Optimal. Leaf size=12 \[ -2 b \sqrt {\frac {b}{x}} \]
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Rubi [A] time = 0.00, antiderivative size = 12, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.222, Rules used = {15, 30} \begin {gather*} -2 b \sqrt {\frac {b}{x}} \end {gather*}
Antiderivative was successfully verified.
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Rule 15
Rule 30
Rubi steps
\begin {align*} \int \left (\frac {b}{x}\right )^{3/2} \, dx &=\left (b \sqrt {\frac {b}{x}} \sqrt {x}\right ) \int \frac {1}{x^{3/2}} \, dx\\ &=-2 b \sqrt {\frac {b}{x}}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 12, normalized size = 1.00 \begin {gather*} -2 x \left (\frac {b}{x}\right )^{3/2} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.01, size = 12, normalized size = 1.00 \begin {gather*} -2 b \sqrt {\frac {b}{x}} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.76, size = 10, normalized size = 0.83 \begin {gather*} -2 \, b \sqrt {\frac {b}{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 12, normalized size = 1.00 \begin {gather*} -\frac {2 \, b^{2} \mathrm {sgn}\relax (x)}{\sqrt {b x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 11, normalized size = 0.92 \begin {gather*} -2 \left (\frac {b}{x}\right )^{\frac {3}{2}} x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.32, size = 10, normalized size = 0.83 \begin {gather*} -2 \, x \left (\frac {b}{x}\right )^{\frac {3}{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.93, size = 10, normalized size = 0.83 \begin {gather*} -2\,b\,\sqrt {\frac {b}{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.42, size = 15, normalized size = 1.25 \begin {gather*} - 2 b^{\frac {3}{2}} x \left (\frac {1}{x}\right )^{\frac {3}{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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