Integrand size = 23, antiderivative size = 19 \[ \int \frac {-17+12 x+12 x^2}{3+12 x+12 x^2} \, dx=-e^5+x-\frac {20 x}{3 (1+2 x)} \]
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Time = 0.01 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.68, 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} \[ \int \frac {-17+12 x+12 x^2}{3+12 x+12 x^2} \, dx=x+\frac {10}{3 (2 x+1)} \]
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Rule 12
Rule 27
Rule 697
Rubi steps \begin{align*} \text {integral}& = \int \frac {-17+12 x+12 x^2}{3 (1+2 x)^2} \, dx \\ & = \frac {1}{3} \int \frac {-17+12 x+12 x^2}{(1+2 x)^2} \, dx \\ & = \frac {1}{3} \int \left (3-\frac {20}{(1+2 x)^2}\right ) \, dx \\ & = x+\frac {10}{3 (1+2 x)} \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.05 \[ \int \frac {-17+12 x+12 x^2}{3+12 x+12 x^2} \, dx=\frac {1}{3} \left (\frac {3}{2}+3 x+\frac {10}{1+2 x}\right ) \]
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Time = 0.47 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.53
method | result | size |
risch | \(x +\frac {5}{3 \left (\frac {1}{2}+x \right )}\) | \(10\) |
default | \(x +\frac {10}{3 \left (1+2 x \right )}\) | \(12\) |
gosper | \(\frac {x \left (6 x -17\right )}{6 x +3}\) | \(16\) |
norman | \(\frac {-\frac {17}{3} x +2 x^{2}}{1+2 x}\) | \(18\) |
parallelrisch | \(\frac {6 x^{2}-17 x}{6 x +3}\) | \(19\) |
meijerg | \(-\frac {23 x}{3 \left (1+2 x \right )}+\frac {x \left (6+6 x \right )}{6 x +3}\) | \(27\) |
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Time = 0.26 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.00 \[ \int \frac {-17+12 x+12 x^2}{3+12 x+12 x^2} \, dx=\frac {6 \, x^{2} + 3 \, x + 10}{3 \, {\left (2 \, x + 1\right )}} \]
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Time = 0.03 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.37 \[ \int \frac {-17+12 x+12 x^2}{3+12 x+12 x^2} \, dx=x + \frac {10}{6 x + 3} \]
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Time = 0.19 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.58 \[ \int \frac {-17+12 x+12 x^2}{3+12 x+12 x^2} \, dx=x + \frac {10}{3 \, {\left (2 \, x + 1\right )}} \]
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Time = 0.27 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.58 \[ \int \frac {-17+12 x+12 x^2}{3+12 x+12 x^2} \, dx=x + \frac {10}{3 \, {\left (2 \, x + 1\right )}} \]
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Time = 0.04 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.58 \[ \int \frac {-17+12 x+12 x^2}{3+12 x+12 x^2} \, dx=x+\frac {5}{3\,\left (x+\frac {1}{2}\right )} \]
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