Optimal. Leaf size=54 \[ \frac {64 x^9}{9}-2 x^8+\frac {x^7}{7}+\frac {64 x^6}{3}+\frac {112 x^5}{5}-4 x^4+\frac {64 x^3}{3}+64 x^2+64 x \]
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Rubi [A] time = 0.02, antiderivative size = 54, normalized size of antiderivative = 1.00, 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} \[ \frac {64 x^9}{9}-2 x^8+\frac {x^7}{7}+\frac {64 x^6}{3}+\frac {112 x^5}{5}-4 x^4+\frac {64 x^3}{3}+64 x^2+64 x \]
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 )^2 \, dx &=\int \left (64+128 x+64 x^2-16 x^3+112 x^4+128 x^5+x^6-16 x^7+64 x^8\right ) \, dx\\ &=64 x+64 x^2+\frac {64 x^3}{3}-4 x^4+\frac {112 x^5}{5}+\frac {64 x^6}{3}+\frac {x^7}{7}-2 x^8+\frac {64 x^9}{9}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 54, normalized size = 1.00 \[ \frac {64 x^9}{9}-2 x^8+\frac {x^7}{7}+\frac {64 x^6}{3}+\frac {112 x^5}{5}-4 x^4+\frac {64 x^3}{3}+64 x^2+64 x \]
Antiderivative was successfully verified.
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fricas [A] time = 0.38, size = 44, normalized size = 0.81 \[ \frac {64}{9} x^{9} - 2 x^{8} + \frac {1}{7} x^{7} + \frac {64}{3} x^{6} + \frac {112}{5} x^{5} - 4 x^{4} + \frac {64}{3} x^{3} + 64 x^{2} + 64 x \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.33, size = 44, normalized size = 0.81 \[ \frac {64}{9} \, x^{9} - 2 \, x^{8} + \frac {1}{7} \, x^{7} + \frac {64}{3} \, x^{6} + \frac {112}{5} \, x^{5} - 4 \, x^{4} + \frac {64}{3} \, x^{3} + 64 \, x^{2} + 64 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 45, normalized size = 0.83 \[ \frac {64}{9} x^{9}-2 x^{8}+\frac {1}{7} x^{7}+\frac {64}{3} x^{6}+\frac {112}{5} x^{5}-4 x^{4}+\frac {64}{3} x^{3}+64 x^{2}+64 x \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.88, size = 44, normalized size = 0.81 \[ \frac {64}{9} \, x^{9} - 2 \, x^{8} + \frac {1}{7} \, x^{7} + \frac {64}{3} \, x^{6} + \frac {112}{5} \, x^{5} - 4 \, x^{4} + \frac {64}{3} \, x^{3} + 64 \, x^{2} + 64 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 44, normalized size = 0.81 \[ \frac {64\,x^9}{9}-2\,x^8+\frac {x^7}{7}+\frac {64\,x^6}{3}+\frac {112\,x^5}{5}-4\,x^4+\frac {64\,x^3}{3}+64\,x^2+64\,x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.06, size = 49, normalized size = 0.91 \[ \frac {64 x^{9}}{9} - 2 x^{8} + \frac {x^{7}}{7} + \frac {64 x^{6}}{3} + \frac {112 x^{5}}{5} - 4 x^{4} + \frac {64 x^{3}}{3} + 64 x^{2} + 64 x \]
Verification of antiderivative is not currently implemented for this CAS.
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