Optimal. Leaf size=96 \[ \frac{4096 x^{17}}{17}-128 x^{16}+\frac{128 x^{15}}{5}+1168 x^{14}+\frac{10241 x^{13}}{13}-448 x^{12}+\frac{25312 x^{11}}{11}+\frac{21488 x^{10}}{5}+1408 x^9+1376 x^8+6784 x^7+7168 x^6+\frac{14336 x^5}{5}+3584 x^4+8192 x^3+8192 x^2+4096 x \]
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Rubi [A] time = 0.0301725, antiderivative size = 96, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.059, Rules used = {2061} \[ \frac{4096 x^{17}}{17}-128 x^{16}+\frac{128 x^{15}}{5}+1168 x^{14}+\frac{10241 x^{13}}{13}-448 x^{12}+\frac{25312 x^{11}}{11}+\frac{21488 x^{10}}{5}+1408 x^9+1376 x^8+6784 x^7+7168 x^6+\frac{14336 x^5}{5}+3584 x^4+8192 x^3+8192 x^2+4096 x \]
Antiderivative was successfully verified.
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Rule 2061
Rubi steps
\begin{align*} \int \left (8+8 x-x^3+8 x^4\right )^4 \, dx &=\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*}
Mathematica [A] time = 0.0015055, size = 96, normalized size = 1. \[ \frac{4096 x^{17}}{17}-128 x^{16}+\frac{128 x^{15}}{5}+1168 x^{14}+\frac{10241 x^{13}}{13}-448 x^{12}+\frac{25312 x^{11}}{11}+\frac{21488 x^{10}}{5}+1408 x^9+1376 x^8+6784 x^7+7168 x^6+\frac{14336 x^5}{5}+3584 x^4+8192 x^3+8192 x^2+4096 x \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 85, normalized size = 0.9 \begin{align*} 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*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.04722, size = 113, normalized size = 1.18 \begin{align*} \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 \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.11129, size = 281, normalized size = 2.93 \begin{align*} \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 \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.073529, size = 94, normalized size = 0.98 \begin{align*} \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 \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.16385, size = 113, normalized size = 1.18 \begin{align*} \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 \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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