Optimal. Leaf size=18 \[ -\frac{(b x+2)^{3/2}}{3 x^{3/2}} \]
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Rubi [A] time = 0.0014173, antiderivative size = 18, 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} \[ -\frac{(b x+2)^{3/2}}{3 x^{3/2}} \]
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 = 0.0132774, size = 18, normalized size = 1. \[ -\frac{(b x+2)^{3/2}}{3 x^{3/2}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 13, 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 = 1.03068, size = 16, normalized size = 0.89 \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 = 1.50226, size = 41, normalized size = 2.28 \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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Sympy [B] time = 2.11646, size = 37, normalized size = 2.06 \begin{align*} - \frac{b^{\frac{3}{2}} \sqrt{1 + \frac{2}{b x}}}{3} - \frac{2 \sqrt{b} \sqrt{1 + \frac{2}{b x}}}{3 x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.23251, size = 39, normalized size = 2.17 \begin{align*} -\frac{{\left (b x + 2\right )}^{\frac{3}{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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