Optimal. Leaf size=14 \[ a x+\frac{2}{3} b x^{3/2} \]
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Rubi [A] time = 0.0022963, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 0, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ a x+\frac{2}{3} b x^{3/2} \]
Antiderivative was successfully verified.
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Rubi steps
\begin{align*} \int \left (a+b \sqrt{x}\right ) \, dx &=a x+\frac{2}{3} b x^{3/2}\\ \end{align*}
Mathematica [A] time = 0.0014288, size = 14, normalized size = 1. \[ a x+\frac{2}{3} b x^{3/2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 11, normalized size = 0.8 \begin{align*} ax+{\frac{2\,b}{3}{x}^{{\frac{3}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.96507, size = 14, normalized size = 1. \begin{align*} \frac{2}{3} \, b x^{\frac{3}{2}} + a x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.4622, size = 28, normalized size = 2. \begin{align*} \frac{2}{3} \, b x^{\frac{3}{2}} + a x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.052043, size = 12, normalized size = 0.86 \begin{align*} a 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 = 1.08628, size = 14, normalized size = 1. \begin{align*} \frac{2}{3} \, b x^{\frac{3}{2}} + a x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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