Integrand size = 22, antiderivative size = 76 \[ \int \left (8+24 x+8 x^2-15 x^3+8 x^4\right )^3 \, dx=512 x+2304 x^2+5120 x^3+5040 x^4-\frac {384 x^5}{5}-2976 x^6+\frac {5528 x^7}{7}+2097 x^8-\frac {2936 x^9}{3}-\frac {4527 x^{10}}{10}+\frac {6936 x^{11}}{11}-240 x^{12}+\frac {512 x^{13}}{13} \]
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Time = 0.02 (sec) , antiderivative size = 76, 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} \[ \int \left (8+24 x+8 x^2-15 x^3+8 x^4\right )^3 \, dx=\frac {512 x^{13}}{13}-240 x^{12}+\frac {6936 x^{11}}{11}-\frac {4527 x^{10}}{10}-\frac {2936 x^9}{3}+2097 x^8+\frac {5528 x^7}{7}-2976 x^6-\frac {384 x^5}{5}+5040 x^4+5120 x^3+2304 x^2+512 x \]
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Rule 2086
Rubi steps \begin{align*} \text {integral}& = \int \left (512+4608 x+15360 x^2+20160 x^3-384 x^4-17856 x^5+5528 x^6+16776 x^7-8808 x^8-4527 x^9+6936 x^{10}-2880 x^{11}+512 x^{12}\right ) \, dx \\ & = 512 x+2304 x^2+5120 x^3+5040 x^4-\frac {384 x^5}{5}-2976 x^6+\frac {5528 x^7}{7}+2097 x^8-\frac {2936 x^9}{3}-\frac {4527 x^{10}}{10}+\frac {6936 x^{11}}{11}-240 x^{12}+\frac {512 x^{13}}{13} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 76, normalized size of antiderivative = 1.00 \[ \int \left (8+24 x+8 x^2-15 x^3+8 x^4\right )^3 \, dx=512 x+2304 x^2+5120 x^3+5040 x^4-\frac {384 x^5}{5}-2976 x^6+\frac {5528 x^7}{7}+2097 x^8-\frac {2936 x^9}{3}-\frac {4527 x^{10}}{10}+\frac {6936 x^{11}}{11}-240 x^{12}+\frac {512 x^{13}}{13} \]
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Time = 0.03 (sec) , antiderivative size = 65, normalized size of antiderivative = 0.86
method | result | size |
gosper | \(512 x +2304 x^{2}+5120 x^{3}+5040 x^{4}-\frac {384}{5} x^{5}-2976 x^{6}+\frac {5528}{7} x^{7}+2097 x^{8}-\frac {2936}{3} x^{9}-\frac {4527}{10} x^{10}+\frac {6936}{11} x^{11}-240 x^{12}+\frac {512}{13} x^{13}\) | \(65\) |
default | \(512 x +2304 x^{2}+5120 x^{3}+5040 x^{4}-\frac {384}{5} x^{5}-2976 x^{6}+\frac {5528}{7} x^{7}+2097 x^{8}-\frac {2936}{3} x^{9}-\frac {4527}{10} x^{10}+\frac {6936}{11} x^{11}-240 x^{12}+\frac {512}{13} x^{13}\) | \(65\) |
norman | \(512 x +2304 x^{2}+5120 x^{3}+5040 x^{4}-\frac {384}{5} x^{5}-2976 x^{6}+\frac {5528}{7} x^{7}+2097 x^{8}-\frac {2936}{3} x^{9}-\frac {4527}{10} x^{10}+\frac {6936}{11} x^{11}-240 x^{12}+\frac {512}{13} x^{13}\) | \(65\) |
risch | \(512 x +2304 x^{2}+5120 x^{3}+5040 x^{4}-\frac {384}{5} x^{5}-2976 x^{6}+\frac {5528}{7} x^{7}+2097 x^{8}-\frac {2936}{3} x^{9}-\frac {4527}{10} x^{10}+\frac {6936}{11} x^{11}-240 x^{12}+\frac {512}{13} x^{13}\) | \(65\) |
parallelrisch | \(512 x +2304 x^{2}+5120 x^{3}+5040 x^{4}-\frac {384}{5} x^{5}-2976 x^{6}+\frac {5528}{7} x^{7}+2097 x^{8}-\frac {2936}{3} x^{9}-\frac {4527}{10} x^{10}+\frac {6936}{11} x^{11}-240 x^{12}+\frac {512}{13} x^{13}\) | \(65\) |
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Time = 0.26 (sec) , antiderivative size = 64, normalized size of antiderivative = 0.84 \[ \int \left (8+24 x+8 x^2-15 x^3+8 x^4\right )^3 \, dx=\frac {512}{13} \, x^{13} - 240 \, x^{12} + \frac {6936}{11} \, x^{11} - \frac {4527}{10} \, x^{10} - \frac {2936}{3} \, x^{9} + 2097 \, x^{8} + \frac {5528}{7} \, x^{7} - 2976 \, x^{6} - \frac {384}{5} \, x^{5} + 5040 \, x^{4} + 5120 \, x^{3} + 2304 \, x^{2} + 512 \, x \]
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Time = 0.03 (sec) , antiderivative size = 73, normalized size of antiderivative = 0.96 \[ \int \left (8+24 x+8 x^2-15 x^3+8 x^4\right )^3 \, dx=\frac {512 x^{13}}{13} - 240 x^{12} + \frac {6936 x^{11}}{11} - \frac {4527 x^{10}}{10} - \frac {2936 x^{9}}{3} + 2097 x^{8} + \frac {5528 x^{7}}{7} - 2976 x^{6} - \frac {384 x^{5}}{5} + 5040 x^{4} + 5120 x^{3} + 2304 x^{2} + 512 x \]
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Time = 0.20 (sec) , antiderivative size = 64, normalized size of antiderivative = 0.84 \[ \int \left (8+24 x+8 x^2-15 x^3+8 x^4\right )^3 \, dx=\frac {512}{13} \, x^{13} - 240 \, x^{12} + \frac {6936}{11} \, x^{11} - \frac {4527}{10} \, x^{10} - \frac {2936}{3} \, x^{9} + 2097 \, x^{8} + \frac {5528}{7} \, x^{7} - 2976 \, x^{6} - \frac {384}{5} \, x^{5} + 5040 \, x^{4} + 5120 \, x^{3} + 2304 \, x^{2} + 512 \, x \]
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Time = 0.29 (sec) , antiderivative size = 64, normalized size of antiderivative = 0.84 \[ \int \left (8+24 x+8 x^2-15 x^3+8 x^4\right )^3 \, dx=\frac {512}{13} \, x^{13} - 240 \, x^{12} + \frac {6936}{11} \, x^{11} - \frac {4527}{10} \, x^{10} - \frac {2936}{3} \, x^{9} + 2097 \, x^{8} + \frac {5528}{7} \, x^{7} - 2976 \, x^{6} - \frac {384}{5} \, x^{5} + 5040 \, x^{4} + 5120 \, x^{3} + 2304 \, x^{2} + 512 \, x \]
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Time = 0.06 (sec) , antiderivative size = 64, normalized size of antiderivative = 0.84 \[ \int \left (8+24 x+8 x^2-15 x^3+8 x^4\right )^3 \, dx=\frac {512\,x^{13}}{13}-240\,x^{12}+\frac {6936\,x^{11}}{11}-\frac {4527\,x^{10}}{10}-\frac {2936\,x^9}{3}+2097\,x^8+\frac {5528\,x^7}{7}-2976\,x^6-\frac {384\,x^5}{5}+5040\,x^4+5120\,x^3+2304\,x^2+512\,x \]
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