Optimal. Leaf size=24 \[ \frac {2 x^{3/2}}{3}-\frac {x^2}{4}+4 \sqrt {x} \]
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Rubi [A] time = 0.00, antiderivative size = 24, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 0, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} -\frac {x^2}{4}+\frac {2 x^{3/2}}{3}+4 \sqrt {x} \end {gather*}
Antiderivative was successfully verified.
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Rubi steps
\begin {align*} \int \left (\frac {2}{\sqrt {x}}+\sqrt {x}-\frac {x}{2}\right ) \, dx &=4 \sqrt {x}+\frac {2 x^{3/2}}{3}-\frac {x^2}{4}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 24, normalized size = 1.00 \begin {gather*} \frac {2 x^{3/2}}{3}-\frac {x^2}{4}+4 \sqrt {x} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.01, size = 24, normalized size = 1.00 \begin {gather*} \frac {1}{12} \left (8 x^{3/2}-3 x^2+48 \sqrt {x}\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.19, size = 14, normalized size = 0.58 \begin {gather*} -\frac {1}{4} \, x^{2} + \frac {2}{3} \, {\left (x + 6\right )} \sqrt {x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.09, size = 16, normalized size = 0.67 \begin {gather*} -\frac {1}{4} \, x^{2} + \frac {2}{3} \, x^{\frac {3}{2}} + 4 \, \sqrt {x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 17, normalized size = 0.71 \begin {gather*} -\frac {x^{2}}{4}+\frac {2 x^{\frac {3}{2}}}{3}+4 \sqrt {x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.05, size = 16, normalized size = 0.67 \begin {gather*} -\frac {1}{4} \, x^{2} + \frac {2}{3} \, x^{\frac {3}{2}} + 4 \, \sqrt {x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 15, normalized size = 0.62 \begin {gather*} \frac {\sqrt {x}\,\left (8\,x-3\,x^{3/2}+48\right )}{12} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.06, size = 19, normalized size = 0.79 \begin {gather*} \frac {2 x^{\frac {3}{2}}}{3} + 4 \sqrt {x} - \frac {x^{2}}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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