Optimal. Leaf size=19 \[ -\frac{(2-b x)^{3/2}}{3 x^{3/2}} \]
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Rubi [A] time = 0.0014399, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.062, Rules used = {37} \[ -\frac{(2-b x)^{3/2}}{3 x^{3/2}} \]
Antiderivative was successfully verified.
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Rule 37
Rubi steps
\begin{align*} \int \frac{\sqrt{2-b x}}{x^{5/2}} \, dx &=-\frac{(2-b x)^{3/2}}{3 x^{3/2}}\\ \end{align*}
Mathematica [A] time = 0.0053656, size = 19, normalized size = 1. \[ -\frac{(2-b x)^{3/2}}{3 x^{3/2}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 14, normalized size = 0.7 \begin{align*} -{\frac{1}{3} \left ( -bx+2 \right ) ^{{\frac{3}{2}}}{x}^{-{\frac{3}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.02419, size = 18, normalized size = 0.95 \begin{align*} -\frac{{\left (-b x + 2\right )}^{\frac{3}{2}}}{3 \, x^{\frac{3}{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.6011, size = 51, normalized size = 2.68 \begin{align*} \frac{{\left (b x - 2\right )} \sqrt{-b x + 2}}{3 \, x^{\frac{3}{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 2.32574, size = 82, normalized size = 4.32 \begin{align*} \begin{cases} \frac{b^{\frac{3}{2}} \sqrt{-1 + \frac{2}{b x}}}{3} - \frac{2 \sqrt{b} \sqrt{-1 + \frac{2}{b x}}}{3 x} & \text{for}\: \frac{2}{\left |{b x}\right |} > 1 \\\frac{i b^{\frac{3}{2}} \sqrt{1 - \frac{2}{b x}}}{3} - \frac{2 i \sqrt{b} \sqrt{1 - \frac{2}{b x}}}{3 x} & \text{otherwise} \end{cases} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.28805, size = 47, normalized size = 2.47 \begin{align*} \frac{{\left (b x - 2\right )} \sqrt{-b x + 2} b^{4}}{3 \,{\left ({\left (b x - 2\right )} b + 2 \, b\right )}^{\frac{3}{2}}{\left | b \right |}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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