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 = 0.0693192, antiderivative size = 44, normalized size of antiderivative = 1., 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 2059
Rule 517
Rule 521
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*}
Mathematica [A] time = 0.0007037, size = 44, normalized size = 1. \[ \frac{256 x^{13}}{13}-\frac{1024 x^{11}}{11}+\frac{544 x^9}{3}-\frac{1312 x^7}{7}+\frac{553 x^5}{5}-38 x^3+9 x \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 35, normalized size = 0.8 \begin{align*} 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*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.14573, size = 46, normalized size = 1.05 \begin{align*} \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 \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.5264, size = 108, normalized size = 2.45 \begin{align*} \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 \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.061542, size = 41, normalized size = 0.93 \begin{align*} \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 \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.12267, size = 46, normalized size = 1.05 \begin{align*} \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 \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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