Integrand size = 23, antiderivative size = 14 \[ \int \frac {1326-260 x+25 x^2}{676-260 x+25 x^2} \, dx=x+\frac {5 x}{\frac {26}{5}-x} \]
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Time = 0.01 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.79, number of steps used = 3, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.087, Rules used = {27, 697} \[ \int \frac {1326-260 x+25 x^2}{676-260 x+25 x^2} \, dx=x+\frac {130}{26-5 x} \]
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Rule 27
Rule 697
Rubi steps \begin{align*} \text {integral}& = \int \frac {1326-260 x+25 x^2}{(-26+5 x)^2} \, dx \\ & = \int \left (1+\frac {650}{(-26+5 x)^2}\right ) \, dx \\ & = \frac {130}{26-5 x}+x \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.79 \[ \int \frac {1326-260 x+25 x^2}{676-260 x+25 x^2} \, dx=\frac {130}{26-5 x}+x \]
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Time = 0.82 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.71
method | result | size |
risch | \(x -\frac {26}{x -\frac {26}{5}}\) | \(10\) |
default | \(x -\frac {130}{5 x -26}\) | \(12\) |
norman | \(\frac {5 x^{2}-\frac {1326}{5}}{5 x -26}\) | \(16\) |
gosper | \(\frac {25 x^{2}-1326}{25 x -130}\) | \(17\) |
parallelrisch | \(\frac {25 x^{2}-1326}{25 x -130}\) | \(17\) |
meijerg | \(-\frac {x}{26 \left (1-\frac {5 x}{26}\right )}+\frac {x \left (-\frac {15 x}{26}+6\right )}{3-\frac {15 x}{26}}\) | \(27\) |
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none
Time = 0.25 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.29 \[ \int \frac {1326-260 x+25 x^2}{676-260 x+25 x^2} \, dx=\frac {5 \, x^{2} - 26 \, x - 130}{5 \, x - 26} \]
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Time = 0.03 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.50 \[ \int \frac {1326-260 x+25 x^2}{676-260 x+25 x^2} \, dx=x - \frac {130}{5 x - 26} \]
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Time = 0.18 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.79 \[ \int \frac {1326-260 x+25 x^2}{676-260 x+25 x^2} \, dx=x - \frac {130}{5 \, x - 26} \]
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Time = 0.27 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.79 \[ \int \frac {1326-260 x+25 x^2}{676-260 x+25 x^2} \, dx=x - \frac {130}{5 \, x - 26} \]
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Time = 11.74 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.64 \[ \int \frac {1326-260 x+25 x^2}{676-260 x+25 x^2} \, dx=x-\frac {26}{x-\frac {26}{5}} \]
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