Optimal. Leaf size=19 \[ -\frac {(2-b x)^{3/2}}{3 x^{3/2}} \]
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Rubi [A] time = 0.00, antiderivative size = 19, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.062, Rules used = {37} \begin {gather*} -\frac {(2-b x)^{3/2}}{3 x^{3/2}} \end {gather*}
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*}
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Mathematica [A] time = 0.01, size = 19, normalized size = 1.00 \begin {gather*} -\frac {(2-b x)^{3/2}}{3 x^{3/2}} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.07, size = 24, normalized size = 1.26 \begin {gather*} \frac {\sqrt {2-b x} (b x-2)}{3 x^{3/2}} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.29, size = 18, normalized size = 0.95 \begin {gather*} \frac {{\left (b x - 2\right )} \sqrt {-b x + 2}}{3 \, x^{\frac {3}{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 1.12, size = 35, normalized size = 1.84 \begin {gather*} \frac {{\left (b x - 2\right )} \sqrt {-b x + 2} b^{4}}{3 \, {\left ({\left (b x - 2\right )} b + 2 \, b\right )}^{\frac {3}{2}} {\left | b \right |}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 14, normalized size = 0.74 \begin {gather*} -\frac {\left (-b x +2\right )^{\frac {3}{2}}}{3 x^{\frac {3}{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.28, size = 13, normalized size = 0.68 \begin {gather*} -\frac {{\left (-b x + 2\right )}^{\frac {3}{2}}}{3 \, x^{\frac {3}{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.22, size = 18, normalized size = 0.95 \begin {gather*} \frac {\sqrt {2-b\,x}\,\left (\frac {b\,x}{3}-\frac {2}{3}\right )}{x^{3/2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 1.51, size = 82, normalized size = 4.32 \begin {gather*} \begin {cases} \frac {b^{\frac {3}{2}} \sqrt {-1 + \frac {2}{b x}}}{3} - \frac {2 \sqrt {b} \sqrt {-1 + \frac {2}{b x}}}{3 x} & \text {for}\: \frac {2}{\left |{b x}\right |} > 1 \\\frac {i b^{\frac {3}{2}} \sqrt {1 - \frac {2}{b x}}}{3} - \frac {2 i \sqrt {b} \sqrt {1 - \frac {2}{b x}}}{3 x} & \text {otherwise} \end {cases} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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