Integrand size = 22, antiderivative size = 10 \[ \int \frac {96-9 x}{256 x^3-32 x^4+x^5} \, dx=\frac {3}{(-16+x) x^2} \]
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Time = 0.01 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20, number of steps used = 3, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.136, Rules used = {1608, 27, 75} \[ \int \frac {96-9 x}{256 x^3-32 x^4+x^5} \, dx=-\frac {3}{(16-x) x^2} \]
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Rule 27
Rule 75
Rule 1608
Rubi steps \begin{align*} \text {integral}& = \int \frac {96-9 x}{x^3 \left (256-32 x+x^2\right )} \, dx \\ & = \int \frac {96-9 x}{(-16+x)^2 x^3} \, dx \\ & = -\frac {3}{(16-x) x^2} \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.00 \[ \int \frac {96-9 x}{256 x^3-32 x^4+x^5} \, dx=\frac {3}{(-16+x) x^2} \]
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Time = 0.02 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.10
method | result | size |
gosper | \(\frac {3}{x^{2} \left (x -16\right )}\) | \(11\) |
norman | \(\frac {3}{x^{2} \left (x -16\right )}\) | \(11\) |
risch | \(\frac {3}{x^{2} \left (x -16\right )}\) | \(11\) |
parallelrisch | \(\frac {3}{x^{2} \left (x -16\right )}\) | \(11\) |
default | \(\frac {3}{256 \left (x -16\right )}-\frac {3}{16 x^{2}}-\frac {3}{256 x}\) | \(19\) |
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none
Time = 0.25 (sec) , antiderivative size = 13, normalized size of antiderivative = 1.30 \[ \int \frac {96-9 x}{256 x^3-32 x^4+x^5} \, dx=\frac {3}{x^{3} - 16 \, x^{2}} \]
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Time = 0.05 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.80 \[ \int \frac {96-9 x}{256 x^3-32 x^4+x^5} \, dx=\frac {3}{x^{3} - 16 x^{2}} \]
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none
Time = 0.19 (sec) , antiderivative size = 13, normalized size of antiderivative = 1.30 \[ \int \frac {96-9 x}{256 x^3-32 x^4+x^5} \, dx=\frac {3}{x^{3} - 16 \, x^{2}} \]
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none
Time = 0.28 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.60 \[ \int \frac {96-9 x}{256 x^3-32 x^4+x^5} \, dx=\frac {3}{256 \, {\left (x - 16\right )}} - \frac {3 \, {\left (x + 16\right )}}{256 \, x^{2}} \]
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Time = 12.00 (sec) , antiderivative size = 15, normalized size of antiderivative = 1.50 \[ \int \frac {96-9 x}{256 x^3-32 x^4+x^5} \, dx=-\frac {3}{16\,x^2-x^3} \]
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