Optimal. Leaf size=14 \[ \frac{1}{4} x^3 \sqrt{x^2} \]
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Rubi [A] time = 0.001058, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 7, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.286, Rules used = {15, 30} \[ \frac{1}{4} x^3 \sqrt{x^2} \]
Antiderivative was successfully verified.
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Rule 15
Rule 30
Rubi steps
\begin{align*} \int \left (x^2\right )^{3/2} \, dx &=\frac{\sqrt{x^2} \int x^3 \, dx}{x}\\ &=\frac{1}{4} x^3 \sqrt{x^2}\\ \end{align*}
Mathematica [A] time = 0.0031073, size = 12, normalized size = 0.86 \[ \frac{1}{4} x \left (x^2\right )^{3/2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 11, normalized size = 0.8 \begin{align*}{\frac{{x}^{3}}{4}\sqrt{{x}^{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.03718, size = 11, normalized size = 0.79 \begin{align*} \frac{1}{4} \,{\left (x^{2}\right )}^{\frac{3}{2}} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.16087, size = 12, normalized size = 0.86 \begin{align*} \frac{1}{4} \, x^{4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.062199, size = 3, normalized size = 0.21 \begin{align*} \frac{x^{4}}{4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.15197, size = 9, normalized size = 0.64 \begin{align*} \frac{1}{4} \, x^{4} \mathrm{sgn}\left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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