Optimal. Leaf size=16 \[ -\frac{\sqrt{b x+2}}{\sqrt{x}} \]
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Rubi [A] time = 0.0012056, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067, Rules used = {37} \[ -\frac{\sqrt{b x+2}}{\sqrt{x}} \]
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 = 0.0034954, size = 16, normalized size = 1. \[ -\frac{\sqrt{b x+2}}{\sqrt{x}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 13, 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 = 1.02366, size = 16, normalized size = 1. \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 = 1.8098, size = 32, 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 = 1.12139, size = 15, normalized size = 0.94 \begin{align*} - \sqrt{b} \sqrt{1 + \frac{2}{b x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.07529, size = 39, normalized size = 2.44 \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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