Optimal. Leaf size=19 \[ -\frac{2 a}{3 x^{3/2}}-\frac{2 b}{\sqrt{x}} \]
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Rubi [A] time = 0.0036581, 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} \[ -\frac{2 a}{3 x^{3/2}}-\frac{2 b}{\sqrt{x}} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int \frac{a+b x}{x^{5/2}} \, dx &=\int \left (\frac{a}{x^{5/2}}+\frac{b}{x^{3/2}}\right ) \, dx\\ &=-\frac{2 a}{3 x^{3/2}}-\frac{2 b}{\sqrt{x}}\\ \end{align*}
Mathematica [A] time = 0.0049646, size = 15, normalized size = 0.79 \[ -\frac{2 (a+3 b x)}{3 x^{3/2}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 12, normalized size = 0.6 \begin{align*} -{\frac{6\,bx+2\,a}{3}{x}^{-{\frac{3}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.992358, size = 15, normalized size = 0.79 \begin{align*} -\frac{2 \,{\left (3 \, b x + a\right )}}{3 \, x^{\frac{3}{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.55319, size = 35, normalized size = 1.84 \begin{align*} -\frac{2 \,{\left (3 \, b x + a\right )}}{3 \, x^{\frac{3}{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.957543, size = 19, normalized size = 1. \begin{align*} - \frac{2 a}{3 x^{\frac{3}{2}}} - \frac{2 b}{\sqrt{x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.23794, size = 15, normalized size = 0.79 \begin{align*} -\frac{2 \,{\left (3 \, b x + a\right )}}{3 \, x^{\frac{3}{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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