Optimal. Leaf size=54 \[ 2 x-\frac {64 x^3}{3}+\frac {336 x^5}{5}-96 x^7+\frac {220 x^9}{3}-32 x^{11}+8 x^{13}-\frac {16 x^{15}}{15}+\frac {x^{17}}{17} \]
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Rubi [A]
time = 0.01, antiderivative size = 54, normalized size of antiderivative = 1.00, number of steps
used = 3, number of rules used = 1, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.059, Rules used = {2086}
\begin {gather*} \frac {x^{17}}{17}-\frac {16 x^{15}}{15}+8 x^{13}-32 x^{11}+\frac {220 x^9}{3}-96 x^7+\frac {336 x^5}{5}-\frac {64 x^3}{3}+2 x \end {gather*}
Antiderivative was successfully verified.
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Rule 2086
Rubi steps
\begin {gather*} \begin {aligned} \text {Integral} &=-2 x+\int \left (-2+\left (-2+\left (-2+x^2\right )^2\right )^2\right )^2 \, dx\\ &=-2 x+\int \left (4-64 x^2+336 x^4-672 x^6+660 x^8-352 x^{10}+104 x^{12}-16 x^{14}+x^{16}\right ) \, dx\\ &=2 x-\frac {64 x^3}{3}+\frac {336 x^5}{5}-96 x^7+\frac {220 x^9}{3}-32 x^{11}+8 x^{13}-\frac {16 x^{15}}{15}+\frac {x^{17}}{17}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 54, normalized size = 1.00 \begin {gather*} 2 x-\frac {64 x^3}{3}+\frac {336 x^5}{5}-96 x^7+\frac {220 x^9}{3}-32 x^{11}+8 x^{13}-\frac {16 x^{15}}{15}+\frac {x^{17}}{17} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.08, size = 45, normalized size = 0.83
method | result | size |
default | \(2 x -\frac {64}{3} x^{3}+\frac {336}{5} x^{5}-96 x^{7}+\frac {220}{3} x^{9}-32 x^{11}+8 x^{13}-\frac {16}{15} x^{15}+\frac {1}{17} x^{17}\) | \(45\) |
norman | \(2 x -\frac {64}{3} x^{3}+\frac {336}{5} x^{5}-96 x^{7}+\frac {220}{3} x^{9}-32 x^{11}+8 x^{13}-\frac {16}{15} x^{15}+\frac {1}{17} x^{17}\) | \(45\) |
risch | \(2 x -\frac {64}{3} x^{3}+\frac {336}{5} x^{5}-96 x^{7}+\frac {220}{3} x^{9}-32 x^{11}+8 x^{13}-\frac {16}{15} x^{15}+\frac {1}{17} x^{17}\) | \(45\) |
parallelrisch | \(2 x -\frac {64}{3} x^{3}+\frac {336}{5} x^{5}-96 x^{7}+\frac {220}{3} x^{9}-32 x^{11}+8 x^{13}-\frac {16}{15} x^{15}+\frac {1}{17} x^{17}\) | \(45\) |
parts | \(2 x -\frac {64}{3} x^{3}+\frac {336}{5} x^{5}-96 x^{7}+\frac {220}{3} x^{9}-32 x^{11}+8 x^{13}-\frac {16}{15} x^{15}+\frac {1}{17} x^{17}\) | \(45\) |
gosper | \(\frac {x \left (15 x^{16}-272 x^{14}+2040 x^{12}-8160 x^{10}+18700 x^{8}-24480 x^{6}+17136 x^{4}-5440 x^{2}+510\right )}{255}\) | \(46\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.34, size = 44, normalized size = 0.81 \begin {gather*} \frac {1}{17} \, x^{17} - \frac {16}{15} \, x^{15} + 8 \, x^{13} - 32 \, x^{11} + \frac {220}{3} \, x^{9} - 96 \, x^{7} + \frac {336}{5} \, x^{5} - \frac {64}{3} \, x^{3} + 2 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.56, size = 44, normalized size = 0.81 \begin {gather*} \frac {1}{17} \, x^{17} - \frac {16}{15} \, x^{15} + 8 \, x^{13} - 32 \, x^{11} + \frac {220}{3} \, x^{9} - 96 \, x^{7} + \frac {336}{5} \, x^{5} - \frac {64}{3} \, x^{3} + 2 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 49, normalized size = 0.91 \begin {gather*} \frac {x^{17}}{17} - \frac {16 x^{15}}{15} + 8 x^{13} - 32 x^{11} + \frac {220 x^{9}}{3} - 96 x^{7} + \frac {336 x^{5}}{5} - \frac {64 x^{3}}{3} + 2 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.45, size = 44, normalized size = 0.81 \begin {gather*} \frac {1}{17} \, x^{17} - \frac {16}{15} \, x^{15} + 8 \, x^{13} - 32 \, x^{11} + \frac {220}{3} \, x^{9} - 96 \, x^{7} + \frac {336}{5} \, x^{5} - \frac {64}{3} \, x^{3} + 2 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.10, size = 44, normalized size = 0.81 \begin {gather*} \frac {x^{17}}{17}-\frac {16\,x^{15}}{15}+8\,x^{13}-32\,x^{11}+\frac {220\,x^9}{3}-96\,x^7+\frac {336\,x^5}{5}-\frac {64\,x^3}{3}+2\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Chatgpt [F] Failed to verify
time = 1.00, size = 25, normalized size = 0.46 \begin {gather*} \frac {\left (x^{2}-2\right )^{5}}{10}-\frac {4 \left (x^{2}-2\right )^{3}}{3}+2 x^{2}-4 \end {gather*}
Warning: Unable to verify antiderivative.
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