Optimal. Leaf size=69 \[ \frac {64 x^{13}}{13}+\frac {192 x^{11}}{11}+\frac {96 x^{10}}{5}+\frac {80 x^9}{3}+48 x^8+\frac {352 x^7}{7}+48 x^6+\frac {252 x^5}{5}+40 x^4+20 x^3+6 x^2+x \]
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Rubi [A] time = 0.02, antiderivative size = 69, 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} \[ \frac {64 x^{13}}{13}+\frac {192 x^{11}}{11}+\frac {96 x^{10}}{5}+\frac {80 x^9}{3}+48 x^8+\frac {352 x^7}{7}+48 x^6+\frac {252 x^5}{5}+40 x^4+20 x^3+6 x^2+x \]
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 )^3 \, dx &=\int \left (1+12 x+60 x^2+160 x^3+252 x^4+288 x^5+352 x^6+384 x^7+240 x^8+192 x^9+192 x^{10}+64 x^{12}\right ) \, dx\\ &=x+6 x^2+20 x^3+40 x^4+\frac {252 x^5}{5}+48 x^6+\frac {352 x^7}{7}+48 x^8+\frac {80 x^9}{3}+\frac {96 x^{10}}{5}+\frac {192 x^{11}}{11}+\frac {64 x^{13}}{13}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 69, normalized size = 1.00 \[ \frac {64 x^{13}}{13}+\frac {192 x^{11}}{11}+\frac {96 x^{10}}{5}+\frac {80 x^9}{3}+48 x^8+\frac {352 x^7}{7}+48 x^6+\frac {252 x^5}{5}+40 x^4+20 x^3+6 x^2+x \]
Antiderivative was successfully verified.
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fricas [A] time = 0.36, size = 57, normalized size = 0.83 \[ \frac {64}{13} x^{13} + \frac {192}{11} x^{11} + \frac {96}{5} x^{10} + \frac {80}{3} x^{9} + 48 x^{8} + \frac {352}{7} x^{7} + 48 x^{6} + \frac {252}{5} x^{5} + 40 x^{4} + 20 x^{3} + 6 x^{2} + x \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.36, size = 57, normalized size = 0.83 \[ \frac {64}{13} \, x^{13} + \frac {192}{11} \, x^{11} + \frac {96}{5} \, x^{10} + \frac {80}{3} \, x^{9} + 48 \, x^{8} + \frac {352}{7} \, x^{7} + 48 \, x^{6} + \frac {252}{5} \, x^{5} + 40 \, x^{4} + 20 \, x^{3} + 6 \, x^{2} + x \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 58, normalized size = 0.84 \[ \frac {64}{13} x^{13}+\frac {192}{11} x^{11}+\frac {96}{5} x^{10}+\frac {80}{3} x^{9}+48 x^{8}+\frac {352}{7} x^{7}+48 x^{6}+\frac {252}{5} x^{5}+40 x^{4}+20 x^{3}+6 x^{2}+x \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.46, size = 57, normalized size = 0.83 \[ \frac {64}{13} \, x^{13} + \frac {192}{11} \, x^{11} + \frac {96}{5} \, x^{10} + \frac {80}{3} \, x^{9} + 48 \, x^{8} + \frac {352}{7} \, x^{7} + 48 \, x^{6} + \frac {252}{5} \, x^{5} + 40 \, x^{4} + 20 \, x^{3} + 6 \, x^{2} + x \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.06, size = 57, normalized size = 0.83 \[ \frac {64\,x^{13}}{13}+\frac {192\,x^{11}}{11}+\frac {96\,x^{10}}{5}+\frac {80\,x^9}{3}+48\,x^8+\frac {352\,x^7}{7}+48\,x^6+\frac {252\,x^5}{5}+40\,x^4+20\,x^3+6\,x^2+x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.07, size = 66, normalized size = 0.96 \[ \frac {64 x^{13}}{13} + \frac {192 x^{11}}{11} + \frac {96 x^{10}}{5} + \frac {80 x^{9}}{3} + 48 x^{8} + \frac {352 x^{7}}{7} + 48 x^{6} + \frac {252 x^{5}}{5} + 40 x^{4} + 20 x^{3} + 6 x^{2} + x \]
Verification of antiderivative is not currently implemented for this CAS.
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