Optimal. Leaf size=21 \[ -\frac{2 (a+b x)^{3/2}}{3 a x^{3/2}} \]
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Rubi [A] time = 0.0019194, antiderivative size = 21, 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} \[ -\frac{2 (a+b x)^{3/2}}{3 a x^{3/2}} \]
Antiderivative was successfully verified.
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Rule 37
Rubi steps
\begin{align*} \int \frac{\sqrt{a+b x}}{x^{5/2}} \, dx &=-\frac{2 (a+b x)^{3/2}}{3 a x^{3/2}}\\ \end{align*}
Mathematica [A] time = 0.0061355, size = 21, normalized size = 1. \[ -\frac{2 (a+b x)^{3/2}}{3 a x^{3/2}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 16, normalized size = 0.8 \begin{align*} -{\frac{2}{3\,a} \left ( bx+a \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 = 1.04145, size = 20, normalized size = 0.95 \begin{align*} -\frac{2 \,{\left (b x + a\right )}^{\frac{3}{2}}}{3 \, a x^{\frac{3}{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.49494, size = 46, normalized size = 2.19 \begin{align*} -\frac{2 \,{\left (b x + a\right )}^{\frac{3}{2}}}{3 \, a x^{\frac{3}{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 2.20224, size = 41, normalized size = 1.95 \begin{align*} - \frac{2 \sqrt{b} \sqrt{\frac{a}{b x} + 1}}{3 x} - \frac{2 b^{\frac{3}{2}} \sqrt{\frac{a}{b x} + 1}}{3 a} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.44095, size = 45, normalized size = 2.14 \begin{align*} -\frac{2 \,{\left (b x + a\right )}^{\frac{3}{2}} b^{4}}{3 \,{\left ({\left (b x + a\right )} b - a b\right )}^{\frac{3}{2}} a{\left | b \right |}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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