Integrand size = 23, antiderivative size = 35 \[ \int \frac {-73-24 x+12 x^2}{15-30 x+15 x^2} \, dx=-2+2 x-\frac {\left (\frac {20}{3}-x\right ) x}{1-x}+\frac {1}{5} (-1-x-\log (4)) \]
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Time = 0.01 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.49, 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} \[ \int \frac {-73-24 x+12 x^2}{15-30 x+15 x^2} \, dx=\frac {4 x}{5}-\frac {17}{3 (1-x)} \]
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Rule 12
Rule 27
Rule 697
Rubi steps \begin{align*} \text {integral}& = \int \frac {-73-24 x+12 x^2}{15 (-1+x)^2} \, dx \\ & = \frac {1}{15} \int \frac {-73-24 x+12 x^2}{(-1+x)^2} \, dx \\ & = \frac {1}{15} \int \left (12-\frac {85}{(-1+x)^2}\right ) \, dx \\ & = -\frac {17}{3 (1-x)}+\frac {4 x}{5} \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.49 \[ \int \frac {-73-24 x+12 x^2}{15-30 x+15 x^2} \, dx=\frac {1}{15} \left (\frac {85}{-1+x}+12 (-1+x)\right ) \]
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Time = 0.09 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.34
method | result | size |
default | \(\frac {4 x}{5}+\frac {17}{3 \left (-1+x \right )}\) | \(12\) |
risch | \(\frac {4 x}{5}+\frac {17}{3 \left (-1+x \right )}\) | \(12\) |
norman | \(\frac {\frac {4 x^{2}}{5}+\frac {73}{15}}{-1+x}\) | \(14\) |
gosper | \(\frac {12 x^{2}+73}{15 x -15}\) | \(15\) |
parallelrisch | \(\frac {12 x^{2}+73}{15 x -15}\) | \(15\) |
meijerg | \(-\frac {97 x}{15 \left (1-x \right )}+\frac {4 x \left (-3 x +6\right )}{15 \left (1-x \right )}\) | \(27\) |
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Time = 0.25 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.49 \[ \int \frac {-73-24 x+12 x^2}{15-30 x+15 x^2} \, dx=\frac {12 \, x^{2} - 12 \, x + 85}{15 \, {\left (x - 1\right )}} \]
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Time = 0.04 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.29 \[ \int \frac {-73-24 x+12 x^2}{15-30 x+15 x^2} \, dx=\frac {4 x}{5} + \frac {17}{3 x - 3} \]
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Time = 0.20 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.31 \[ \int \frac {-73-24 x+12 x^2}{15-30 x+15 x^2} \, dx=\frac {4}{5} \, x + \frac {17}{3 \, {\left (x - 1\right )}} \]
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Time = 0.26 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.31 \[ \int \frac {-73-24 x+12 x^2}{15-30 x+15 x^2} \, dx=\frac {4}{5} \, x + \frac {17}{3 \, {\left (x - 1\right )}} \]
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Time = 0.04 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.37 \[ \int \frac {-73-24 x+12 x^2}{15-30 x+15 x^2} \, dx=\frac {4\,x}{5}+\frac {17}{3\,\left (x-1\right )} \]
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