Integrand size = 17, antiderivative size = 96 \[ \int \left (8+8 x-x^3+8 x^4\right )^4 \, dx=4096 x+8192 x^2+8192 x^3+3584 x^4+\frac {14336 x^5}{5}+7168 x^6+6784 x^7+1376 x^8+1408 x^9+\frac {21488 x^{10}}{5}+\frac {25312 x^{11}}{11}-448 x^{12}+\frac {10241 x^{13}}{13}+1168 x^{14}+\frac {128 x^{15}}{5}-128 x^{16}+\frac {4096 x^{17}}{17} \]
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Time = 0.02 (sec) , antiderivative size = 96, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.059, Rules used = {2086} \[ \int \left (8+8 x-x^3+8 x^4\right )^4 \, dx=\frac {4096 x^{17}}{17}-128 x^{16}+\frac {128 x^{15}}{5}+1168 x^{14}+\frac {10241 x^{13}}{13}-448 x^{12}+\frac {25312 x^{11}}{11}+\frac {21488 x^{10}}{5}+1408 x^9+1376 x^8+6784 x^7+7168 x^6+\frac {14336 x^5}{5}+3584 x^4+8192 x^3+8192 x^2+4096 x \]
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Rule 2086
Rubi steps \begin{align*} \text {integral}& = \int \left (4096+16384 x+24576 x^2+14336 x^3+14336 x^4+43008 x^5+47488 x^6+11008 x^7+12672 x^8+42976 x^9+25312 x^{10}-5376 x^{11}+10241 x^{12}+16352 x^{13}+384 x^{14}-2048 x^{15}+4096 x^{16}\right ) \, dx \\ & = 4096 x+8192 x^2+8192 x^3+3584 x^4+\frac {14336 x^5}{5}+7168 x^6+6784 x^7+1376 x^8+1408 x^9+\frac {21488 x^{10}}{5}+\frac {25312 x^{11}}{11}-448 x^{12}+\frac {10241 x^{13}}{13}+1168 x^{14}+\frac {128 x^{15}}{5}-128 x^{16}+\frac {4096 x^{17}}{17} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 96, normalized size of antiderivative = 1.00 \[ \int \left (8+8 x-x^3+8 x^4\right )^4 \, dx=4096 x+8192 x^2+8192 x^3+3584 x^4+\frac {14336 x^5}{5}+7168 x^6+6784 x^7+1376 x^8+1408 x^9+\frac {21488 x^{10}}{5}+\frac {25312 x^{11}}{11}-448 x^{12}+\frac {10241 x^{13}}{13}+1168 x^{14}+\frac {128 x^{15}}{5}-128 x^{16}+\frac {4096 x^{17}}{17} \]
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Time = 0.03 (sec) , antiderivative size = 85, normalized size of antiderivative = 0.89
method | result | size |
gosper | \(4096 x +8192 x^{2}+8192 x^{3}+3584 x^{4}+\frac {14336}{5} x^{5}+7168 x^{6}+6784 x^{7}+1376 x^{8}+1408 x^{9}+\frac {21488}{5} x^{10}+\frac {25312}{11} x^{11}-448 x^{12}+\frac {10241}{13} x^{13}+1168 x^{14}+\frac {128}{5} x^{15}-128 x^{16}+\frac {4096}{17} x^{17}\) | \(85\) |
default | \(4096 x +8192 x^{2}+8192 x^{3}+3584 x^{4}+\frac {14336}{5} x^{5}+7168 x^{6}+6784 x^{7}+1376 x^{8}+1408 x^{9}+\frac {21488}{5} x^{10}+\frac {25312}{11} x^{11}-448 x^{12}+\frac {10241}{13} x^{13}+1168 x^{14}+\frac {128}{5} x^{15}-128 x^{16}+\frac {4096}{17} x^{17}\) | \(85\) |
norman | \(4096 x +8192 x^{2}+8192 x^{3}+3584 x^{4}+\frac {14336}{5} x^{5}+7168 x^{6}+6784 x^{7}+1376 x^{8}+1408 x^{9}+\frac {21488}{5} x^{10}+\frac {25312}{11} x^{11}-448 x^{12}+\frac {10241}{13} x^{13}+1168 x^{14}+\frac {128}{5} x^{15}-128 x^{16}+\frac {4096}{17} x^{17}\) | \(85\) |
risch | \(4096 x +8192 x^{2}+8192 x^{3}+3584 x^{4}+\frac {14336}{5} x^{5}+7168 x^{6}+6784 x^{7}+1376 x^{8}+1408 x^{9}+\frac {21488}{5} x^{10}+\frac {25312}{11} x^{11}-448 x^{12}+\frac {10241}{13} x^{13}+1168 x^{14}+\frac {128}{5} x^{15}-128 x^{16}+\frac {4096}{17} x^{17}\) | \(85\) |
parallelrisch | \(4096 x +8192 x^{2}+8192 x^{3}+3584 x^{4}+\frac {14336}{5} x^{5}+7168 x^{6}+6784 x^{7}+1376 x^{8}+1408 x^{9}+\frac {21488}{5} x^{10}+\frac {25312}{11} x^{11}-448 x^{12}+\frac {10241}{13} x^{13}+1168 x^{14}+\frac {128}{5} x^{15}-128 x^{16}+\frac {4096}{17} x^{17}\) | \(85\) |
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Time = 0.28 (sec) , antiderivative size = 84, normalized size of antiderivative = 0.88 \[ \int \left (8+8 x-x^3+8 x^4\right )^4 \, dx=\frac {4096}{17} \, x^{17} - 128 \, x^{16} + \frac {128}{5} \, x^{15} + 1168 \, x^{14} + \frac {10241}{13} \, x^{13} - 448 \, x^{12} + \frac {25312}{11} \, x^{11} + \frac {21488}{5} \, x^{10} + 1408 \, x^{9} + 1376 \, x^{8} + 6784 \, x^{7} + 7168 \, x^{6} + \frac {14336}{5} \, x^{5} + 3584 \, x^{4} + 8192 \, x^{3} + 8192 \, x^{2} + 4096 \, x \]
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Time = 0.03 (sec) , antiderivative size = 94, normalized size of antiderivative = 0.98 \[ \int \left (8+8 x-x^3+8 x^4\right )^4 \, dx=\frac {4096 x^{17}}{17} - 128 x^{16} + \frac {128 x^{15}}{5} + 1168 x^{14} + \frac {10241 x^{13}}{13} - 448 x^{12} + \frac {25312 x^{11}}{11} + \frac {21488 x^{10}}{5} + 1408 x^{9} + 1376 x^{8} + 6784 x^{7} + 7168 x^{6} + \frac {14336 x^{5}}{5} + 3584 x^{4} + 8192 x^{3} + 8192 x^{2} + 4096 x \]
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Time = 0.19 (sec) , antiderivative size = 84, normalized size of antiderivative = 0.88 \[ \int \left (8+8 x-x^3+8 x^4\right )^4 \, dx=\frac {4096}{17} \, x^{17} - 128 \, x^{16} + \frac {128}{5} \, x^{15} + 1168 \, x^{14} + \frac {10241}{13} \, x^{13} - 448 \, x^{12} + \frac {25312}{11} \, x^{11} + \frac {21488}{5} \, x^{10} + 1408 \, x^{9} + 1376 \, x^{8} + 6784 \, x^{7} + 7168 \, x^{6} + \frac {14336}{5} \, x^{5} + 3584 \, x^{4} + 8192 \, x^{3} + 8192 \, x^{2} + 4096 \, x \]
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Time = 0.29 (sec) , antiderivative size = 84, normalized size of antiderivative = 0.88 \[ \int \left (8+8 x-x^3+8 x^4\right )^4 \, dx=\frac {4096}{17} \, x^{17} - 128 \, x^{16} + \frac {128}{5} \, x^{15} + 1168 \, x^{14} + \frac {10241}{13} \, x^{13} - 448 \, x^{12} + \frac {25312}{11} \, x^{11} + \frac {21488}{5} \, x^{10} + 1408 \, x^{9} + 1376 \, x^{8} + 6784 \, x^{7} + 7168 \, x^{6} + \frac {14336}{5} \, x^{5} + 3584 \, x^{4} + 8192 \, x^{3} + 8192 \, x^{2} + 4096 \, x \]
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Time = 0.20 (sec) , antiderivative size = 84, normalized size of antiderivative = 0.88 \[ \int \left (8+8 x-x^3+8 x^4\right )^4 \, dx=\frac {4096\,x^{17}}{17}-128\,x^{16}+\frac {128\,x^{15}}{5}+1168\,x^{14}+\frac {10241\,x^{13}}{13}-448\,x^{12}+\frac {25312\,x^{11}}{11}+\frac {21488\,x^{10}}{5}+1408\,x^9+1376\,x^8+6784\,x^7+7168\,x^6+\frac {14336\,x^5}{5}+3584\,x^4+8192\,x^3+8192\,x^2+4096\,x \]
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