Optimal. Leaf size=16 \[ \frac{\sqrt{x}}{\sqrt{2-b x}} \]
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Rubi [A] time = 0.0013493, antiderivative size = 16, 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} \[ \frac{\sqrt{x}}{\sqrt{2-b x}} \]
Antiderivative was successfully verified.
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Rule 37
Rubi steps
\begin{align*} \int \frac{1}{\sqrt{x} (2-b x)^{3/2}} \, dx &=\frac{\sqrt{x}}{\sqrt{2-b x}}\\ \end{align*}
Mathematica [A] time = 0.0037654, size = 16, normalized size = 1. \[ \frac{\sqrt{x}}{\sqrt{2-b x}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 13, normalized size = 0.8 \begin{align*}{\sqrt{x}{\frac{1}{\sqrt{-bx+2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.01769, size = 16, normalized size = 1. \begin{align*} \frac{\sqrt{x}}{\sqrt{-b x + 2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.5107, size = 47, normalized size = 2.94 \begin{align*} -\frac{\sqrt{-b x + 2} \sqrt{x}}{b x - 2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 1.12369, size = 39, normalized size = 2.44 \begin{align*} \begin{cases} \frac{1}{\sqrt{b} \sqrt{-1 + \frac{2}{b x}}} & \text{for}\: \frac{2}{\left |{b x}\right |} > 1 \\- \frac{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 = 1.08857, size = 68, normalized size = 4.25 \begin{align*} -\frac{4 \, \sqrt{-b} b}{{\left ({\left (\sqrt{-b x + 2} \sqrt{-b} - \sqrt{{\left (b x - 2\right )} b + 2 \, b}\right )}^{2} - 2 \, b\right )}{\left | b \right |}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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