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 {x^2}{2}+\frac {2 x^{3/2}}{3} \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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IntegrateAlgebraic [A] time = 0.01, size = 18, normalized size = 1.06 \begin {gather*} \frac {1}{6} \left (3 \sqrt {x}+4\right ) x^{3/2} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.43, 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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giac [A] time = 0.35, 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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maple [A] time = 0.00, size = 12, normalized size = 0.71 \begin {gather*} \frac {x^{2}}{2}+\frac {2 x^{\frac {3}{2}}}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.73, 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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mupad [B] time = 0.02, 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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sympy [A] time = 0.14, 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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