Integrand size = 60, antiderivative size = 24 \[ \int \frac {2-156 x+122 x^2-8 x^3+1352 x^4-208 x^5+8 x^6}{1+52 x^2-4 x^3+676 x^4-104 x^5+4 x^6} \, dx=2 x+\frac {3}{1+x^2+(25-2 x) x^2}+\log (2) \]
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Time = 0.06 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.83, number of steps used = 3, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.033, Rules used = {2099, 1602} \[ \int \frac {2-156 x+122 x^2-8 x^3+1352 x^4-208 x^5+8 x^6}{1+52 x^2-4 x^3+676 x^4-104 x^5+4 x^6} \, dx=\frac {3}{-2 x^3+26 x^2+1}+2 x \]
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Rule 1602
Rule 2099
Rubi steps \begin{align*} \text {integral}& = \int \left (2+\frac {6 x (-26+3 x)}{\left (-1-26 x^2+2 x^3\right )^2}\right ) \, dx \\ & = 2 x+6 \int \frac {x (-26+3 x)}{\left (-1-26 x^2+2 x^3\right )^2} \, dx \\ & = 2 x+\frac {3}{1+26 x^2-2 x^3} \\ \end{align*}
Time = 0.02 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.92 \[ \int \frac {2-156 x+122 x^2-8 x^3+1352 x^4-208 x^5+8 x^6}{1+52 x^2-4 x^3+676 x^4-104 x^5+4 x^6} \, dx=2 \left (x-\frac {3}{2 \left (-1-26 x^2+2 x^3\right )}\right ) \]
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Time = 0.04 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.79
method | result | size |
default | \(2 x -\frac {3}{2 \left (x^{3}-13 x^{2}-\frac {1}{2}\right )}\) | \(19\) |
risch | \(2 x -\frac {3}{2 \left (x^{3}-13 x^{2}-\frac {1}{2}\right )}\) | \(19\) |
norman | \(\frac {4 x^{4}-676 x^{2}-2 x -29}{2 x^{3}-26 x^{2}-1}\) | \(31\) |
parallelrisch | \(\frac {8 x^{4}-1352 x^{2}-4 x -58}{4 x^{3}-52 x^{2}-2}\) | \(32\) |
gosper | \(\frac {2 x \left (2 x^{3}-29 x^{2}+39 x -1\right )}{2 x^{3}-26 x^{2}-1}\) | \(33\) |
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Time = 0.29 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.25 \[ \int \frac {2-156 x+122 x^2-8 x^3+1352 x^4-208 x^5+8 x^6}{1+52 x^2-4 x^3+676 x^4-104 x^5+4 x^6} \, dx=\frac {4 \, x^{4} - 52 \, x^{3} - 2 \, x - 3}{2 \, x^{3} - 26 \, x^{2} - 1} \]
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Time = 0.05 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.62 \[ \int \frac {2-156 x+122 x^2-8 x^3+1352 x^4-208 x^5+8 x^6}{1+52 x^2-4 x^3+676 x^4-104 x^5+4 x^6} \, dx=2 x - \frac {3}{2 x^{3} - 26 x^{2} - 1} \]
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Time = 0.19 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.83 \[ \int \frac {2-156 x+122 x^2-8 x^3+1352 x^4-208 x^5+8 x^6}{1+52 x^2-4 x^3+676 x^4-104 x^5+4 x^6} \, dx=2 \, x - \frac {3}{2 \, x^{3} - 26 \, x^{2} - 1} \]
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Time = 0.27 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.83 \[ \int \frac {2-156 x+122 x^2-8 x^3+1352 x^4-208 x^5+8 x^6}{1+52 x^2-4 x^3+676 x^4-104 x^5+4 x^6} \, dx=2 \, x - \frac {3}{2 \, x^{3} - 26 \, x^{2} - 1} \]
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Time = 12.32 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.83 \[ \int \frac {2-156 x+122 x^2-8 x^3+1352 x^4-208 x^5+8 x^6}{1+52 x^2-4 x^3+676 x^4-104 x^5+4 x^6} \, dx=2\,x+\frac {3}{2\,\left (-x^3+13\,x^2+\frac {1}{2}\right )} \]
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