Integrand size = 17, antiderivative size = 69 \[ \int \left (1+4 x+4 x^2+4 x^4\right )^3 \, dx=x+6 x^2+20 x^3+40 x^4+\frac {252 x^5}{5}+48 x^6+\frac {352 x^7}{7}+48 x^8+\frac {80 x^9}{3}+\frac {96 x^{10}}{5}+\frac {192 x^{11}}{11}+\frac {64 x^{13}}{13} \]
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Time = 0.01 (sec) , antiderivative size = 69, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.059, Rules used = {2086} \[ \int \left (1+4 x+4 x^2+4 x^4\right )^3 \, dx=\frac {64 x^{13}}{13}+\frac {192 x^{11}}{11}+\frac {96 x^{10}}{5}+\frac {80 x^9}{3}+48 x^8+\frac {352 x^7}{7}+48 x^6+\frac {252 x^5}{5}+40 x^4+20 x^3+6 x^2+x \]
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Rule 2086
Rubi steps \begin{align*} \text {integral}& = \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*}
Time = 0.00 (sec) , antiderivative size = 69, normalized size of antiderivative = 1.00 \[ \int \left (1+4 x+4 x^2+4 x^4\right )^3 \, dx=x+6 x^2+20 x^3+40 x^4+\frac {252 x^5}{5}+48 x^6+\frac {352 x^7}{7}+48 x^8+\frac {80 x^9}{3}+\frac {96 x^{10}}{5}+\frac {192 x^{11}}{11}+\frac {64 x^{13}}{13} \]
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Time = 0.03 (sec) , antiderivative size = 58, normalized size of antiderivative = 0.84
method | result | size |
gosper | \(x +6 x^{2}+20 x^{3}+40 x^{4}+\frac {252}{5} x^{5}+48 x^{6}+\frac {352}{7} x^{7}+48 x^{8}+\frac {80}{3} x^{9}+\frac {96}{5} x^{10}+\frac {192}{11} x^{11}+\frac {64}{13} x^{13}\) | \(58\) |
default | \(x +6 x^{2}+20 x^{3}+40 x^{4}+\frac {252}{5} x^{5}+48 x^{6}+\frac {352}{7} x^{7}+48 x^{8}+\frac {80}{3} x^{9}+\frac {96}{5} x^{10}+\frac {192}{11} x^{11}+\frac {64}{13} x^{13}\) | \(58\) |
norman | \(x +6 x^{2}+20 x^{3}+40 x^{4}+\frac {252}{5} x^{5}+48 x^{6}+\frac {352}{7} x^{7}+48 x^{8}+\frac {80}{3} x^{9}+\frac {96}{5} x^{10}+\frac {192}{11} x^{11}+\frac {64}{13} x^{13}\) | \(58\) |
risch | \(x +6 x^{2}+20 x^{3}+40 x^{4}+\frac {252}{5} x^{5}+48 x^{6}+\frac {352}{7} x^{7}+48 x^{8}+\frac {80}{3} x^{9}+\frac {96}{5} x^{10}+\frac {192}{11} x^{11}+\frac {64}{13} x^{13}\) | \(58\) |
parallelrisch | \(x +6 x^{2}+20 x^{3}+40 x^{4}+\frac {252}{5} x^{5}+48 x^{6}+\frac {352}{7} x^{7}+48 x^{8}+\frac {80}{3} x^{9}+\frac {96}{5} x^{10}+\frac {192}{11} x^{11}+\frac {64}{13} x^{13}\) | \(58\) |
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Time = 0.27 (sec) , antiderivative size = 57, normalized size of antiderivative = 0.83 \[ \int \left (1+4 x+4 x^2+4 x^4\right )^3 \, dx=\frac {64}{13} \, x^{13} + \frac {192}{11} \, x^{11} + \frac {96}{5} \, x^{10} + \frac {80}{3} \, x^{9} + 48 \, x^{8} + \frac {352}{7} \, x^{7} + 48 \, x^{6} + \frac {252}{5} \, x^{5} + 40 \, x^{4} + 20 \, x^{3} + 6 \, x^{2} + x \]
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Time = 0.03 (sec) , antiderivative size = 66, normalized size of antiderivative = 0.96 \[ \int \left (1+4 x+4 x^2+4 x^4\right )^3 \, dx=\frac {64 x^{13}}{13} + \frac {192 x^{11}}{11} + \frac {96 x^{10}}{5} + \frac {80 x^{9}}{3} + 48 x^{8} + \frac {352 x^{7}}{7} + 48 x^{6} + \frac {252 x^{5}}{5} + 40 x^{4} + 20 x^{3} + 6 x^{2} + x \]
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Time = 0.20 (sec) , antiderivative size = 57, normalized size of antiderivative = 0.83 \[ \int \left (1+4 x+4 x^2+4 x^4\right )^3 \, dx=\frac {64}{13} \, x^{13} + \frac {192}{11} \, x^{11} + \frac {96}{5} \, x^{10} + \frac {80}{3} \, x^{9} + 48 \, x^{8} + \frac {352}{7} \, x^{7} + 48 \, x^{6} + \frac {252}{5} \, x^{5} + 40 \, x^{4} + 20 \, x^{3} + 6 \, x^{2} + x \]
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Time = 0.28 (sec) , antiderivative size = 57, normalized size of antiderivative = 0.83 \[ \int \left (1+4 x+4 x^2+4 x^4\right )^3 \, dx=\frac {64}{13} \, x^{13} + \frac {192}{11} \, x^{11} + \frac {96}{5} \, x^{10} + \frac {80}{3} \, x^{9} + 48 \, x^{8} + \frac {352}{7} \, x^{7} + 48 \, x^{6} + \frac {252}{5} \, x^{5} + 40 \, x^{4} + 20 \, x^{3} + 6 \, x^{2} + x \]
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Time = 0.06 (sec) , antiderivative size = 57, normalized size of antiderivative = 0.83 \[ \int \left (1+4 x+4 x^2+4 x^4\right )^3 \, dx=\frac {64\,x^{13}}{13}+\frac {192\,x^{11}}{11}+\frac {96\,x^{10}}{5}+\frac {80\,x^9}{3}+48\,x^8+\frac {352\,x^7}{7}+48\,x^6+\frac {252\,x^5}{5}+40\,x^4+20\,x^3+6\,x^2+x \]
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