Optimal. Leaf size=17 \[ 2 \sqrt {x}+\frac {2 x^{5/2}}{5} \]
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Rubi [A]
time = 0.00, antiderivative size = 17, normalized size of antiderivative = 1.00, 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 = {14}
\begin {gather*} \frac {2 x^{5/2}}{5}+2 \sqrt {x} \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin {align*} \int \frac {1+x^2}{\sqrt {x}} \, dx &=\int \left (\frac {1}{\sqrt {x}}+x^{3/2}\right ) \, dx\\ &=2 \sqrt {x}+\frac {2 x^{5/2}}{5}\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 14, normalized size = 0.82 \begin {gather*} \frac {2}{5} \sqrt {x} \left (5+x^2\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.01, size = 12, normalized size = 0.71
method | result | size |
gosper | \(\frac {2 \sqrt {x}\, \left (x^{2}+5\right )}{5}\) | \(11\) |
risch | \(\frac {2 \sqrt {x}\, \left (x^{2}+5\right )}{5}\) | \(11\) |
derivativedivides | \(\frac {2 x^{\frac {5}{2}}}{5}+2 \sqrt {x}\) | \(12\) |
default | \(\frac {2 x^{\frac {5}{2}}}{5}+2 \sqrt {x}\) | \(12\) |
trager | \(\left (\frac {2 x^{2}}{5}+2\right ) \sqrt {x}\) | \(12\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 1.48, size = 11, normalized size = 0.65 \begin {gather*} \frac {2}{5} \, x^{\frac {5}{2}} + 2 \, \sqrt {x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.41, size = 10, normalized size = 0.59 \begin {gather*} \frac {2}{5} \, {\left (x^{2} + 5\right )} \sqrt {x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.07, size = 14, normalized size = 0.82 \begin {gather*} \frac {2 x^{\frac {5}{2}}}{5} + 2 \sqrt {x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.73, size = 11, normalized size = 0.65 \begin {gather*} \frac {2}{5} \, x^{\frac {5}{2}} + 2 \, \sqrt {x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.02, size = 10, normalized size = 0.59 \begin {gather*} \frac {2\,\sqrt {x}\,\left (x^2+5\right )}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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