Optimal. Leaf size=19 \[ \frac{1}{5} b^2 x^4 \sqrt{b x^2} \]
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Rubi [A] time = 0.0018269, antiderivative size = 19, 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} \[ \frac{1}{5} b^2 x^4 \sqrt{b x^2} \]
Antiderivative was successfully verified.
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Rule 15
Rule 30
Rubi steps
\begin{align*} \int \frac{\left (b x^2\right )^{5/2}}{x} \, dx &=\frac{\left (b^2 \sqrt{b x^2}\right ) \int x^4 \, dx}{x}\\ &=\frac{1}{5} b^2 x^4 \sqrt{b x^2}\\ \end{align*}
Mathematica [A] time = 0.001281, size = 17, normalized size = 0.89 \[ \frac{1}{5} b x^2 \left (b x^2\right )^{3/2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 10, normalized size = 0.5 \begin{align*}{\frac{1}{5} \left ( b{x}^{2} \right ) ^{{\frac{5}{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: ValueError} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.2514, size = 34, normalized size = 1.79 \begin{align*} \frac{1}{5} \, \sqrt{b x^{2}} b^{2} x^{4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 1.01782, size = 12, normalized size = 0.63 \begin{align*} \frac{b^{\frac{5}{2}} \left (x^{2}\right )^{\frac{5}{2}}}{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.27814, size = 14, normalized size = 0.74 \begin{align*} \frac{1}{5} \, b^{\frac{5}{2}} x^{5} \mathrm{sgn}\left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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