Optimal. Leaf size=21 \[ -\frac {2 (a+b x)^{3/2}}{3 a x^{3/2}} \]
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Rubi [A] time = 0.00, antiderivative size = 21, normalized size of antiderivative = 1.00, 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*}
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Mathematica [A] time = 0.01, size = 21, normalized size = 1.00 \[ -\frac {2 (a+b x)^{3/2}}{3 a x^{3/2}} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.41, size = 15, normalized size = 0.71 \[ -\frac {2 \, {\left (b x + a\right )}^{\frac {3}{2}}}{3 \, a x^{\frac {3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 1.33, size = 33, normalized size = 1.57 \[ -\frac {2 \, {\left (b x + a\right )}^{\frac {3}{2}} b^{4}}{3 \, {\left ({\left (b x + a\right )} b - a b\right )}^{\frac {3}{2}} a {\left | b \right |}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 16, normalized size = 0.76 \[ -\frac {2 \left (b x +a \right )^{\frac {3}{2}}}{3 a \,x^{\frac {3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.36, size = 15, normalized size = 0.71 \[ -\frac {2 \, {\left (b x + a\right )}^{\frac {3}{2}}}{3 \, a x^{\frac {3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.24, size = 21, normalized size = 1.00 \[ -\frac {\left (\frac {2\,b\,x}{3\,a}+\frac {2}{3}\right )\,\sqrt {a+b\,x}}{x^{3/2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 1.46, size = 41, normalized size = 1.95 \[ - \frac {2 \sqrt {b} \sqrt {\frac {a}{b x} + 1}}{3 x} - \frac {2 b^{\frac {3}{2}} \sqrt {\frac {a}{b x} + 1}}{3 a} \]
Verification of antiderivative is not currently implemented for this CAS.
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