Optimal. Leaf size=12 \[ -\frac{2}{b \sqrt{b x}} \]
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Rubi [A] time = 0.0012317, antiderivative size = 12, normalized size of antiderivative = 1., 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} \[ -\frac{2}{b \sqrt{b x}} \]
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*}
Mathematica [A] time = 0.0011217, size = 10, normalized size = 0.83 \[ -\frac{2 x}{(b x)^{3/2}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 9, normalized size = 0.8 \begin{align*} -2\,{\frac{x}{ \left ( bx \right ) ^{3/2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.964424, size = 14, normalized size = 1.17 \begin{align*} -\frac{2}{\sqrt{b x} b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.65251, size = 30, normalized size = 2.5 \begin{align*} -\frac{2 \, \sqrt{b x}}{b^{2} x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.059365, size = 10, normalized size = 0.83 \begin{align*} - \frac{2}{b \sqrt{b x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.15002, size = 14, normalized size = 1.17 \begin{align*} -\frac{2}{\sqrt{b x} b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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