Integrand size = 22, antiderivative size = 52 \[ \int \left (8+24 x+8 x^2-15 x^3+8 x^4\right )^2 \, dx=64 x+192 x^2+\frac {704 x^3}{3}+36 x^4-\frac {528 x^5}{5}+24 x^6+\frac {353 x^7}{7}-30 x^8+\frac {64 x^9}{9} \]
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Time = 0.01 (sec) , antiderivative size = 52, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {2086} \[ \int \left (8+24 x+8 x^2-15 x^3+8 x^4\right )^2 \, dx=\frac {64 x^9}{9}-30 x^8+\frac {353 x^7}{7}+24 x^6-\frac {528 x^5}{5}+36 x^4+\frac {704 x^3}{3}+192 x^2+64 x \]
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Rule 2086
Rubi steps \begin{align*} \text {integral}& = \int \left (64+384 x+704 x^2+144 x^3-528 x^4+144 x^5+353 x^6-240 x^7+64 x^8\right ) \, dx \\ & = 64 x+192 x^2+\frac {704 x^3}{3}+36 x^4-\frac {528 x^5}{5}+24 x^6+\frac {353 x^7}{7}-30 x^8+\frac {64 x^9}{9} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 52, normalized size of antiderivative = 1.00 \[ \int \left (8+24 x+8 x^2-15 x^3+8 x^4\right )^2 \, dx=64 x+192 x^2+\frac {704 x^3}{3}+36 x^4-\frac {528 x^5}{5}+24 x^6+\frac {353 x^7}{7}-30 x^8+\frac {64 x^9}{9} \]
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Time = 0.02 (sec) , antiderivative size = 45, normalized size of antiderivative = 0.87
method | result | size |
gosper | \(64 x +192 x^{2}+\frac {704}{3} x^{3}+36 x^{4}-\frac {528}{5} x^{5}+24 x^{6}+\frac {353}{7} x^{7}-30 x^{8}+\frac {64}{9} x^{9}\) | \(45\) |
default | \(64 x +192 x^{2}+\frac {704}{3} x^{3}+36 x^{4}-\frac {528}{5} x^{5}+24 x^{6}+\frac {353}{7} x^{7}-30 x^{8}+\frac {64}{9} x^{9}\) | \(45\) |
norman | \(64 x +192 x^{2}+\frac {704}{3} x^{3}+36 x^{4}-\frac {528}{5} x^{5}+24 x^{6}+\frac {353}{7} x^{7}-30 x^{8}+\frac {64}{9} x^{9}\) | \(45\) |
risch | \(64 x +192 x^{2}+\frac {704}{3} x^{3}+36 x^{4}-\frac {528}{5} x^{5}+24 x^{6}+\frac {353}{7} x^{7}-30 x^{8}+\frac {64}{9} x^{9}\) | \(45\) |
parallelrisch | \(64 x +192 x^{2}+\frac {704}{3} x^{3}+36 x^{4}-\frac {528}{5} x^{5}+24 x^{6}+\frac {353}{7} x^{7}-30 x^{8}+\frac {64}{9} x^{9}\) | \(45\) |
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Time = 0.24 (sec) , antiderivative size = 44, normalized size of antiderivative = 0.85 \[ \int \left (8+24 x+8 x^2-15 x^3+8 x^4\right )^2 \, dx=\frac {64}{9} \, x^{9} - 30 \, x^{8} + \frac {353}{7} \, x^{7} + 24 \, x^{6} - \frac {528}{5} \, x^{5} + 36 \, x^{4} + \frac {704}{3} \, x^{3} + 192 \, x^{2} + 64 \, x \]
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Time = 0.02 (sec) , antiderivative size = 49, normalized size of antiderivative = 0.94 \[ \int \left (8+24 x+8 x^2-15 x^3+8 x^4\right )^2 \, dx=\frac {64 x^{9}}{9} - 30 x^{8} + \frac {353 x^{7}}{7} + 24 x^{6} - \frac {528 x^{5}}{5} + 36 x^{4} + \frac {704 x^{3}}{3} + 192 x^{2} + 64 x \]
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Time = 0.19 (sec) , antiderivative size = 44, normalized size of antiderivative = 0.85 \[ \int \left (8+24 x+8 x^2-15 x^3+8 x^4\right )^2 \, dx=\frac {64}{9} \, x^{9} - 30 \, x^{8} + \frac {353}{7} \, x^{7} + 24 \, x^{6} - \frac {528}{5} \, x^{5} + 36 \, x^{4} + \frac {704}{3} \, x^{3} + 192 \, x^{2} + 64 \, x \]
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Time = 0.29 (sec) , antiderivative size = 44, normalized size of antiderivative = 0.85 \[ \int \left (8+24 x+8 x^2-15 x^3+8 x^4\right )^2 \, dx=\frac {64}{9} \, x^{9} - 30 \, x^{8} + \frac {353}{7} \, x^{7} + 24 \, x^{6} - \frac {528}{5} \, x^{5} + 36 \, x^{4} + \frac {704}{3} \, x^{3} + 192 \, x^{2} + 64 \, x \]
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Time = 0.02 (sec) , antiderivative size = 44, normalized size of antiderivative = 0.85 \[ \int \left (8+24 x+8 x^2-15 x^3+8 x^4\right )^2 \, dx=\frac {64\,x^9}{9}-30\,x^8+\frac {353\,x^7}{7}+24\,x^6-\frac {528\,x^5}{5}+36\,x^4+\frac {704\,x^3}{3}+192\,x^2+64\,x \]
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