Optimal. Leaf size=11 \[ \frac {1}{15} \left (x^3+1\right )^5 \]
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Rubi [A] time = 0.00, antiderivative size = 11, normalized size of antiderivative = 1.00, 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*}
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Mathematica [B] time = 0.00, 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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fricas [B] time = 0.34, size = 26, normalized size = 2.36 \[ \frac {1}{15} x^{15} + \frac {1}{3} x^{12} + \frac {2}{3} x^{9} + \frac {2}{3} x^{6} + \frac {1}{3} x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.87, size = 9, normalized size = 0.82 \[ \frac {1}{15} \, {\left (x^{3} + 1\right )}^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.00, size = 27, normalized size = 2.45 \[ \frac {1}{15} x^{15}+\frac {1}{3} x^{12}+\frac {2}{3} x^{9}+\frac {2}{3} x^{6}+\frac {1}{3} x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.42, size = 9, normalized size = 0.82 \[ \frac {1}{15} \, {\left (x^{3} + 1\right )}^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 26, normalized size = 2.36 \[ \frac {x^{15}}{15}+\frac {x^{12}}{3}+\frac {2\,x^9}{3}+\frac {2\,x^6}{3}+\frac {x^3}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.06, size = 27, normalized size = 2.45 \[ \frac {x^{15}}{15} + \frac {x^{12}}{3} + \frac {2 x^{9}}{3} + \frac {2 x^{6}}{3} + \frac {x^{3}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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