Optimal. Leaf size=12 \[ \frac {1}{3} x^3 (x+2)^6 \]
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Rubi [A] time = 0.00, antiderivative size = 12, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.071, Rules used = {74} \[ \frac {1}{3} x^3 (x+2)^6 \]
Antiderivative was successfully verified.
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Rule 74
Rubi steps
\begin {align*} \int x^2 (2+x)^5 (2+3 x) \, dx &=\frac {1}{3} x^3 (2+x)^6\\ \end {align*}
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Mathematica [B] time = 0.00, size = 42, normalized size = 3.50 \[ \frac {x^9}{3}+4 x^8+20 x^7+\frac {160 x^6}{3}+80 x^5+64 x^4+\frac {64 x^3}{3} \]
Antiderivative was successfully verified.
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fricas [B] time = 0.78, size = 36, normalized size = 3.00 \[ \frac {1}{3} x^{9} + 4 x^{8} + 20 x^{7} + \frac {160}{3} x^{6} + 80 x^{5} + 64 x^{4} + \frac {64}{3} x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 1.04, size = 36, normalized size = 3.00 \[ \frac {1}{3} \, x^{9} + 4 \, x^{8} + 20 \, x^{7} + \frac {160}{3} \, x^{6} + 80 \, x^{5} + 64 \, x^{4} + \frac {64}{3} \, x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.00, size = 37, normalized size = 3.08 \[ \frac {1}{3} x^{9}+4 x^{8}+20 x^{7}+\frac {160}{3} x^{6}+80 x^{5}+64 x^{4}+\frac {64}{3} x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 1.14, size = 36, normalized size = 3.00 \[ \frac {1}{3} \, x^{9} + 4 \, x^{8} + 20 \, x^{7} + \frac {160}{3} \, x^{6} + 80 \, x^{5} + 64 \, x^{4} + \frac {64}{3} \, x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 36, normalized size = 3.00 \[ \frac {x^9}{3}+4\,x^8+20\,x^7+\frac {160\,x^6}{3}+80\,x^5+64\,x^4+\frac {64\,x^3}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.14, size = 37, normalized size = 3.08 \[ \frac {x^{9}}{3} + 4 x^{8} + 20 x^{7} + \frac {160 x^{6}}{3} + 80 x^{5} + 64 x^{4} + \frac {64 x^{3}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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