Integrand size = 83, antiderivative size = 27 \[ \int \frac {-3125+20625 x-49125 x^2+49775 x^3-19650 x^4+3300 x^5-200 x^6+e^{10} \left (-5+33 x-10 x^2\right )}{125 x^2-825 x^3+1965 x^4-1991 x^5+786 x^6-132 x^7+8 x^8} \, dx=\frac {25+\frac {e^{10}}{(1-2 x)^2 (5-x)^2}-x}{x} \]
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Leaf count is larger than twice the leaf count of optimal. \(69\) vs. \(2(27)=54\).
Time = 0.12 (sec) , antiderivative size = 69, normalized size of antiderivative = 2.56, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.012, Rules used = {2099} \[ \int \frac {-3125+20625 x-49125 x^2+49775 x^3-19650 x^4+3300 x^5-200 x^6+e^{10} \left (-5+33 x-10 x^2\right )}{125 x^2-825 x^3+1965 x^4-1991 x^5+786 x^6-132 x^7+8 x^8} \, dx=\frac {29 e^{10}}{18225 (5-x)}+\frac {625+e^{10}}{25 x}+\frac {e^{10}}{405 (5-x)^2}+\frac {56 e^{10}}{729 (1-2 x)}+\frac {8 e^{10}}{81 (1-2 x)^2} \]
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Rule 2099
Rubi steps \begin{align*} \text {integral}& = \int \left (-\frac {2 e^{10}}{405 (-5+x)^3}+\frac {29 e^{10}}{18225 (-5+x)^2}+\frac {-625-e^{10}}{25 x^2}-\frac {32 e^{10}}{81 (-1+2 x)^3}+\frac {112 e^{10}}{729 (-1+2 x)^2}\right ) \, dx \\ & = \frac {8 e^{10}}{81 (1-2 x)^2}+\frac {56 e^{10}}{729 (1-2 x)}+\frac {e^{10}}{405 (5-x)^2}+\frac {29 e^{10}}{18225 (5-x)}+\frac {625+e^{10}}{25 x} \\ \end{align*}
Time = 0.03 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.26 \[ \int \frac {-3125+20625 x-49125 x^2+49775 x^3-19650 x^4+3300 x^5-200 x^6+e^{10} \left (-5+33 x-10 x^2\right )}{125 x^2-825 x^3+1965 x^4-1991 x^5+786 x^6-132 x^7+8 x^8} \, dx=\frac {e^{10}+25 \left (5-11 x+2 x^2\right )^2}{x \left (5-11 x+2 x^2\right )^2} \]
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Time = 0.23 (sec) , antiderivative size = 41, normalized size of antiderivative = 1.52
method | result | size |
norman | \(\frac {100 x^{4}-1100 x^{3}+{\mathrm e}^{10}+3525 x^{2}-2750 x +625}{x \left (2 x^{2}-11 x +5\right )^{2}}\) | \(41\) |
gosper | \(\frac {100 x^{4}-1100 x^{3}+{\mathrm e}^{10}+3525 x^{2}-2750 x +625}{x \left (4 x^{4}-44 x^{3}+141 x^{2}-110 x +25\right )}\) | \(51\) |
risch | \(\frac {100 x^{4}-1100 x^{3}+{\mathrm e}^{10}+3525 x^{2}-2750 x +625}{x \left (4 x^{4}-44 x^{3}+141 x^{2}-110 x +25\right )}\) | \(52\) |
default | \(\frac {8 \,{\mathrm e}^{10}}{81 \left (-1+2 x \right )^{2}}-\frac {56 \,{\mathrm e}^{10}}{729 \left (-1+2 x \right )}-\frac {-\frac {{\mathrm e}^{10}}{25}-25}{x}+\frac {{\mathrm e}^{10}}{405 \left (-5+x \right )^{2}}-\frac {29 \,{\mathrm e}^{10}}{18225 \left (-5+x \right )}\) | \(53\) |
parallelrisch | \(\frac {15625+11000 x^{5}-118500 x^{4}+360250 x^{3}+25 \,{\mathrm e}^{10}-214375 x^{2}}{25 x \left (4 x^{4}-44 x^{3}+141 x^{2}-110 x +25\right )}\) | \(56\) |
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Leaf count of result is larger than twice the leaf count of optimal. 49 vs. \(2 (24) = 48\).
Time = 0.25 (sec) , antiderivative size = 49, normalized size of antiderivative = 1.81 \[ \int \frac {-3125+20625 x-49125 x^2+49775 x^3-19650 x^4+3300 x^5-200 x^6+e^{10} \left (-5+33 x-10 x^2\right )}{125 x^2-825 x^3+1965 x^4-1991 x^5+786 x^6-132 x^7+8 x^8} \, dx=\frac {100 \, x^{4} - 1100 \, x^{3} + 3525 \, x^{2} - 2750 \, x + e^{10} + 625}{4 \, x^{5} - 44 \, x^{4} + 141 \, x^{3} - 110 \, x^{2} + 25 \, x} \]
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Leaf count of result is larger than twice the leaf count of optimal. 48 vs. \(2 (19) = 38\).
Time = 0.52 (sec) , antiderivative size = 48, normalized size of antiderivative = 1.78 \[ \int \frac {-3125+20625 x-49125 x^2+49775 x^3-19650 x^4+3300 x^5-200 x^6+e^{10} \left (-5+33 x-10 x^2\right )}{125 x^2-825 x^3+1965 x^4-1991 x^5+786 x^6-132 x^7+8 x^8} \, dx=- \frac {- 100 x^{4} + 1100 x^{3} - 3525 x^{2} + 2750 x - e^{10} - 625}{4 x^{5} - 44 x^{4} + 141 x^{3} - 110 x^{2} + 25 x} \]
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Leaf count of result is larger than twice the leaf count of optimal. 49 vs. \(2 (24) = 48\).
Time = 0.20 (sec) , antiderivative size = 49, normalized size of antiderivative = 1.81 \[ \int \frac {-3125+20625 x-49125 x^2+49775 x^3-19650 x^4+3300 x^5-200 x^6+e^{10} \left (-5+33 x-10 x^2\right )}{125 x^2-825 x^3+1965 x^4-1991 x^5+786 x^6-132 x^7+8 x^8} \, dx=\frac {100 \, x^{4} - 1100 \, x^{3} + 3525 \, x^{2} - 2750 \, x + e^{10} + 625}{4 \, x^{5} - 44 \, x^{4} + 141 \, x^{3} - 110 \, x^{2} + 25 \, x} \]
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none
Time = 0.29 (sec) , antiderivative size = 48, normalized size of antiderivative = 1.78 \[ \int \frac {-3125+20625 x-49125 x^2+49775 x^3-19650 x^4+3300 x^5-200 x^6+e^{10} \left (-5+33 x-10 x^2\right )}{125 x^2-825 x^3+1965 x^4-1991 x^5+786 x^6-132 x^7+8 x^8} \, dx=\frac {e^{10} + 625}{25 \, x} - \frac {4 \, x^{3} e^{10} - 44 \, x^{2} e^{10} + 141 \, x e^{10} - 110 \, e^{10}}{25 \, {\left (2 \, x^{2} - 11 \, x + 5\right )}^{2}} \]
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Time = 15.97 (sec) , antiderivative size = 53, normalized size of antiderivative = 1.96 \[ \int \frac {-3125+20625 x-49125 x^2+49775 x^3-19650 x^4+3300 x^5-200 x^6+e^{10} \left (-5+33 x-10 x^2\right )}{125 x^2-825 x^3+1965 x^4-1991 x^5+786 x^6-132 x^7+8 x^8} \, dx=\frac {8\,{\mathrm {e}}^{10}}{81\,{\left (2\,x-1\right )}^2}-\frac {56\,{\mathrm {e}}^{10}}{729\,\left (2\,x-1\right )}+\frac {\frac {{\mathrm {e}}^{10}}{25}+25}{x}-\frac {29\,{\mathrm {e}}^{10}}{18225\,\left (x-5\right )}+\frac {{\mathrm {e}}^{10}}{405\,{\left (x-5\right )}^2} \]
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