Integrand size = 22, antiderivative size = 14 \[ \int \frac {-1+4 x^3}{\sqrt {-1-2 x+2 x^4}} \, dx=\sqrt {-1-2 x+2 x^4} \]
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Time = 0.01 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {1602} \[ \int \frac {-1+4 x^3}{\sqrt {-1-2 x+2 x^4}} \, dx=\sqrt {2 x^4-2 x-1} \]
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Rule 1602
Rubi steps \begin{align*} \text {integral}& = \sqrt {-1-2 x+2 x^4} \\ \end{align*}
Time = 0.02 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.00 \[ \int \frac {-1+4 x^3}{\sqrt {-1-2 x+2 x^4}} \, dx=\sqrt {-1-2 x+2 x^4} \]
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Time = 0.88 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.93
method | result | size |
gosper | \(\sqrt {2 x^{4}-2 x -1}\) | \(13\) |
default | \(\sqrt {2 x^{4}-2 x -1}\) | \(13\) |
trager | \(\sqrt {2 x^{4}-2 x -1}\) | \(13\) |
risch | \(\sqrt {2 x^{4}-2 x -1}\) | \(13\) |
elliptic | \(\sqrt {2 x^{4}-2 x -1}\) | \(13\) |
pseudoelliptic | \(\sqrt {2 x^{4}-2 x -1}\) | \(13\) |
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none
Time = 0.24 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.86 \[ \int \frac {-1+4 x^3}{\sqrt {-1-2 x+2 x^4}} \, dx=\sqrt {2 \, x^{4} - 2 \, x - 1} \]
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Time = 0.08 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.86 \[ \int \frac {-1+4 x^3}{\sqrt {-1-2 x+2 x^4}} \, dx=\sqrt {2 x^{4} - 2 x - 1} \]
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none
Time = 0.17 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.86 \[ \int \frac {-1+4 x^3}{\sqrt {-1-2 x+2 x^4}} \, dx=\sqrt {2 \, x^{4} - 2 \, x - 1} \]
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none
Time = 0.26 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.86 \[ \int \frac {-1+4 x^3}{\sqrt {-1-2 x+2 x^4}} \, dx=\sqrt {2 \, x^{4} - 2 \, x - 1} \]
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Time = 0.17 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.86 \[ \int \frac {-1+4 x^3}{\sqrt {-1-2 x+2 x^4}} \, dx=\sqrt {2\,x^4-2\,x-1} \]
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