Optimal. Leaf size=22 \[ \frac {4 x^7}{7}+\frac {2 x^6}{3}+\frac {x^5}{5} \]
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Rubi [A] time = 0.01, antiderivative size = 22, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.154, Rules used = {647, 43} \[ \frac {4 x^7}{7}+\frac {2 x^6}{3}+\frac {x^5}{5} \]
Antiderivative was successfully verified.
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Rule 43
Rule 647
Rubi steps
\begin {align*} \int x^2 \left (x+2 x^2\right )^2 \, dx &=\int x^4 (1+2 x)^2 \, dx\\ &=\int \left (x^4+4 x^5+4 x^6\right ) \, dx\\ &=\frac {x^5}{5}+\frac {2 x^6}{3}+\frac {4 x^7}{7}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 22, normalized size = 1.00 \[ \frac {4 x^7}{7}+\frac {2 x^6}{3}+\frac {x^5}{5} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.37, size = 16, normalized size = 0.73 \[ \frac {4}{7} x^{7} + \frac {2}{3} x^{6} + \frac {1}{5} x^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.01, size = 16, normalized size = 0.73 \[ \frac {4}{7} \, x^{7} + \frac {2}{3} \, x^{6} + \frac {1}{5} \, x^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 17, normalized size = 0.77 \[ \frac {4}{7} x^{7}+\frac {2}{3} x^{6}+\frac {1}{5} x^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.42, size = 16, normalized size = 0.73 \[ \frac {4}{7} \, x^{7} + \frac {2}{3} \, x^{6} + \frac {1}{5} \, x^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 15, normalized size = 0.68 \[ \frac {x^5\,\left (60\,x^2+70\,x+21\right )}{105} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.06, size = 17, normalized size = 0.77 \[ \frac {4 x^{7}}{7} + \frac {2 x^{6}}{3} + \frac {x^{5}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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