Optimal. Leaf size=84 \[ \frac {65536 x^{25}}{25}-\frac {524288 x^{23}}{23}+\frac {1884160 x^{21}}{21}-\frac {4014080 x^{19}}{19}+\frac {5633536 x^{17}}{17}-\frac {1094656 x^{15}}{3}+\frac {3764416 x^{13}}{13}-\frac {1841600 x^{11}}{11}+\frac {634321 x^9}{9}-\frac {149700 x^7}{7}+4590 x^5-684 x^3+81 x \]
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Rubi [A] time = 0.09, antiderivative size = 84, 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} \[ \frac {65536 x^{25}}{25}-\frac {524288 x^{23}}{23}+\frac {1884160 x^{21}}{21}-\frac {4014080 x^{19}}{19}+\frac {5633536 x^{17}}{17}-\frac {1094656 x^{15}}{3}+\frac {3764416 x^{13}}{13}-\frac {1841600 x^{11}}{11}+\frac {634321 x^9}{9}-\frac {149700 x^7}{7}+4590 x^5-684 x^3+81 x \]
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 )^4 \, dx &=\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*}
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Mathematica [A] time = 0.00, size = 84, normalized size = 1.00 \[ \frac {65536 x^{25}}{25}-\frac {524288 x^{23}}{23}+\frac {1884160 x^{21}}{21}-\frac {4014080 x^{19}}{19}+\frac {5633536 x^{17}}{17}-\frac {1094656 x^{15}}{3}+\frac {3764416 x^{13}}{13}-\frac {1841600 x^{11}}{11}+\frac {634321 x^9}{9}-\frac {149700 x^7}{7}+4590 x^5-684 x^3+81 x \]
Antiderivative was successfully verified.
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fricas [A] time = 0.49, size = 64, normalized size = 0.76 \[ \frac {65536}{25} x^{25} - \frac {524288}{23} x^{23} + \frac {1884160}{21} x^{21} - \frac {4014080}{19} x^{19} + \frac {5633536}{17} x^{17} - \frac {1094656}{3} x^{15} + \frac {3764416}{13} x^{13} - \frac {1841600}{11} x^{11} + \frac {634321}{9} x^{9} - \frac {149700}{7} x^{7} + 4590 x^{5} - 684 x^{3} + 81 x \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.38, size = 64, normalized size = 0.76 \[ \frac {65536}{25} \, x^{25} - \frac {524288}{23} \, x^{23} + \frac {1884160}{21} \, x^{21} - \frac {4014080}{19} \, x^{19} + \frac {5633536}{17} \, x^{17} - \frac {1094656}{3} \, x^{15} + \frac {3764416}{13} \, x^{13} - \frac {1841600}{11} \, x^{11} + \frac {634321}{9} \, x^{9} - \frac {149700}{7} \, x^{7} + 4590 \, x^{5} - 684 \, x^{3} + 81 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 65, normalized size = 0.77 \[ \frac {65536}{25} x^{25}-\frac {524288}{23} x^{23}+\frac {1884160}{21} x^{21}-\frac {4014080}{19} x^{19}+\frac {5633536}{17} x^{17}-\frac {1094656}{3} x^{15}+\frac {3764416}{13} x^{13}-\frac {1841600}{11} x^{11}+\frac {634321}{9} x^{9}-\frac {149700}{7} x^{7}+4590 x^{5}-684 x^{3}+81 x \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.49, size = 64, normalized size = 0.76 \[ \frac {65536}{25} \, x^{25} - \frac {524288}{23} \, x^{23} + \frac {1884160}{21} \, x^{21} - \frac {4014080}{19} \, x^{19} + \frac {5633536}{17} \, x^{17} - \frac {1094656}{3} \, x^{15} + \frac {3764416}{13} \, x^{13} - \frac {1841600}{11} \, x^{11} + \frac {634321}{9} \, x^{9} - \frac {149700}{7} \, x^{7} + 4590 \, x^{5} - 684 \, x^{3} + 81 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.17, size = 64, normalized size = 0.76 \[ \frac {65536\,x^{25}}{25}-\frac {524288\,x^{23}}{23}+\frac {1884160\,x^{21}}{21}-\frac {4014080\,x^{19}}{19}+\frac {5633536\,x^{17}}{17}-\frac {1094656\,x^{15}}{3}+\frac {3764416\,x^{13}}{13}-\frac {1841600\,x^{11}}{11}+\frac {634321\,x^9}{9}-\frac {149700\,x^7}{7}+4590\,x^5-684\,x^3+81\,x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.08, size = 80, normalized size = 0.95 \[ \frac {65536 x^{25}}{25} - \frac {524288 x^{23}}{23} + \frac {1884160 x^{21}}{21} - \frac {4014080 x^{19}}{19} + \frac {5633536 x^{17}}{17} - \frac {1094656 x^{15}}{3} + \frac {3764416 x^{13}}{13} - \frac {1841600 x^{11}}{11} + \frac {634321 x^{9}}{9} - \frac {149700 x^{7}}{7} + 4590 x^{5} - 684 x^{3} + 81 x \]
Verification of antiderivative is not currently implemented for this CAS.
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