Optimal. Leaf size=19 \[ \frac{x^3}{4 b \sqrt{\frac{b}{x^2}}} \]
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Rubi [A] time = 0.0020934, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.222, Rules used = {15, 30} \[ \frac{x^3}{4 b \sqrt{\frac{b}{x^2}}} \]
Antiderivative was successfully verified.
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Rule 15
Rule 30
Rubi steps
\begin{align*} \int \frac{1}{\left (\frac{b}{x^2}\right )^{3/2}} \, dx &=\frac{\int x^3 \, dx}{b \sqrt{\frac{b}{x^2}} x}\\ &=\frac{x^3}{4 b \sqrt{\frac{b}{x^2}}}\\ \end{align*}
Mathematica [A] time = 0.0016903, size = 14, normalized size = 0.74 \[ \frac{x}{4 \left (\frac{b}{x^2}\right )^{3/2}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 11, normalized size = 0.6 \begin{align*}{\frac{x}{4} \left ({\frac{b}{{x}^{2}}} \right ) ^{-{\frac{3}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.9582, size = 14, normalized size = 0.74 \begin{align*} \frac{x}{4 \, \left (\frac{b}{x^{2}}\right )^{\frac{3}{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.68737, size = 34, normalized size = 1.79 \begin{align*} \frac{x^{5} \sqrt{\frac{b}{x^{2}}}}{4 \, b^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.656018, size = 15, normalized size = 0.79 \begin{align*} \frac{x}{4 b^{\frac{3}{2}} \left (\frac{1}{x^{2}}\right )^{\frac{3}{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.17682, size = 11, normalized size = 0.58 \begin{align*} \frac{x^{4}}{4 \, b^{\frac{3}{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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