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 = 0.01, antiderivative size = 45, 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} \[ \frac {16 x^9}{9}+\frac {32 x^7}{7}+\frac {16 x^6}{3}+\frac {24 x^5}{5}+8 x^4+8 x^3+4 x^2+x \]
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*}
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Mathematica [A] time = 0.00, size = 45, normalized size = 1.00 \[ \frac {16 x^9}{9}+\frac {32 x^7}{7}+\frac {16 x^6}{3}+\frac {24 x^5}{5}+8 x^4+8 x^3+4 x^2+x \]
Antiderivative was successfully verified.
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fricas [A] time = 0.34, size = 37, normalized size = 0.82 \[ \frac {16}{9} x^{9} + \frac {32}{7} x^{7} + \frac {16}{3} x^{6} + \frac {24}{5} x^{5} + 8 x^{4} + 8 x^{3} + 4 x^{2} + x \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.25, size = 37, normalized size = 0.82 \[ \frac {16}{9} \, x^{9} + \frac {32}{7} \, x^{7} + \frac {16}{3} \, x^{6} + \frac {24}{5} \, x^{5} + 8 \, x^{4} + 8 \, x^{3} + 4 \, x^{2} + x \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 38, normalized size = 0.84 \[ \frac {16}{9} x^{9}+\frac {32}{7} x^{7}+\frac {16}{3} x^{6}+\frac {24}{5} x^{5}+8 x^{4}+8 x^{3}+4 x^{2}+x \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.57, size = 37, normalized size = 0.82 \[ \frac {16}{9} \, x^{9} + \frac {32}{7} \, x^{7} + \frac {16}{3} \, x^{6} + \frac {24}{5} \, x^{5} + 8 \, x^{4} + 8 \, x^{3} + 4 \, x^{2} + x \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 37, normalized size = 0.82 \[ \frac {16\,x^9}{9}+\frac {32\,x^7}{7}+\frac {16\,x^6}{3}+\frac {24\,x^5}{5}+8\,x^4+8\,x^3+4\,x^2+x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.06, size = 42, normalized size = 0.93 \[ \frac {16 x^{9}}{9} + \frac {32 x^{7}}{7} + \frac {16 x^{6}}{3} + \frac {24 x^{5}}{5} + 8 x^{4} + 8 x^{3} + 4 x^{2} + x \]
Verification of antiderivative is not currently implemented for this CAS.
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