Optimal. Leaf size=21 \[ -\frac{2 a}{3 x^{3/2}}-\frac{2 b}{5 x^{5/2}} \]
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Rubi [A] time = 0.0039515, antiderivative size = 21, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077, Rules used = {14} \[ -\frac{2 a}{3 x^{3/2}}-\frac{2 b}{5 x^{5/2}} \]
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin{align*} \int \frac{a+\frac{b}{x}}{x^{5/2}} \, dx &=\int \left (\frac{b}{x^{7/2}}+\frac{a}{x^{5/2}}\right ) \, dx\\ &=-\frac{2 b}{5 x^{5/2}}-\frac{2 a}{3 x^{3/2}}\\ \end{align*}
Mathematica [A] time = 0.0048483, size = 17, normalized size = 0.81 \[ -\frac{2 (5 a x+3 b)}{15 x^{5/2}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 14, normalized size = 0.7 \begin{align*} -{\frac{10\,ax+6\,b}{15}{x}^{-{\frac{5}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.02217, size = 18, normalized size = 0.86 \begin{align*} -\frac{2 \, a}{3 \, x^{\frac{3}{2}}} - \frac{2 \, b}{5 \, x^{\frac{5}{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.87178, size = 39, normalized size = 1.86 \begin{align*} -\frac{2 \,{\left (5 \, a x + 3 \, b\right )}}{15 \, x^{\frac{5}{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.904358, size = 20, normalized size = 0.95 \begin{align*} - \frac{2 a}{3 x^{\frac{3}{2}}} - \frac{2 b}{5 x^{\frac{5}{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.13033, size = 18, normalized size = 0.86 \begin{align*} -\frac{2 \,{\left (5 \, a x + 3 \, b\right )}}{15 \, x^{\frac{5}{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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