Optimal. Leaf size=16 \[ \frac{x^3}{2 \sqrt{b x^2}} \]
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Rubi [A] time = 0.0015693, antiderivative size = 16, 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} \[ \frac{x^3}{2 \sqrt{b x^2}} \]
Antiderivative was successfully verified.
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Rule 15
Rule 30
Rubi steps
\begin{align*} \int \frac{x^2}{\sqrt{b x^2}} \, dx &=\frac{x \int x \, dx}{\sqrt{b x^2}}\\ &=\frac{x^3}{2 \sqrt{b x^2}}\\ \end{align*}
Mathematica [A] time = 0.001293, size = 16, normalized size = 1. \[ \frac{x^3}{2 \sqrt{b x^2}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 13, normalized size = 0.8 \begin{align*}{\frac{{x}^{3}}{2}{\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 = 1.04913, size = 11, normalized size = 0.69 \begin{align*} \frac{x^{2}}{2 \, \sqrt{b}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.46197, size = 28, normalized size = 1.75 \begin{align*} \frac{\sqrt{b x^{2}} x}{2 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.553627, size = 15, normalized size = 0.94 \begin{align*} \frac{x^{3}}{2 \sqrt{b} \sqrt{x^{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.19381, size = 18, normalized size = 1.12 \begin{align*} \frac{\sqrt{b x^{2}} x}{2 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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