Integrand size = 23, antiderivative size = 26 \[ \int \frac {-43+40 x-10 x^2}{12-12 x+3 x^2} \, dx=5-5 e^3-\frac {1}{2-x}+\frac {5 x}{3}-5 (5+x) \]
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Time = 0.01 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.58, number of steps used = 4, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.130, Rules used = {27, 12, 697} \[ \int \frac {-43+40 x-10 x^2}{12-12 x+3 x^2} \, dx=-\frac {10 x}{3}-\frac {1}{2-x} \]
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Rule 12
Rule 27
Rule 697
Rubi steps \begin{align*} \text {integral}& = \int \frac {-43+40 x-10 x^2}{3 (-2+x)^2} \, dx \\ & = \frac {1}{3} \int \frac {-43+40 x-10 x^2}{(-2+x)^2} \, dx \\ & = \frac {1}{3} \int \left (-10-\frac {3}{(-2+x)^2}\right ) \, dx \\ & = -\frac {1}{2-x}-\frac {10 x}{3} \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.65 \[ \int \frac {-43+40 x-10 x^2}{12-12 x+3 x^2} \, dx=\frac {1}{3} \left (\frac {3}{-2+x}-10 (-2+x)\right ) \]
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Time = 0.07 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.38
method | result | size |
default | \(-\frac {10 x}{3}+\frac {1}{-2+x}\) | \(10\) |
risch | \(-\frac {10 x}{3}+\frac {1}{-2+x}\) | \(10\) |
norman | \(\frac {-\frac {10 x^{2}}{3}+\frac {43}{3}}{-2+x}\) | \(14\) |
gosper | \(-\frac {10 x^{2}-43}{3 \left (-2+x \right )}\) | \(15\) |
parallelrisch | \(-\frac {10 x^{2}-43}{3 \left (-2+x \right )}\) | \(15\) |
meijerg | \(\frac {37 x}{12 \left (1-\frac {x}{2}\right )}-\frac {10 x \left (-\frac {3 x}{2}+6\right )}{9 \left (1-\frac {x}{2}\right )}\) | \(27\) |
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Time = 0.24 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.65 \[ \int \frac {-43+40 x-10 x^2}{12-12 x+3 x^2} \, dx=-\frac {10 \, x^{2} - 20 \, x - 3}{3 \, {\left (x - 2\right )}} \]
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Time = 0.03 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.31 \[ \int \frac {-43+40 x-10 x^2}{12-12 x+3 x^2} \, dx=- \frac {10 x}{3} + \frac {1}{x - 2} \]
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Time = 0.17 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.35 \[ \int \frac {-43+40 x-10 x^2}{12-12 x+3 x^2} \, dx=-\frac {10}{3} \, x + \frac {1}{x - 2} \]
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Time = 0.26 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.35 \[ \int \frac {-43+40 x-10 x^2}{12-12 x+3 x^2} \, dx=-\frac {10}{3} \, x + \frac {1}{x - 2} \]
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Time = 8.09 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.35 \[ \int \frac {-43+40 x-10 x^2}{12-12 x+3 x^2} \, dx=\frac {1}{x-2}-\frac {10\,x}{3} \]
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