Optimal. Leaf size=17 \[ \frac{5}{16} \left (x^4-3 x^2\right )^{8/5} \]
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Rubi [A] time = 0.0102869, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 23, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.043, Rules used = {1588} \[ \frac{5}{16} \left (x^4-3 x^2\right )^{8/5} \]
Antiderivative was successfully verified.
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Rule 1588
Rubi steps
\begin{align*} \int \left (-3 x+2 x^3\right ) \left (-3 x^2+x^4\right )^{3/5} \, dx &=\frac{5}{16} \left (-3 x^2+x^4\right )^{8/5}\\ \end{align*}
Mathematica [C] time = 0.0545341, size = 75, normalized size = 4.41 \[ \frac{5 \left (x^2 \left (x^2-3\right )\right )^{3/5} \left (16 x^4 \, _2F_1\left (-\frac{3}{5},\frac{13}{5};\frac{18}{5};\frac{x^2}{3}\right )-39 x^2 \, _2F_1\left (-\frac{3}{5},\frac{8}{5};\frac{13}{5};\frac{x^2}{3}\right )\right )}{208 \left (1-\frac{x^2}{3}\right )^{3/5}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 22, normalized size = 1.3 \begin{align*}{\frac{5\,{x}^{2} \left ({x}^{2}-3 \right ) }{16} \left ({x}^{4}-3\,{x}^{2} \right ) ^{{\frac{3}{5}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.964498, size = 18, normalized size = 1.06 \begin{align*} \frac{5}{16} \,{\left (x^{4} - 3 \, x^{2}\right )}^{\frac{8}{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.9955, size = 35, normalized size = 2.06 \begin{align*} \frac{5}{16} \,{\left (x^{4} - 3 \, x^{2}\right )}^{\frac{8}{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 1.24886, size = 36, normalized size = 2.12 \begin{align*} \frac{5 x^{4} \left (x^{4} - 3 x^{2}\right )^{\frac{3}{5}}}{16} - \frac{15 x^{2} \left (x^{4} - 3 x^{2}\right )^{\frac{3}{5}}}{16} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.08591, size = 18, normalized size = 1.06 \begin{align*} \frac{5}{16} \,{\left (x^{4} - 3 \, x^{2}\right )}^{\frac{8}{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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