Integrand size = 19, antiderivative size = 63 \[ \int \left (3-19 x^2+32 x^4-16 x^6\right )^3 \, dx=27 x-171 x^3+\frac {4113 x^5}{5}-2605 x^7+\frac {16448 x^9}{3}-\frac {84912 x^{11}}{11}+\frac {93440 x^{13}}{13}-\frac {21248 x^{15}}{5}+\frac {24576 x^{17}}{17}-\frac {4096 x^{19}}{19} \]
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Time = 0.05 (sec) , antiderivative size = 63, 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} \[ \int \left (3-19 x^2+32 x^4-16 x^6\right )^3 \, dx=-\frac {4096 x^{19}}{19}+\frac {24576 x^{17}}{17}-\frac {21248 x^{15}}{5}+\frac {93440 x^{13}}{13}-\frac {84912 x^{11}}{11}+\frac {16448 x^9}{3}-2605 x^7+\frac {4113 x^5}{5}-171 x^3+27 x \]
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Rule 531
Rule 535
Rule 2084
Rubi steps \begin{align*} \text {integral}& = -\int (-1+x)^3 (1+x)^3 (-1+2 x)^3 (1+2 x)^3 \left (-3+4 x^2\right )^3 \, dx \\ & = -\int (-1+2 x)^3 (1+2 x)^3 \left (-1+x^2\right )^3 \left (-3+4 x^2\right )^3 \, dx \\ & = -\int \left (-1+x^2\right )^3 \left (-3+4 x^2\right )^3 \left (-1+4 x^2\right )^3 \, dx \\ & = -\int \left (-27+513 x^2-4113 x^4+18235 x^6-49344 x^8+84912 x^{10}-93440 x^{12}+63744 x^{14}-24576 x^{16}+4096 x^{18}\right ) \, dx \\ & = 27 x-171 x^3+\frac {4113 x^5}{5}-2605 x^7+\frac {16448 x^9}{3}-\frac {84912 x^{11}}{11}+\frac {93440 x^{13}}{13}-\frac {21248 x^{15}}{5}+\frac {24576 x^{17}}{17}-\frac {4096 x^{19}}{19} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 63, normalized size of antiderivative = 1.00 \[ \int \left (3-19 x^2+32 x^4-16 x^6\right )^3 \, dx=27 x-171 x^3+\frac {4113 x^5}{5}-2605 x^7+\frac {16448 x^9}{3}-\frac {84912 x^{11}}{11}+\frac {93440 x^{13}}{13}-\frac {21248 x^{15}}{5}+\frac {24576 x^{17}}{17}-\frac {4096 x^{19}}{19} \]
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Time = 0.03 (sec) , antiderivative size = 50, normalized size of antiderivative = 0.79
method | result | size |
default | \(27 x -171 x^{3}+\frac {4113}{5} x^{5}-2605 x^{7}+\frac {16448}{3} x^{9}-\frac {84912}{11} x^{11}+\frac {93440}{13} x^{13}-\frac {21248}{5} x^{15}+\frac {24576}{17} x^{17}-\frac {4096}{19} x^{19}\) | \(50\) |
norman | \(27 x -171 x^{3}+\frac {4113}{5} x^{5}-2605 x^{7}+\frac {16448}{3} x^{9}-\frac {84912}{11} x^{11}+\frac {93440}{13} x^{13}-\frac {21248}{5} x^{15}+\frac {24576}{17} x^{17}-\frac {4096}{19} x^{19}\) | \(50\) |
risch | \(27 x -171 x^{3}+\frac {4113}{5} x^{5}-2605 x^{7}+\frac {16448}{3} x^{9}-\frac {84912}{11} x^{11}+\frac {93440}{13} x^{13}-\frac {21248}{5} x^{15}+\frac {24576}{17} x^{17}-\frac {4096}{19} x^{19}\) | \(50\) |
parallelrisch | \(27 x -171 x^{3}+\frac {4113}{5} x^{5}-2605 x^{7}+\frac {16448}{3} x^{9}-\frac {84912}{11} x^{11}+\frac {93440}{13} x^{13}-\frac {21248}{5} x^{15}+\frac {24576}{17} x^{17}-\frac {4096}{19} x^{19}\) | \(50\) |
gosper | \(-\frac {x \left (149360640 x^{18}-1001594880 x^{16}+2944271616 x^{14}-4979884800 x^{12}+5348182320 x^{10}-3798583360 x^{8}+1804835175 x^{6}-569926071 x^{4}+118474785 x^{2}-18706545\right )}{692835}\) | \(51\) |
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Time = 0.24 (sec) , antiderivative size = 49, normalized size of antiderivative = 0.78 \[ \int \left (3-19 x^2+32 x^4-16 x^6\right )^3 \, dx=-\frac {4096}{19} \, x^{19} + \frac {24576}{17} \, x^{17} - \frac {21248}{5} \, x^{15} + \frac {93440}{13} \, x^{13} - \frac {84912}{11} \, x^{11} + \frac {16448}{3} \, x^{9} - 2605 \, x^{7} + \frac {4113}{5} \, x^{5} - 171 \, x^{3} + 27 \, x \]
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Time = 0.03 (sec) , antiderivative size = 60, normalized size of antiderivative = 0.95 \[ \int \left (3-19 x^2+32 x^4-16 x^6\right )^3 \, dx=- \frac {4096 x^{19}}{19} + \frac {24576 x^{17}}{17} - \frac {21248 x^{15}}{5} + \frac {93440 x^{13}}{13} - \frac {84912 x^{11}}{11} + \frac {16448 x^{9}}{3} - 2605 x^{7} + \frac {4113 x^{5}}{5} - 171 x^{3} + 27 x \]
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Time = 0.19 (sec) , antiderivative size = 49, normalized size of antiderivative = 0.78 \[ \int \left (3-19 x^2+32 x^4-16 x^6\right )^3 \, dx=-\frac {4096}{19} \, x^{19} + \frac {24576}{17} \, x^{17} - \frac {21248}{5} \, x^{15} + \frac {93440}{13} \, x^{13} - \frac {84912}{11} \, x^{11} + \frac {16448}{3} \, x^{9} - 2605 \, x^{7} + \frac {4113}{5} \, x^{5} - 171 \, x^{3} + 27 \, x \]
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Time = 0.28 (sec) , antiderivative size = 49, normalized size of antiderivative = 0.78 \[ \int \left (3-19 x^2+32 x^4-16 x^6\right )^3 \, dx=-\frac {4096}{19} \, x^{19} + \frac {24576}{17} \, x^{17} - \frac {21248}{5} \, x^{15} + \frac {93440}{13} \, x^{13} - \frac {84912}{11} \, x^{11} + \frac {16448}{3} \, x^{9} - 2605 \, x^{7} + \frac {4113}{5} \, x^{5} - 171 \, x^{3} + 27 \, x \]
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Time = 0.05 (sec) , antiderivative size = 49, normalized size of antiderivative = 0.78 \[ \int \left (3-19 x^2+32 x^4-16 x^6\right )^3 \, dx=-\frac {4096\,x^{19}}{19}+\frac {24576\,x^{17}}{17}-\frac {21248\,x^{15}}{5}+\frac {93440\,x^{13}}{13}-\frac {84912\,x^{11}}{11}+\frac {16448\,x^9}{3}-2605\,x^7+\frac {4113\,x^5}{5}-171\,x^3+27\,x \]
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