Optimal. Leaf size=19 \[ \frac {2 x^{3/2}}{3}+\frac {2 x^{7/2}}{7} \]
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Rubi [A]
time = 0.00, antiderivative size = 19, 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^{7/2}}{7}+\frac {2 x^{3/2}}{3} \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin {align*} \int \sqrt {x} \left (1+x^2\right ) \, dx &=\int \left (\sqrt {x}+x^{5/2}\right ) \, dx\\ &=\frac {2 x^{3/2}}{3}+\frac {2 x^{7/2}}{7}\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 16, normalized size = 0.84 \begin {gather*} \frac {2}{21} x^{3/2} \left (7+3 x^2\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.01, size = 12, normalized size = 0.63
method | result | size |
derivativedivides | \(\frac {2 x^{\frac {3}{2}}}{3}+\frac {2 x^{\frac {7}{2}}}{7}\) | \(12\) |
default | \(\frac {2 x^{\frac {3}{2}}}{3}+\frac {2 x^{\frac {7}{2}}}{7}\) | \(12\) |
gosper | \(\frac {2 x^{\frac {3}{2}} \left (3 x^{2}+7\right )}{21}\) | \(13\) |
trager | \(\frac {2 x^{\frac {3}{2}} \left (3 x^{2}+7\right )}{21}\) | \(13\) |
risch | \(\frac {2 x^{\frac {3}{2}} \left (3 x^{2}+7\right )}{21}\) | \(13\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 3.38, size = 11, normalized size = 0.58 \begin {gather*} \frac {2}{7} \, x^{\frac {7}{2}} + \frac {2}{3} \, x^{\frac {3}{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.71, size = 14, normalized size = 0.74 \begin {gather*} \frac {2}{21} \, {\left (3 \, x^{3} + 7 \, x\right )} \sqrt {x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.51, size = 15, normalized size = 0.79 \begin {gather*} \frac {2 x^{\frac {7}{2}}}{7} + \frac {2 x^{\frac {3}{2}}}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.45, size = 11, normalized size = 0.58 \begin {gather*} \frac {2}{7} \, x^{\frac {7}{2}} + \frac {2}{3} \, x^{\frac {3}{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.02, size = 12, normalized size = 0.63 \begin {gather*} \frac {2\,x^{3/2}\,\left (3\,x^2+7\right )}{21} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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