Optimal. Leaf size=76 \[ \frac {512 x^{13}}{13}-240 x^{12}+\frac {6936 x^{11}}{11}-\frac {4527 x^{10}}{10}-\frac {2936 x^9}{3}+2097 x^8+\frac {5528 x^7}{7}-2976 x^6-\frac {384 x^5}{5}+5040 x^4+5120 x^3+2304 x^2+512 x \]
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Rubi [A] time = 0.02, antiderivative size = 76, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {2061} \[ \frac {512 x^{13}}{13}-240 x^{12}+\frac {6936 x^{11}}{11}-\frac {4527 x^{10}}{10}-\frac {2936 x^9}{3}+2097 x^8+\frac {5528 x^7}{7}-2976 x^6-\frac {384 x^5}{5}+5040 x^4+5120 x^3+2304 x^2+512 x \]
Antiderivative was successfully verified.
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Rule 2061
Rubi steps
\begin {align*} \int \left (8+24 x+8 x^2-15 x^3+8 x^4\right )^3 \, dx &=\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*}
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Mathematica [A] time = 0.00, size = 76, normalized size = 1.00 \[ \frac {512 x^{13}}{13}-240 x^{12}+\frac {6936 x^{11}}{11}-\frac {4527 x^{10}}{10}-\frac {2936 x^9}{3}+2097 x^8+\frac {5528 x^7}{7}-2976 x^6-\frac {384 x^5}{5}+5040 x^4+5120 x^3+2304 x^2+512 x \]
Antiderivative was successfully verified.
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fricas [A] time = 0.34, size = 64, normalized size = 0.84 \[ \frac {512}{13} x^{13} - 240 x^{12} + \frac {6936}{11} x^{11} - \frac {4527}{10} x^{10} - \frac {2936}{3} x^{9} + 2097 x^{8} + \frac {5528}{7} x^{7} - 2976 x^{6} - \frac {384}{5} x^{5} + 5040 x^{4} + 5120 x^{3} + 2304 x^{2} + 512 x \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.38, size = 64, normalized size = 0.84 \[ \frac {512}{13} \, x^{13} - 240 \, x^{12} + \frac {6936}{11} \, x^{11} - \frac {4527}{10} \, x^{10} - \frac {2936}{3} \, x^{9} + 2097 \, x^{8} + \frac {5528}{7} \, x^{7} - 2976 \, x^{6} - \frac {384}{5} \, x^{5} + 5040 \, x^{4} + 5120 \, x^{3} + 2304 \, x^{2} + 512 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 65, normalized size = 0.86 \[ \frac {512}{13} x^{13}-240 x^{12}+\frac {6936}{11} x^{11}-\frac {4527}{10} x^{10}-\frac {2936}{3} x^{9}+2097 x^{8}+\frac {5528}{7} x^{7}-2976 x^{6}-\frac {384}{5} x^{5}+5040 x^{4}+5120 x^{3}+2304 x^{2}+512 x \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.65, size = 64, normalized size = 0.84 \[ \frac {512}{13} \, x^{13} - 240 \, x^{12} + \frac {6936}{11} \, x^{11} - \frac {4527}{10} \, x^{10} - \frac {2936}{3} \, x^{9} + 2097 \, x^{8} + \frac {5528}{7} \, x^{7} - 2976 \, x^{6} - \frac {384}{5} \, x^{5} + 5040 \, x^{4} + 5120 \, x^{3} + 2304 \, x^{2} + 512 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.08, size = 64, normalized size = 0.84 \[ \frac {512\,x^{13}}{13}-240\,x^{12}+\frac {6936\,x^{11}}{11}-\frac {4527\,x^{10}}{10}-\frac {2936\,x^9}{3}+2097\,x^8+\frac {5528\,x^7}{7}-2976\,x^6-\frac {384\,x^5}{5}+5040\,x^4+5120\,x^3+2304\,x^2+512\,x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.08, size = 73, normalized size = 0.96 \[ \frac {512 x^{13}}{13} - 240 x^{12} + \frac {6936 x^{11}}{11} - \frac {4527 x^{10}}{10} - \frac {2936 x^{9}}{3} + 2097 x^{8} + \frac {5528 x^{7}}{7} - 2976 x^{6} - \frac {384 x^{5}}{5} + 5040 x^{4} + 5120 x^{3} + 2304 x^{2} + 512 x \]
Verification of antiderivative is not currently implemented for this CAS.
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