Optimal. Leaf size=44 \[ \frac {256 x^{13}}{13}-\frac {1024 x^{11}}{11}+\frac {544 x^9}{3}-\frac {1312 x^7}{7}+\frac {553 x^5}{5}-38 x^3+9 x \]
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Rubi [A] time = 0.07, antiderivative size = 44, normalized size of antiderivative = 1.00, number of steps used = 5, number of rules used = 3, integrand size = 19, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.158, Rules used = {2059, 517, 521} \[ \frac {256 x^{13}}{13}-\frac {1024 x^{11}}{11}+\frac {544 x^9}{3}-\frac {1312 x^7}{7}+\frac {553 x^5}{5}-38 x^3+9 x \]
Antiderivative was successfully verified.
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Rule 517
Rule 521
Rule 2059
Rubi steps
\begin {align*} \int \left (3-19 x^2+32 x^4-16 x^6\right )^2 \, dx &=\int (-1+x)^2 (1+x)^2 (-1+2 x)^2 (1+2 x)^2 \left (-3+4 x^2\right )^2 \, dx\\ &=\int (-1+2 x)^2 (1+2 x)^2 \left (-1+x^2\right )^2 \left (-3+4 x^2\right )^2 \, dx\\ &=\int \left (-1+x^2\right )^2 \left (-3+4 x^2\right )^2 \left (-1+4 x^2\right )^2 \, dx\\ &=\int \left (9-114 x^2+553 x^4-1312 x^6+1632 x^8-1024 x^{10}+256 x^{12}\right ) \, dx\\ &=9 x-38 x^3+\frac {553 x^5}{5}-\frac {1312 x^7}{7}+\frac {544 x^9}{3}-\frac {1024 x^{11}}{11}+\frac {256 x^{13}}{13}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 44, normalized size = 1.00 \[ \frac {256 x^{13}}{13}-\frac {1024 x^{11}}{11}+\frac {544 x^9}{3}-\frac {1312 x^7}{7}+\frac {553 x^5}{5}-38 x^3+9 x \]
Antiderivative was successfully verified.
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fricas [A] time = 0.65, size = 34, normalized size = 0.77 \[ \frac {256}{13} x^{13} - \frac {1024}{11} x^{11} + \frac {544}{3} x^{9} - \frac {1312}{7} x^{7} + \frac {553}{5} x^{5} - 38 x^{3} + 9 x \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.36, size = 34, normalized size = 0.77 \[ \frac {256}{13} \, x^{13} - \frac {1024}{11} \, x^{11} + \frac {544}{3} \, x^{9} - \frac {1312}{7} \, x^{7} + \frac {553}{5} \, x^{5} - 38 \, x^{3} + 9 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 35, normalized size = 0.80 \[ \frac {256}{13} x^{13}-\frac {1024}{11} x^{11}+\frac {544}{3} x^{9}-\frac {1312}{7} x^{7}+\frac {553}{5} x^{5}-38 x^{3}+9 x \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.75, size = 34, normalized size = 0.77 \[ \frac {256}{13} \, x^{13} - \frac {1024}{11} \, x^{11} + \frac {544}{3} \, x^{9} - \frac {1312}{7} \, x^{7} + \frac {553}{5} \, x^{5} - 38 \, x^{3} + 9 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 34, normalized size = 0.77 \[ \frac {256\,x^{13}}{13}-\frac {1024\,x^{11}}{11}+\frac {544\,x^9}{3}-\frac {1312\,x^7}{7}+\frac {553\,x^5}{5}-38\,x^3+9\,x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.06, size = 41, normalized size = 0.93 \[ \frac {256 x^{13}}{13} - \frac {1024 x^{11}}{11} + \frac {544 x^{9}}{3} - \frac {1312 x^{7}}{7} + \frac {553 x^{5}}{5} - 38 x^{3} + 9 x \]
Verification of antiderivative is not currently implemented for this CAS.
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