Optimal. Leaf size=11 \[ -\frac{1}{\sqrt{b x^2}} \]
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Rubi [A] time = 0.0013983, antiderivative size = 11, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154, Rules used = {15, 30} \[ -\frac{1}{\sqrt{b x^2}} \]
Antiderivative was successfully verified.
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Rule 15
Rule 30
Rubi steps
\begin{align*} \int \frac{1}{x \sqrt{b x^2}} \, dx &=\frac{x \int \frac{1}{x^2} \, dx}{\sqrt{b x^2}}\\ &=-\frac{1}{\sqrt{b x^2}}\\ \end{align*}
Mathematica [A] time = 0.0020552, size = 15, normalized size = 1.36 \[ -\frac{b x^2}{\left (b x^2\right )^{3/2}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 10, normalized size = 0.9 \begin{align*} -{\frac{1}{\sqrt{b{x}^{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.01831, size = 11, normalized size = 1. \begin{align*} -\frac{1}{\sqrt{b} x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.29474, size = 30, normalized size = 2.73 \begin{align*} -\frac{\sqrt{b x^{2}}}{b x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.44829, size = 14, normalized size = 1.27 \begin{align*} - \frac{1}{\sqrt{b} \sqrt{x^{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.16428, size = 12, normalized size = 1.09 \begin{align*} -\frac{1}{\sqrt{b x^{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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