Integrand size = 15, antiderivative size = 21 \[ \int \left (1+4 x+4 x^2+4 x^4\right ) \, dx=x+2 x^2+\frac {4 x^3}{3}+\frac {4 x^5}{5} \]
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Time = 0.00 (sec) , antiderivative size = 21, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \left (1+4 x+4 x^2+4 x^4\right ) \, dx=\frac {4 x^5}{5}+\frac {4 x^3}{3}+2 x^2+x \]
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Rubi steps \begin{align*} \text {integral}& = x+2 x^2+\frac {4 x^3}{3}+\frac {4 x^5}{5} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 21, normalized size of antiderivative = 1.00 \[ \int \left (1+4 x+4 x^2+4 x^4\right ) \, dx=x+2 x^2+\frac {4 x^3}{3}+\frac {4 x^5}{5} \]
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Time = 0.02 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.86
method | result | size |
gosper | \(x +2 x^{2}+\frac {4}{3} x^{3}+\frac {4}{5} x^{5}\) | \(18\) |
default | \(x +2 x^{2}+\frac {4}{3} x^{3}+\frac {4}{5} x^{5}\) | \(18\) |
norman | \(x +2 x^{2}+\frac {4}{3} x^{3}+\frac {4}{5} x^{5}\) | \(18\) |
risch | \(x +2 x^{2}+\frac {4}{3} x^{3}+\frac {4}{5} x^{5}\) | \(18\) |
parallelrisch | \(x +2 x^{2}+\frac {4}{3} x^{3}+\frac {4}{5} x^{5}\) | \(18\) |
parts | \(x +2 x^{2}+\frac {4}{3} x^{3}+\frac {4}{5} x^{5}\) | \(18\) |
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Time = 0.24 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.81 \[ \int \left (1+4 x+4 x^2+4 x^4\right ) \, dx=\frac {4}{5} \, x^{5} + \frac {4}{3} \, x^{3} + 2 \, x^{2} + x \]
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Time = 0.02 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.90 \[ \int \left (1+4 x+4 x^2+4 x^4\right ) \, dx=\frac {4 x^{5}}{5} + \frac {4 x^{3}}{3} + 2 x^{2} + x \]
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Time = 0.19 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.81 \[ \int \left (1+4 x+4 x^2+4 x^4\right ) \, dx=\frac {4}{5} \, x^{5} + \frac {4}{3} \, x^{3} + 2 \, x^{2} + x \]
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Time = 0.30 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.81 \[ \int \left (1+4 x+4 x^2+4 x^4\right ) \, dx=\frac {4}{5} \, x^{5} + \frac {4}{3} \, x^{3} + 2 \, x^{2} + x \]
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Time = 0.02 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.81 \[ \int \left (1+4 x+4 x^2+4 x^4\right ) \, dx=\frac {4\,x^5}{5}+\frac {4\,x^3}{3}+2\,x^2+x \]
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