Optimal. Leaf size=15 \[ \frac{\sqrt{x}}{\sqrt{b x+2}} \]
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Rubi [A] time = 0.0013378, antiderivative size = 15, 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} \[ \frac{\sqrt{x}}{\sqrt{b x+2}} \]
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 = 0.0032298, size = 15, normalized size = 1. \[ \frac{\sqrt{x}}{\sqrt{b x+2}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 12, 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 = 1.08694, size = 15, 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 = 1.48699, size = 31, normalized size = 2.07 \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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Sympy [A] time = 1.11237, size = 15, normalized size = 1. \begin{align*} \frac{1}{\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 = 1.07288, size = 59, normalized size = 3.93 \begin{align*} \frac{4 \, b^{\frac{3}{2}}}{{\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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