} {\left (x^{2} + \sqrt {x}\right )}}{9 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 11, normalized size = 0.55 \begin {gather*} \frac {4}{9} \, {\left (x^{\frac {3}{2}} + 1\right )}^{\frac {3}{2}} - \frac {4}{9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 18, normalized size = 0.90 \begin {gather*} \frac {4 \sqrt {x^{\frac {5}{2}}+x}\, \left (x^{\frac {3}{2}}+1\right )}{9 \sqrt {x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \sqrt {x^{\frac {5}{2}} + x}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.32, size = 27, normalized size = 1.35 \begin {gather*} \frac {2\,x\,\sqrt {x+x^{5/2}}\,{{}}_2{\mathrm {F}}_1\left (-\frac {1}{2},1;\ 2;\ -x^{3/2}\right )}{3\,\sqrt {x^{3/2}+1}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \sqrt {x^{\frac {5}{2}} + x}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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