Integrand size = 26, antiderivative size = 17 \[ \int \frac {-9-3 e^5+6 x-x^2}{9-6 x+x^2} \, dx=6+\frac {3 e^5}{-3+x}-x+\log (25) \]
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Time = 0.01 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.94, number of steps used = 3, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {27, 697} \[ \int \frac {-9-3 e^5+6 x-x^2}{9-6 x+x^2} \, dx=-x-\frac {3 e^5}{3-x} \]
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Rule 27
Rule 697
Rubi steps \begin{align*} \text {integral}& = \int \frac {-9-3 e^5+6 x-x^2}{(-3+x)^2} \, dx \\ & = \int \left (-1-\frac {3 e^5}{(-3+x)^2}\right ) \, dx \\ & = -\frac {3 e^5}{3-x}-x \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.82 \[ \int \frac {-9-3 e^5+6 x-x^2}{9-6 x+x^2} \, dx=\frac {3 e^5}{-3+x}-x \]
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Time = 0.10 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.82
method | result | size |
default | \(-x +\frac {3 \,{\mathrm e}^{5}}{-3+x}\) | \(14\) |
risch | \(-x +\frac {3 \,{\mathrm e}^{5}}{-3+x}\) | \(14\) |
gosper | \(\frac {-x^{2}+3 \,{\mathrm e}^{5}+9}{-3+x}\) | \(18\) |
parallelrisch | \(\frac {-x^{2}+3 \,{\mathrm e}^{5}+9}{-3+x}\) | \(18\) |
meijerg | \(\frac {x}{1-\frac {x}{3}}-\frac {{\mathrm e}^{5} x}{3 \left (1-\frac {x}{3}\right )}-\frac {x \left (-x +6\right )}{3 \left (1-\frac {x}{3}\right )}\) | \(38\) |
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Time = 0.23 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.06 \[ \int \frac {-9-3 e^5+6 x-x^2}{9-6 x+x^2} \, dx=-\frac {x^{2} - 3 \, x - 3 \, e^{5}}{x - 3} \]
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Time = 0.04 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.47 \[ \int \frac {-9-3 e^5+6 x-x^2}{9-6 x+x^2} \, dx=- x + \frac {3 e^{5}}{x - 3} \]
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Time = 0.18 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.76 \[ \int \frac {-9-3 e^5+6 x-x^2}{9-6 x+x^2} \, dx=-x + \frac {3 \, e^{5}}{x - 3} \]
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Time = 0.26 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.76 \[ \int \frac {-9-3 e^5+6 x-x^2}{9-6 x+x^2} \, dx=-x + \frac {3 \, e^{5}}{x - 3} \]
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Time = 0.05 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.76 \[ \int \frac {-9-3 e^5+6 x-x^2}{9-6 x+x^2} \, dx=\frac {3\,{\mathrm {e}}^5}{x-3}-x \]
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