Optimal. Leaf size=21 \[ \frac{2}{3} a x^{3/2}+\frac{2}{5} b x^{5/2} \]
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Rubi [A] time = 0.0041047, antiderivative size = 21, 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} \[ \frac{2}{3} a x^{3/2}+\frac{2}{5} b x^{5/2} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int \sqrt{x} (a+b x) \, dx &=\int \left (a \sqrt{x}+b x^{3/2}\right ) \, dx\\ &=\frac{2}{3} a x^{3/2}+\frac{2}{5} b x^{5/2}\\ \end{align*}
Mathematica [A] time = 0.004014, size = 17, normalized size = 0.81 \[ \frac{2}{15} x^{3/2} (5 a+3 b x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 14, normalized size = 0.7 \begin{align*}{\frac{6\,bx+10\,a}{15}{x}^{{\frac{3}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.00839, size = 18, normalized size = 0.86 \begin{align*} \frac{2}{5} \, b x^{\frac{5}{2}} + \frac{2}{3} \, a x^{\frac{3}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.57422, size = 43, normalized size = 2.05 \begin{align*} \frac{2}{15} \,{\left (3 \, b x^{2} + 5 \, a x\right )} \sqrt{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 2.04054, size = 19, normalized size = 0.9 \begin{align*} \frac{2 a x^{\frac{3}{2}}}{3} + \frac{2 b x^{\frac{5}{2}}}{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.25034, size = 18, normalized size = 0.86 \begin{align*} \frac{2}{5} \, b x^{\frac{5}{2}} + \frac{2}{3} \, a x^{\frac{3}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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