Optimal. Leaf size=20 \[ -\frac{2 \sqrt{a-b x}}{a \sqrt{x}} \]
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Rubi [A] time = 0.0017315, antiderivative size = 20, normalized size of antiderivative = 1., 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} \[ -\frac{2 \sqrt{a-b x}}{a \sqrt{x}} \]
Antiderivative was successfully verified.
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Rule 37
Rubi steps
\begin{align*} \int \frac{1}{x^{3/2} \sqrt{a-b x}} \, dx &=-\frac{2 \sqrt{a-b x}}{a \sqrt{x}}\\ \end{align*}
Mathematica [A] time = 0.0106507, size = 20, normalized size = 1. \[ -\frac{2 \sqrt{a-b x}}{a \sqrt{x}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 17, normalized size = 0.9 \begin{align*} -2\,{\frac{\sqrt{-bx+a}}{a\sqrt{x}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.996761, size = 22, normalized size = 1.1 \begin{align*} -\frac{2 \, \sqrt{-b x + a}}{a \sqrt{x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.08596, size = 42, normalized size = 2.1 \begin{align*} -\frac{2 \, \sqrt{-b x + a}}{a \sqrt{x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 1.23314, size = 49, normalized size = 2.45 \begin{align*} \begin{cases} - \frac{2 \sqrt{b} \sqrt{\frac{a}{b x} - 1}}{a} & \text{for}\: \frac{\left |{a}\right |}{\left |{b}\right | \left |{x}\right |} > 1 \\- \frac{2 i \sqrt{b} \sqrt{- \frac{a}{b x} + 1}}{a} & \text{otherwise} \end{cases} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.08071, size = 47, normalized size = 2.35 \begin{align*} -\frac{2 \, \sqrt{-b x + a} b^{2}}{\sqrt{{\left (b x - a\right )} b + a b} a{\left | b \right |}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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