Optimal. Leaf size=12 \[ -\frac {2}{b \sqrt {b x}} \]
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Rubi [A] time = 0.00, antiderivative size = 12, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {32} \begin {gather*} -\frac {2}{b \sqrt {b x}} \end {gather*}
Antiderivative was successfully verified.
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Rule 32
Rubi steps
\begin {align*} \int \frac {1}{(b x)^{3/2}} \, dx &=-\frac {2}{b \sqrt {b x}}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 10, normalized size = 0.83 \begin {gather*} -\frac {2 x}{(b x)^{3/2}} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.01, size = 15, normalized size = 1.25 \begin {gather*} -\frac {2 \sqrt {b x}}{b^2 x} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.14, size = 13, normalized size = 1.08 \begin {gather*} -\frac {2 \, \sqrt {b x}}{b^{2} x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 10, normalized size = 0.83 \begin {gather*} -\frac {2}{\sqrt {b x} b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 9, normalized size = 0.75 \begin {gather*} -\frac {2 x}{\left (b x \right )^{\frac {3}{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.30, size = 10, normalized size = 0.83 \begin {gather*} -\frac {2}{\sqrt {b x} b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 10, normalized size = 0.83 \begin {gather*} -\frac {2}{b\,\sqrt {b\,x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.06, size = 10, normalized size = 0.83 \begin {gather*} - \frac {2}{b \sqrt {b x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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