Optimal. Leaf size=11 \[ \frac{1}{15} \left (x^3+1\right )^5 \]
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Rubi [A] time = 0.0017565, antiderivative size = 11, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091, Rules used = {261} \[ \frac{1}{15} \left (x^3+1\right )^5 \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin{align*} \int x^2 \left (1+x^3\right )^4 \, dx &=\frac{1}{15} \left (1+x^3\right )^5\\ \end{align*}
Mathematica [B] time = 0.0014124, size = 36, normalized size = 3.27 \[ \frac{x^{15}}{15}+\frac{x^{12}}{3}+\frac{2 x^9}{3}+\frac{2 x^6}{3}+\frac{x^3}{3} \]
Antiderivative was successfully verified.
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Maple [B] time = 0.001, size = 27, normalized size = 2.5 \begin{align*}{\frac{{x}^{15}}{15}}+{\frac{{x}^{12}}{3}}+{\frac{2\,{x}^{9}}{3}}+{\frac{2\,{x}^{6}}{3}}+{\frac{{x}^{3}}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.929509, size = 12, normalized size = 1.09 \begin{align*} \frac{1}{15} \,{\left (x^{3} + 1\right )}^{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.56919, size = 70, normalized size = 6.36 \begin{align*} \frac{1}{15} x^{15} + \frac{1}{3} x^{12} + \frac{2}{3} x^{9} + \frac{2}{3} x^{6} + \frac{1}{3} x^{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.050945, size = 27, normalized size = 2.45 \begin{align*} \frac{x^{15}}{15} + \frac{x^{12}}{3} + \frac{2 x^{9}}{3} + \frac{2 x^{6}}{3} + \frac{x^{3}}{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.05947, size = 12, normalized size = 1.09 \begin{align*} \frac{1}{15} \,{\left (x^{3} + 1\right )}^{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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