Integrand size = 51, antiderivative size = 25 \[ \int \frac {-71+96 e^2-80 e^4+32 e^6-8 e^8-3 x+3 x^2-x^3}{-1+3 x-3 x^2+x^3} \, dx=25+\frac {4 \left (2+\left (-1+e^2\right )^2\right )^2}{(1-x)^2}-x \]
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Time = 0.03 (sec) , antiderivative size = 25, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.020, Rules used = {2099} \[ \int \frac {-71+96 e^2-80 e^4+32 e^6-8 e^8-3 x+3 x^2-x^3}{-1+3 x-3 x^2+x^3} \, dx=\frac {4 \left (3-2 e^2+e^4\right )^2}{(1-x)^2}-x \]
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Rule 2099
Rubi steps \begin{align*} \text {integral}& = \int \left (-1-\frac {8 \left (3-2 e^2+e^4\right )^2}{(-1+x)^3}\right ) \, dx \\ & = \frac {4 \left (3-2 e^2+e^4\right )^2}{(1-x)^2}-x \\ \end{align*}
Time = 0.02 (sec) , antiderivative size = 23, normalized size of antiderivative = 0.92 \[ \int \frac {-71+96 e^2-80 e^4+32 e^6-8 e^8-3 x+3 x^2-x^3}{-1+3 x-3 x^2+x^3} \, dx=\frac {4 \left (3-2 e^2+e^4\right )^2}{(-1+x)^2}-x \]
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Time = 0.12 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.20
method | result | size |
default | \(-x -\frac {-72+96 \,{\mathrm e}^{2}-80 \,{\mathrm e}^{4}-8 \,{\mathrm e}^{8}+32 \,{\mathrm e}^{6}}{2 \left (-1+x \right )^{2}}\) | \(30\) |
gosper | \(\frac {4 \,{\mathrm e}^{8}-16 \,{\mathrm e}^{6}-x^{3}+40 \,{\mathrm e}^{4}-48 \,{\mathrm e}^{2}+3 x +34}{x^{2}-2 x +1}\) | \(44\) |
parallelrisch | \(\frac {4 \,{\mathrm e}^{8}-16 \,{\mathrm e}^{6}-x^{3}+40 \,{\mathrm e}^{4}-48 \,{\mathrm e}^{2}+3 x +34}{x^{2}-2 x +1}\) | \(44\) |
risch | \(-x +\frac {4 \,{\mathrm e}^{8}}{x^{2}-2 x +1}-\frac {16 \,{\mathrm e}^{6}}{x^{2}-2 x +1}+\frac {40 \,{\mathrm e}^{4}}{x^{2}-2 x +1}-\frac {48 \,{\mathrm e}^{2}}{x^{2}-2 x +1}+\frac {36}{x^{2}-2 x +1}\) | \(73\) |
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Time = 0.30 (sec) , antiderivative size = 39, normalized size of antiderivative = 1.56 \[ \int \frac {-71+96 e^2-80 e^4+32 e^6-8 e^8-3 x+3 x^2-x^3}{-1+3 x-3 x^2+x^3} \, dx=-\frac {x^{3} - 2 \, x^{2} + x - 4 \, e^{8} + 16 \, e^{6} - 40 \, e^{4} + 48 \, e^{2} - 36}{x^{2} - 2 \, x + 1} \]
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Time = 0.13 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.28 \[ \int \frac {-71+96 e^2-80 e^4+32 e^6-8 e^8-3 x+3 x^2-x^3}{-1+3 x-3 x^2+x^3} \, dx=- x - \frac {- 4 e^{8} - 40 e^{4} - 36 + 48 e^{2} + 16 e^{6}}{x^{2} - 2 x + 1} \]
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Time = 0.17 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.28 \[ \int \frac {-71+96 e^2-80 e^4+32 e^6-8 e^8-3 x+3 x^2-x^3}{-1+3 x-3 x^2+x^3} \, dx=-x + \frac {4 \, {\left (e^{8} - 4 \, e^{6} + 10 \, e^{4} - 12 \, e^{2} + 9\right )}}{x^{2} - 2 \, x + 1} \]
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Time = 0.26 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.08 \[ \int \frac {-71+96 e^2-80 e^4+32 e^6-8 e^8-3 x+3 x^2-x^3}{-1+3 x-3 x^2+x^3} \, dx=-x + \frac {4 \, {\left (e^{8} - 4 \, e^{6} + 10 \, e^{4} - 12 \, e^{2} + 9\right )}}{{\left (x - 1\right )}^{2}} \]
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Time = 0.10 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.12 \[ \int \frac {-71+96 e^2-80 e^4+32 e^6-8 e^8-3 x+3 x^2-x^3}{-1+3 x-3 x^2+x^3} \, dx=\frac {40\,{\mathrm {e}}^4-48\,{\mathrm {e}}^2-16\,{\mathrm {e}}^6+4\,{\mathrm {e}}^8+36}{{\left (x-1\right )}^2}-x \]
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