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 = 0.00, antiderivative size = 21, 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*} \frac {2}{3} a x^{3/2}+\frac {2}{5} b x^{5/2} \end {gather*}
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*}
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Mathematica [A] time = 0.00, size = 17, normalized size = 0.81 \begin {gather*} \frac {2}{15} x^{3/2} (5 a+3 b x) \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.01, size = 21, normalized size = 1.00 \begin {gather*} \frac {2}{15} \left (5 a x^{3/2}+3 b x^{5/2}\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.99, size = 16, normalized size = 0.76 \begin {gather*} \frac {2}{15} \, {\left (3 \, b x^{2} + 5 \, a x\right )} \sqrt {x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.86, size = 13, normalized size = 0.62 \begin {gather*} \frac {2}{5} \, b x^{\frac {5}{2}} + \frac {2}{3} \, a x^{\frac {3}{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 14, normalized size = 0.67 \begin {gather*} \frac {2 \left (3 b x +5 a \right ) x^{\frac {3}{2}}}{15} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.34, size = 13, normalized size = 0.62 \begin {gather*} \frac {2}{5} \, b x^{\frac {5}{2}} + \frac {2}{3} \, a x^{\frac {3}{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 13, normalized size = 0.62 \begin {gather*} \frac {2\,x^{3/2}\,\left (5\,a+3\,b\,x\right )}{15} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 1.62, size = 19, normalized size = 0.90 \begin {gather*} \frac {2 a x^{\frac {3}{2}}}{3} + \frac {2 b x^{\frac {5}{2}}}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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