Integrand size = 19, antiderivative size = 44 \[ \int \left (3-19 x^2+32 x^4-16 x^6\right )^2 \, dx=9 x-38 x^3+\frac {553 x^5}{5}-\frac {1312 x^7}{7}+\frac {544 x^9}{3}-\frac {1024 x^{11}}{11}+\frac {256 x^{13}}{13} \]
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Time = 0.05 (sec) , antiderivative size = 44, normalized size of antiderivative = 1.00, number of steps used = 5, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.158, Rules used = {2084, 531, 535} \[ \int \left (3-19 x^2+32 x^4-16 x^6\right )^2 \, dx=\frac {256 x^{13}}{13}-\frac {1024 x^{11}}{11}+\frac {544 x^9}{3}-\frac {1312 x^7}{7}+\frac {553 x^5}{5}-38 x^3+9 x \]
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Rule 531
Rule 535
Rule 2084
Rubi steps \begin{align*} \text {integral}& = \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*}
Time = 0.00 (sec) , antiderivative size = 44, normalized size of antiderivative = 1.00 \[ \int \left (3-19 x^2+32 x^4-16 x^6\right )^2 \, dx=9 x-38 x^3+\frac {553 x^5}{5}-\frac {1312 x^7}{7}+\frac {544 x^9}{3}-\frac {1024 x^{11}}{11}+\frac {256 x^{13}}{13} \]
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Time = 0.03 (sec) , antiderivative size = 35, normalized size of antiderivative = 0.80
method | result | size |
default | \(9 x -38 x^{3}+\frac {553}{5} x^{5}-\frac {1312}{7} x^{7}+\frac {544}{3} x^{9}-\frac {1024}{11} x^{11}+\frac {256}{13} x^{13}\) | \(35\) |
norman | \(9 x -38 x^{3}+\frac {553}{5} x^{5}-\frac {1312}{7} x^{7}+\frac {544}{3} x^{9}-\frac {1024}{11} x^{11}+\frac {256}{13} x^{13}\) | \(35\) |
risch | \(9 x -38 x^{3}+\frac {553}{5} x^{5}-\frac {1312}{7} x^{7}+\frac {544}{3} x^{9}-\frac {1024}{11} x^{11}+\frac {256}{13} x^{13}\) | \(35\) |
parallelrisch | \(9 x -38 x^{3}+\frac {553}{5} x^{5}-\frac {1312}{7} x^{7}+\frac {544}{3} x^{9}-\frac {1024}{11} x^{11}+\frac {256}{13} x^{13}\) | \(35\) |
gosper | \(\frac {x \left (295680 x^{12}-1397760 x^{10}+2722720 x^{8}-2814240 x^{6}+1660659 x^{4}-570570 x^{2}+135135\right )}{15015}\) | \(36\) |
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Time = 0.27 (sec) , antiderivative size = 34, normalized size of antiderivative = 0.77 \[ \int \left (3-19 x^2+32 x^4-16 x^6\right )^2 \, dx=\frac {256}{13} \, x^{13} - \frac {1024}{11} \, x^{11} + \frac {544}{3} \, x^{9} - \frac {1312}{7} \, x^{7} + \frac {553}{5} \, x^{5} - 38 \, x^{3} + 9 \, x \]
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Time = 0.03 (sec) , antiderivative size = 41, normalized size of antiderivative = 0.93 \[ \int \left (3-19 x^2+32 x^4-16 x^6\right )^2 \, dx=\frac {256 x^{13}}{13} - \frac {1024 x^{11}}{11} + \frac {544 x^{9}}{3} - \frac {1312 x^{7}}{7} + \frac {553 x^{5}}{5} - 38 x^{3} + 9 x \]
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Time = 0.19 (sec) , antiderivative size = 34, normalized size of antiderivative = 0.77 \[ \int \left (3-19 x^2+32 x^4-16 x^6\right )^2 \, dx=\frac {256}{13} \, x^{13} - \frac {1024}{11} \, x^{11} + \frac {544}{3} \, x^{9} - \frac {1312}{7} \, x^{7} + \frac {553}{5} \, x^{5} - 38 \, x^{3} + 9 \, x \]
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Time = 0.28 (sec) , antiderivative size = 34, normalized size of antiderivative = 0.77 \[ \int \left (3-19 x^2+32 x^4-16 x^6\right )^2 \, dx=\frac {256}{13} \, x^{13} - \frac {1024}{11} \, x^{11} + \frac {544}{3} \, x^{9} - \frac {1312}{7} \, x^{7} + \frac {553}{5} \, x^{5} - 38 \, x^{3} + 9 \, x \]
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Time = 0.01 (sec) , antiderivative size = 34, normalized size of antiderivative = 0.77 \[ \int \left (3-19 x^2+32 x^4-16 x^6\right )^2 \, dx=\frac {256\,x^{13}}{13}-\frac {1024\,x^{11}}{11}+\frac {544\,x^9}{3}-\frac {1312\,x^7}{7}+\frac {553\,x^5}{5}-38\,x^3+9\,x \]
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