Optimal. Leaf size=19 \[ -\frac{2 \sqrt{a+b x}}{a \sqrt{x}} \]
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Rubi [A] time = 0.001619, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067, 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 = 0.004231, size = 19, normalized size = 1. \[ -\frac{2 \sqrt{a+b x}}{a \sqrt{x}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 16, normalized size = 0.8 \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 = 1.05798, size = 20, normalized size = 1.05 \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 = 1.9059, size = 41, normalized size = 2.16 \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 = 1.01257, size = 19, normalized size = 1. \begin{align*} - \frac{2 \sqrt{b} \sqrt{\frac{a}{b x} + 1}}{a} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.06644, size = 45, normalized size = 2.37 \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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