Optimal. Leaf size=9 \[ \sqrt{b x^2} \]
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Rubi [A] time = 0.0008505, antiderivative size = 9, 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, 8} \[ \sqrt{b x^2} \]
Antiderivative was successfully verified.
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Rule 15
Rule 8
Rubi steps
\begin{align*} \int \frac{\sqrt{b x^2}}{x} \, dx &=\frac{\sqrt{b x^2} \int 1 \, dx}{x}\\ &=\sqrt{b x^2}\\ \end{align*}
Mathematica [A] time = 0.0016626, size = 14, normalized size = 1.56 \[ \frac{b x^2}{\sqrt{b x^2}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 8, normalized size = 0.9 \begin{align*} \sqrt{b{x}^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: RuntimeError} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.23001, size = 18, normalized size = 2. \begin{align*} \sqrt{b x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.190571, size = 10, normalized size = 1.11 \begin{align*} \sqrt{b} \sqrt{x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.1058, size = 9, normalized size = 1. \begin{align*} \sqrt{b} x \mathrm{sgn}\left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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