Integrand size = 19, antiderivative size = 84 \[ \int \left (3-19 x^2+32 x^4-16 x^6\right )^4 \, dx=81 x-684 x^3+4590 x^5-\frac {149700 x^7}{7}+\frac {634321 x^9}{9}-\frac {1841600 x^{11}}{11}+\frac {3764416 x^{13}}{13}-\frac {1094656 x^{15}}{3}+\frac {5633536 x^{17}}{17}-\frac {4014080 x^{19}}{19}+\frac {1884160 x^{21}}{21}-\frac {524288 x^{23}}{23}+\frac {65536 x^{25}}{25} \]
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Time = 0.05 (sec) , antiderivative size = 84, 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} \[ \int \left (3-19 x^2+32 x^4-16 x^6\right )^4 \, dx=\frac {65536 x^{25}}{25}-\frac {524288 x^{23}}{23}+\frac {1884160 x^{21}}{21}-\frac {4014080 x^{19}}{19}+\frac {5633536 x^{17}}{17}-\frac {1094656 x^{15}}{3}+\frac {3764416 x^{13}}{13}-\frac {1841600 x^{11}}{11}+\frac {634321 x^9}{9}-\frac {149700 x^7}{7}+4590 x^5-684 x^3+81 x \]
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Rule 531
Rule 535
Rule 2084
Rubi steps \begin{align*} \text {integral}& = \int (-1+x)^4 (1+x)^4 (-1+2 x)^4 (1+2 x)^4 \left (-3+4 x^2\right )^4 \, dx \\ & = \int (-1+2 x)^4 (1+2 x)^4 \left (-1+x^2\right )^4 \left (-3+4 x^2\right )^4 \, dx \\ & = \int \left (-1+x^2\right )^4 \left (-3+4 x^2\right )^4 \left (-1+4 x^2\right )^4 \, dx \\ & = \int \left (81-2052 x^2+22950 x^4-149700 x^6+634321 x^8-1841600 x^{10}+3764416 x^{12}-5473280 x^{14}+5633536 x^{16}-4014080 x^{18}+1884160 x^{20}-524288 x^{22}+65536 x^{24}\right ) \, dx \\ & = 81 x-684 x^3+4590 x^5-\frac {149700 x^7}{7}+\frac {634321 x^9}{9}-\frac {1841600 x^{11}}{11}+\frac {3764416 x^{13}}{13}-\frac {1094656 x^{15}}{3}+\frac {5633536 x^{17}}{17}-\frac {4014080 x^{19}}{19}+\frac {1884160 x^{21}}{21}-\frac {524288 x^{23}}{23}+\frac {65536 x^{25}}{25} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 84, normalized size of antiderivative = 1.00 \[ \int \left (3-19 x^2+32 x^4-16 x^6\right )^4 \, dx=81 x-684 x^3+4590 x^5-\frac {149700 x^7}{7}+\frac {634321 x^9}{9}-\frac {1841600 x^{11}}{11}+\frac {3764416 x^{13}}{13}-\frac {1094656 x^{15}}{3}+\frac {5633536 x^{17}}{17}-\frac {4014080 x^{19}}{19}+\frac {1884160 x^{21}}{21}-\frac {524288 x^{23}}{23}+\frac {65536 x^{25}}{25} \]
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Time = 0.04 (sec) , antiderivative size = 65, normalized size of antiderivative = 0.77
method | result | size |
default | \(81 x -684 x^{3}+4590 x^{5}-\frac {149700}{7} x^{7}+\frac {634321}{9} x^{9}-\frac {1841600}{11} x^{11}+\frac {3764416}{13} x^{13}-\frac {1094656}{3} x^{15}+\frac {5633536}{17} x^{17}-\frac {4014080}{19} x^{19}+\frac {1884160}{21} x^{21}-\frac {524288}{23} x^{23}+\frac {65536}{25} x^{25}\) | \(65\) |
norman | \(81 x -684 x^{3}+4590 x^{5}-\frac {149700}{7} x^{7}+\frac {634321}{9} x^{9}-\frac {1841600}{11} x^{11}+\frac {3764416}{13} x^{13}-\frac {1094656}{3} x^{15}+\frac {5633536}{17} x^{17}-\frac {4014080}{19} x^{19}+\frac {1884160}{21} x^{21}-\frac {524288}{23} x^{23}+\frac {65536}{25} x^{25}\) | \(65\) |
risch | \(81 x -684 x^{3}+4590 x^{5}-\frac {149700}{7} x^{7}+\frac {634321}{9} x^{9}-\frac {1841600}{11} x^{11}+\frac {3764416}{13} x^{13}-\frac {1094656}{3} x^{15}+\frac {5633536}{17} x^{17}-\frac {4014080}{19} x^{19}+\frac {1884160}{21} x^{21}-\frac {524288}{23} x^{23}+\frac {65536}{25} x^{25}\) | \(65\) |
parallelrisch | \(81 x -684 x^{3}+4590 x^{5}-\frac {149700}{7} x^{7}+\frac {634321}{9} x^{9}-\frac {1841600}{11} x^{11}+\frac {3764416}{13} x^{13}-\frac {1094656}{3} x^{15}+\frac {5633536}{17} x^{17}-\frac {4014080}{19} x^{19}+\frac {1884160}{21} x^{21}-\frac {524288}{23} x^{23}+\frac {65536}{25} x^{25}\) | \(65\) |
gosper | \(\frac {x \left (4386184298496 x^{24}-38140733030400 x^{22}+150122379264000 x^{20}-353491826688000 x^{18}+554471344627200 x^{16}-610524871756800 x^{14}+484508289988800 x^{12}-280123520040000 x^{10}+117927076992725 x^{8}-35782502827500 x^{6}+7679972049750 x^{4}-1144466423100 x^{2}+135528918525\right )}{1673196525}\) | \(66\) |
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Time = 0.26 (sec) , antiderivative size = 64, normalized size of antiderivative = 0.76 \[ \int \left (3-19 x^2+32 x^4-16 x^6\right )^4 \, dx=\frac {65536}{25} \, x^{25} - \frac {524288}{23} \, x^{23} + \frac {1884160}{21} \, x^{21} - \frac {4014080}{19} \, x^{19} + \frac {5633536}{17} \, x^{17} - \frac {1094656}{3} \, x^{15} + \frac {3764416}{13} \, x^{13} - \frac {1841600}{11} \, x^{11} + \frac {634321}{9} \, x^{9} - \frac {149700}{7} \, x^{7} + 4590 \, x^{5} - 684 \, x^{3} + 81 \, x \]
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Time = 0.03 (sec) , antiderivative size = 80, normalized size of antiderivative = 0.95 \[ \int \left (3-19 x^2+32 x^4-16 x^6\right )^4 \, dx=\frac {65536 x^{25}}{25} - \frac {524288 x^{23}}{23} + \frac {1884160 x^{21}}{21} - \frac {4014080 x^{19}}{19} + \frac {5633536 x^{17}}{17} - \frac {1094656 x^{15}}{3} + \frac {3764416 x^{13}}{13} - \frac {1841600 x^{11}}{11} + \frac {634321 x^{9}}{9} - \frac {149700 x^{7}}{7} + 4590 x^{5} - 684 x^{3} + 81 x \]
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Time = 0.20 (sec) , antiderivative size = 64, normalized size of antiderivative = 0.76 \[ \int \left (3-19 x^2+32 x^4-16 x^6\right )^4 \, dx=\frac {65536}{25} \, x^{25} - \frac {524288}{23} \, x^{23} + \frac {1884160}{21} \, x^{21} - \frac {4014080}{19} \, x^{19} + \frac {5633536}{17} \, x^{17} - \frac {1094656}{3} \, x^{15} + \frac {3764416}{13} \, x^{13} - \frac {1841600}{11} \, x^{11} + \frac {634321}{9} \, x^{9} - \frac {149700}{7} \, x^{7} + 4590 \, x^{5} - 684 \, x^{3} + 81 \, x \]
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Time = 0.27 (sec) , antiderivative size = 64, normalized size of antiderivative = 0.76 \[ \int \left (3-19 x^2+32 x^4-16 x^6\right )^4 \, dx=\frac {65536}{25} \, x^{25} - \frac {524288}{23} \, x^{23} + \frac {1884160}{21} \, x^{21} - \frac {4014080}{19} \, x^{19} + \frac {5633536}{17} \, x^{17} - \frac {1094656}{3} \, x^{15} + \frac {3764416}{13} \, x^{13} - \frac {1841600}{11} \, x^{11} + \frac {634321}{9} \, x^{9} - \frac {149700}{7} \, x^{7} + 4590 \, x^{5} - 684 \, x^{3} + 81 \, x \]
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Time = 0.08 (sec) , antiderivative size = 64, normalized size of antiderivative = 0.76 \[ \int \left (3-19 x^2+32 x^4-16 x^6\right )^4 \, dx=\frac {65536\,x^{25}}{25}-\frac {524288\,x^{23}}{23}+\frac {1884160\,x^{21}}{21}-\frac {4014080\,x^{19}}{19}+\frac {5633536\,x^{17}}{17}-\frac {1094656\,x^{15}}{3}+\frac {3764416\,x^{13}}{13}-\frac {1841600\,x^{11}}{11}+\frac {634321\,x^9}{9}-\frac {149700\,x^7}{7}+4590\,x^5-684\,x^3+81\,x \]
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