Optimal. Leaf size=19 \[ 2 a \sqrt {x}+\frac {2}{3} b x^{3/2} \]
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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 = {43} \begin {gather*} 2 a \sqrt {x}+\frac {2}{3} b x^{3/2} \end {gather*}
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin {align*} \int \frac {a+b x}{\sqrt {x}} \, dx &=\int \left (\frac {a}{\sqrt {x}}+b \sqrt {x}\right ) \, dx\\ &=2 a \sqrt {x}+\frac {2}{3} b x^{3/2}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 16, normalized size = 0.84 \begin {gather*} \frac {2}{3} \sqrt {x} (3 a+b x) \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.01, size = 20, normalized size = 1.05 \begin {gather*} \frac {2}{3} \left (3 a \sqrt {x}+b x^{3/2}\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.92, size = 12, normalized size = 0.63 \begin {gather*} \frac {2}{3} \, {\left (b x + 3 \, a\right )} \sqrt {x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.08, size = 13, normalized size = 0.68 \begin {gather*} \frac {2}{3} \, b x^{\frac {3}{2}} + 2 \, a \sqrt {x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 13, normalized size = 0.68 \begin {gather*} \frac {2 \left (b x +3 a \right ) \sqrt {x}}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.32, size = 13, normalized size = 0.68 \begin {gather*} \frac {2}{3} \, b x^{\frac {3}{2}} + 2 \, a \sqrt {x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 12, normalized size = 0.63 \begin {gather*} \frac {2\,\sqrt {x}\,\left (3\,a+b\,x\right )}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.16, size = 17, normalized size = 0.89 \begin {gather*} 2 a \sqrt {x} + \frac {2 b x^{\frac {3}{2}}}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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