Optimal. Leaf size=17 \[ -\frac{\sqrt{2-b x}}{\sqrt{x}} \]
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Rubi [A] time = 0.001366, antiderivative size = 17, 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} \[ -\frac{\sqrt{2-b x}}{\sqrt{x}} \]
Antiderivative was successfully verified.
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Rule 37
Rubi steps
\begin{align*} \int \frac{1}{x^{3/2} \sqrt{2-b x}} \, dx &=-\frac{\sqrt{2-b x}}{\sqrt{x}}\\ \end{align*}
Mathematica [A] time = 0.0038564, size = 17, normalized size = 1. \[ -\frac{\sqrt{2-b x}}{\sqrt{x}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 14, normalized size = 0.8 \begin{align*} -{\sqrt{-bx+2}{\frac{1}{\sqrt{x}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.00026, size = 18, normalized size = 1.06 \begin{align*} -\frac{\sqrt{-b x + 2}}{\sqrt{x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.54185, size = 34, normalized size = 2. \begin{align*} -\frac{\sqrt{-b x + 2}}{\sqrt{x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 1.17606, size = 39, normalized size = 2.29 \begin{align*} \begin{cases} - \sqrt{b} \sqrt{-1 + \frac{2}{b x}} & \text{for}\: \frac{2}{\left |{b x}\right |} > 1 \\- i \sqrt{b} \sqrt{1 - \frac{2}{b x}} & \text{otherwise} \end{cases} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.06825, size = 41, normalized size = 2.41 \begin{align*} -\frac{\sqrt{-b x + 2} b^{2}}{\sqrt{{\left (b x - 2\right )} b + 2 \, b}{\left | b \right |}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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