Optimal. Leaf size=19 \[ 2 a \sqrt{x}+\frac{2}{3} b x^{3/2} \]
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Rubi [A] time = 0.0036023, antiderivative size = 19, normalized size of antiderivative = 1., 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} \[ 2 a \sqrt{x}+\frac{2}{3} b x^{3/2} \]
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*}
Mathematica [A] time = 0.0047361, size = 16, normalized size = 0.84 \[ \frac{2}{3} \sqrt{x} (3 a+b x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 13, normalized size = 0.7 \begin{align*}{\frac{2\,bx+6\,a}{3}\sqrt{x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.989671, size = 18, normalized size = 0.95 \begin{align*} \frac{2}{3} \, b x^{\frac{3}{2}} + 2 \, a \sqrt{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.50122, size = 34, normalized size = 1.79 \begin{align*} \frac{2}{3} \,{\left (b x + 3 \, a\right )} \sqrt{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.17349, size = 17, normalized size = 0.89 \begin{align*} 2 a \sqrt{x} + \frac{2 b x^{\frac{3}{2}}}{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.2328, size = 18, normalized size = 0.95 \begin{align*} \frac{2}{3} \, b x^{\frac{3}{2}} + 2 \, a \sqrt{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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