Optimal. Leaf size=45 \[ \frac{16 x^9}{9}+\frac{32 x^7}{7}+\frac{16 x^6}{3}+\frac{24 x^5}{5}+8 x^4+8 x^3+4 x^2+x \]
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Rubi [A] time = 0.0148994, antiderivative size = 45, 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} \[ \frac{16 x^9}{9}+\frac{32 x^7}{7}+\frac{16 x^6}{3}+\frac{24 x^5}{5}+8 x^4+8 x^3+4 x^2+x \]
Antiderivative was successfully verified.
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Rule 2061
Rubi steps
\begin{align*} \int \left (1+4 x+4 x^2+4 x^4\right )^2 \, dx &=\int \left (1+8 x+24 x^2+32 x^3+24 x^4+32 x^5+32 x^6+16 x^8\right ) \, dx\\ &=x+4 x^2+8 x^3+8 x^4+\frac{24 x^5}{5}+\frac{16 x^6}{3}+\frac{32 x^7}{7}+\frac{16 x^9}{9}\\ \end{align*}
Mathematica [A] time = 0.001273, size = 45, normalized size = 1. \[ \frac{16 x^9}{9}+\frac{32 x^7}{7}+\frac{16 x^6}{3}+\frac{24 x^5}{5}+8 x^4+8 x^3+4 x^2+x \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 38, normalized size = 0.8 \begin{align*} x+4\,{x}^{2}+8\,{x}^{3}+8\,{x}^{4}+{\frac{24\,{x}^{5}}{5}}+{\frac{16\,{x}^{6}}{3}}+{\frac{32\,{x}^{7}}{7}}+{\frac{16\,{x}^{9}}{9}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.78079, size = 50, normalized size = 1.11 \begin{align*} \frac{16}{9} \, x^{9} + \frac{32}{7} \, x^{7} + \frac{16}{3} \, x^{6} + \frac{24}{5} \, x^{5} + 8 \, x^{4} + 8 \, x^{3} + 4 \, x^{2} + x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.0902, size = 96, normalized size = 2.13 \begin{align*} \frac{16}{9} x^{9} + \frac{32}{7} x^{7} + \frac{16}{3} x^{6} + \frac{24}{5} x^{5} + 8 x^{4} + 8 x^{3} + 4 x^{2} + x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.058814, size = 42, normalized size = 0.93 \begin{align*} \frac{16 x^{9}}{9} + \frac{32 x^{7}}{7} + \frac{16 x^{6}}{3} + \frac{24 x^{5}}{5} + 8 x^{4} + 8 x^{3} + 4 x^{2} + x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.12127, size = 50, normalized size = 1.11 \begin{align*} \frac{16}{9} \, x^{9} + \frac{32}{7} \, x^{7} + \frac{16}{3} \, x^{6} + \frac{24}{5} \, x^{5} + 8 \, x^{4} + 8 \, x^{3} + 4 \, x^{2} + x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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