Integrand size = 18, antiderivative size = 14 \[ \int \frac {2-x^2}{\left (1-6 x+x^3\right )^5} \, dx=\frac {1}{12 \left (1-6 x+x^3\right )^4} \]
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Time = 0.00 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {1602} \[ \int \frac {2-x^2}{\left (1-6 x+x^3\right )^5} \, dx=\frac {1}{12 \left (x^3-6 x+1\right )^4} \]
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Rule 1602
Rubi steps \begin{align*} \text {integral}& = \frac {1}{12 \left (1-6 x+x^3\right )^4} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.00 \[ \int \frac {2-x^2}{\left (1-6 x+x^3\right )^5} \, dx=\frac {1}{12 \left (1-6 x+x^3\right )^4} \]
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Time = 0.05 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.93
method | result | size |
gosper | \(\frac {1}{12 \left (x^{3}-6 x +1\right )^{4}}\) | \(13\) |
default | \(\frac {1}{12 \left (x^{3}-6 x +1\right )^{4}}\) | \(13\) |
norman | \(\frac {1}{12 \left (x^{3}-6 x +1\right )^{4}}\) | \(13\) |
risch | \(\frac {1}{12 \left (x^{3}-6 x +1\right )^{4}}\) | \(13\) |
parallelrisch | \(\frac {1}{12 \left (x^{3}-6 x +1\right )^{4}}\) | \(13\) |
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Leaf count of result is larger than twice the leaf count of optimal. 57 vs. \(2 (12) = 24\).
Time = 0.23 (sec) , antiderivative size = 57, normalized size of antiderivative = 4.07 \[ \int \frac {2-x^2}{\left (1-6 x+x^3\right )^5} \, dx=\frac {1}{12 \, {\left (x^{12} - 24 \, x^{10} + 4 \, x^{9} + 216 \, x^{8} - 72 \, x^{7} - 858 \, x^{6} + 432 \, x^{5} + 1224 \, x^{4} - 860 \, x^{3} + 216 \, x^{2} - 24 \, x + 1\right )}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 56 vs. \(2 (12) = 24\).
Time = 0.08 (sec) , antiderivative size = 56, normalized size of antiderivative = 4.00 \[ \int \frac {2-x^2}{\left (1-6 x+x^3\right )^5} \, dx=\frac {1}{12 x^{12} - 288 x^{10} + 48 x^{9} + 2592 x^{8} - 864 x^{7} - 10296 x^{6} + 5184 x^{5} + 14688 x^{4} - 10320 x^{3} + 2592 x^{2} - 288 x + 12} \]
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none
Time = 0.19 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.86 \[ \int \frac {2-x^2}{\left (1-6 x+x^3\right )^5} \, dx=\frac {1}{12 \, {\left (x^{3} - 6 \, x + 1\right )}^{4}} \]
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none
Time = 0.29 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.86 \[ \int \frac {2-x^2}{\left (1-6 x+x^3\right )^5} \, dx=\frac {1}{12 \, {\left (x^{3} - 6 \, x + 1\right )}^{4}} \]
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Time = 9.37 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.86 \[ \int \frac {2-x^2}{\left (1-6 x+x^3\right )^5} \, dx=\frac {1}{12\,{\left (x^3-6\,x+1\right )}^4} \]
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