Integrand size = 16, antiderivative size = 11 \[ \int \frac {-1+4 x^5}{\left (1+x+x^5\right )^2} \, dx=-\frac {x}{1+x+x^5} \]
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Time = 0.01 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.062, Rules used = {1602} \[ \int \frac {-1+4 x^5}{\left (1+x+x^5\right )^2} \, dx=-\frac {x}{x^5+x+1} \]
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Rule 1602
Rubi steps \begin{align*} \text {integral}& = -\frac {x}{1+x+x^5} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.00 \[ \int \frac {-1+4 x^5}{\left (1+x+x^5\right )^2} \, dx=-\frac {x}{1+x+x^5} \]
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Time = 0.05 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.09
method | result | size |
gosper | \(-\frac {x}{x^{5}+x +1}\) | \(12\) |
norman | \(-\frac {x}{x^{5}+x +1}\) | \(12\) |
risch | \(-\frac {x}{x^{5}+x +1}\) | \(12\) |
parallelrisch | \(-\frac {x}{x^{5}+x +1}\) | \(12\) |
default | \(-\frac {-3 x^{2}+5 x -1}{7 \left (x^{3}-x^{2}+1\right )}+\frac {-3 x -1}{7 x^{2}+7 x +7}\) | \(41\) |
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none
Time = 0.30 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.00 \[ \int \frac {-1+4 x^5}{\left (1+x+x^5\right )^2} \, dx=-\frac {x}{x^{5} + x + 1} \]
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Time = 0.04 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.73 \[ \int \frac {-1+4 x^5}{\left (1+x+x^5\right )^2} \, dx=- \frac {x}{x^{5} + x + 1} \]
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none
Time = 0.19 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.00 \[ \int \frac {-1+4 x^5}{\left (1+x+x^5\right )^2} \, dx=-\frac {x}{x^{5} + x + 1} \]
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none
Time = 0.29 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.00 \[ \int \frac {-1+4 x^5}{\left (1+x+x^5\right )^2} \, dx=-\frac {x}{x^{5} + x + 1} \]
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Time = 9.46 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.00 \[ \int \frac {-1+4 x^5}{\left (1+x+x^5\right )^2} \, dx=-\frac {x}{x^5+x+1} \]
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