Optimal. Leaf size=17 \[ \frac {2 x^{3/2}}{3}+\frac {x^2}{2} \]
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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 = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {14}
\begin {gather*} \frac {2 x^{3/2}}{3}+\frac {x^2}{2} \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin {align*} \int \left (1+\sqrt {x}\right ) \sqrt {x} \, dx &=\int \left (\sqrt {x}+x\right ) \, dx\\ &=\frac {2 x^{3/2}}{3}+\frac {x^2}{2}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 17, normalized size = 1.00 \begin {gather*} \frac {2 x^{3/2}}{3}+\frac {x^2}{2} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.01, size = 12, normalized size = 0.71
method | result | size |
derivativedivides | \(\frac {2 x^{\frac {3}{2}}}{3}+\frac {x^{2}}{2}\) | \(12\) |
default | \(\frac {2 x^{\frac {3}{2}}}{3}+\frac {x^{2}}{2}\) | \(12\) |
trager | \(\frac {\left (1+x \right ) \left (-1+x \right )}{2}+\frac {2 x^{\frac {3}{2}}}{3}\) | \(15\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 26 vs.
\(2 (11) = 22\).
time = 1.91, size = 26, normalized size = 1.53 \begin {gather*} \frac {1}{2} \, {\left (\sqrt {x} + 1\right )}^{4} - \frac {4}{3} \, {\left (\sqrt {x} + 1\right )}^{3} + {\left (\sqrt {x} + 1\right )}^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.52, size = 11, normalized size = 0.65 \begin {gather*} \frac {1}{2} \, x^{2} + \frac {2}{3} \, x^{\frac {3}{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 12, normalized size = 0.71 \begin {gather*} \frac {2 x^{\frac {3}{2}}}{3} + \frac {x^{2}}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.49, size = 11, normalized size = 0.65 \begin {gather*} \frac {1}{2} \, x^{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 = 0.03, size = 11, normalized size = 0.65 \begin {gather*} \frac {x^2}{2}+\frac {2\,x^{3/2}}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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