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 = 0.0165229, antiderivative size = 54, 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} \[ \frac{64 x^9}{9}-2 x^8+\frac{x^7}{7}+\frac{64 x^6}{3}+\frac{112 x^5}{5}-4 x^4+\frac{64 x^3}{3}+64 x^2+64 x \]
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*}
Mathematica [A] time = 0.0012604, size = 54, normalized size = 1. \[ \frac{64 x^9}{9}-2 x^8+\frac{x^7}{7}+\frac{64 x^6}{3}+\frac{112 x^5}{5}-4 x^4+\frac{64 x^3}{3}+64 x^2+64 x \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 45, normalized size = 0.8 \begin{align*} 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*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.13361, size = 59, normalized size = 1.09 \begin{align*} \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 \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.06795, size = 116, normalized size = 2.15 \begin{align*} \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 \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.058537, size = 49, normalized size = 0.91 \begin{align*} \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 \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.10815, size = 59, normalized size = 1.09 \begin{align*} \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 \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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