Optimal. Leaf size=19 \[ \frac{x^3}{2 b \sqrt{b x^2}} \]
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Rubi [A] time = 0.0017728, 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} \[ \frac{x^3}{2 b \sqrt{b x^2}} \]
Antiderivative was successfully verified.
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Rule 15
Rule 30
Rubi steps
\begin{align*} \int \frac{x^4}{\left (b x^2\right )^{3/2}} \, dx &=\frac{x \int x \, dx}{b \sqrt{b x^2}}\\ &=\frac{x^3}{2 b \sqrt{b x^2}}\\ \end{align*}
Mathematica [A] time = 0.0014046, size = 16, normalized size = 0.84 \[ \frac{x^5}{2 \left (b x^2\right )^{3/2}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 13, normalized size = 0.7 \begin{align*}{\frac{{x}^{5}}{2} \left ( 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 = 1.01793, size = 20, normalized size = 1.05 \begin{align*} \frac{x^{3}}{2 \, \sqrt{b x^{2}} b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.44799, size = 31, normalized size = 1.63 \begin{align*} \frac{\sqrt{b x^{2}} x}{2 \, b^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.684098, size = 15, normalized size = 0.79 \begin{align*} \frac{x^{5}}{2 b^{\frac{3}{2}} \left (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 = 1.16032, size = 18, normalized size = 0.95 \begin{align*} \frac{\sqrt{b x^{2}} x}{2 \, b^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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