Integrand size = 84, antiderivative size = 23 \[ \int \frac {-10000-30000 x-19600 x^2+200 x^3+792 x^5-24 x^6+48 x^7+64 x^8+e^4 \left (16 x^5+32 x^6\right )+e^2 \left (400 x^2+800 x^3+8 x^5-64 x^6-96 x^7\right )}{x^5} \, dx=\left (-2-\left (e^2-\frac {25}{x^2}-x\right ) (2+4 x)\right )^2 \]
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Leaf count is larger than twice the leaf count of optimal. \(82\) vs. \(2(23)=46\).
Time = 0.04 (sec) , antiderivative size = 82, normalized size of antiderivative = 3.57, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.012, Rules used = {14} \[ \int \frac {-10000-30000 x-19600 x^2+200 x^3+792 x^5-24 x^6+48 x^7+64 x^8+e^4 \left (16 x^5+32 x^6\right )+e^2 \left (400 x^2+800 x^3+8 x^5-64 x^6-96 x^7\right )}{x^5} \, dx=16 x^4+\frac {2500}{x^4}+16 \left (1-2 e^2\right ) x^3+\frac {10000}{x^3}-4 \left (3+8 e^2-4 e^4\right ) x^2+\frac {200 \left (49-e^2\right )}{x^2}+8 \left (99+e^2+2 e^4\right ) x-\frac {200 \left (1+4 e^2\right )}{x} \]
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Rule 14
Rubi steps \begin{align*} \text {integral}& = \int \left (8 \left (99+e^2+2 e^4\right )-\frac {10000}{x^5}-\frac {30000}{x^4}+\frac {400 \left (-49+e^2\right )}{x^3}+\frac {200 \left (1+4 e^2\right )}{x^2}+8 \left (-3-8 e^2+4 e^4\right ) x-48 \left (-1+2 e^2\right ) x^2+64 x^3\right ) \, dx \\ & = \frac {2500}{x^4}+\frac {10000}{x^3}+\frac {200 \left (49-e^2\right )}{x^2}-\frac {200 \left (1+4 e^2\right )}{x}+8 \left (99+e^2+2 e^4\right ) x-4 \left (3+8 e^2-4 e^4\right ) x^2+16 \left (1-2 e^2\right ) x^3+16 x^4 \\ \end{align*}
Leaf count is larger than twice the leaf count of optimal. \(85\) vs. \(2(23)=46\).
Time = 0.03 (sec) , antiderivative size = 85, normalized size of antiderivative = 3.70 \[ \int \frac {-10000-30000 x-19600 x^2+200 x^3+792 x^5-24 x^6+48 x^7+64 x^8+e^4 \left (16 x^5+32 x^6\right )+e^2 \left (400 x^2+800 x^3+8 x^5-64 x^6-96 x^7\right )}{x^5} \, dx=8 \left (\frac {625}{2 x^4}+\frac {1250}{x^3}-\frac {25 \left (-49+e^2\right )}{x^2}-\frac {25 \left (1+4 e^2\right )}{x}+\left (99+e^2+2 e^4\right ) x+\frac {1}{2} \left (-3-8 e^2+4 e^4\right ) x^2-2 \left (-1+2 e^2\right ) x^3+2 x^4\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. \(76\) vs. \(2(22)=44\).
Time = 0.08 (sec) , antiderivative size = 77, normalized size of antiderivative = 3.35
method | result | size |
norman | \(\frac {2500+\left (-800 \,{\mathrm e}^{2}-200\right ) x^{3}+\left (-200 \,{\mathrm e}^{2}+9800\right ) x^{2}+\left (-32 \,{\mathrm e}^{2}+16\right ) x^{7}+\left (16 \,{\mathrm e}^{4}-32 \,{\mathrm e}^{2}-12\right ) x^{6}+\left (16 \,{\mathrm e}^{4}+8 \,{\mathrm e}^{2}+792\right ) x^{5}+10000 x +16 x^{8}}{x^{4}}\) | \(77\) |
risch | \(16 x^{2} {\mathrm e}^{4}-32 x^{3} {\mathrm e}^{2}+16 x^{4}+16 x \,{\mathrm e}^{4}-32 x^{2} {\mathrm e}^{2}+16 x^{3}+8 \,{\mathrm e}^{2} x -12 x^{2}+792 x +\frac {\left (-800 \,{\mathrm e}^{2}-200\right ) x^{3}+\left (-200 \,{\mathrm e}^{2}+9800\right ) x^{2}+10000 x +2500}{x^{4}}\) | \(80\) |
default | \(-32 x^{3} {\mathrm e}^{2}+16 x^{4}-32 x^{2} {\mathrm e}^{2}+16 x^{2} {\mathrm e}^{4}+16 x^{3}+8 \,{\mathrm e}^{2} x +16 x \,{\mathrm e}^{4}-12 x^{2}+792 x +\frac {2500}{x^{4}}+\frac {10000}{x^{3}}-\frac {8 \left (100 \,{\mathrm e}^{2}+25\right )}{x}-\frac {4 \left (-2450+50 \,{\mathrm e}^{2}\right )}{x^{2}}\) | \(83\) |
parallelrisch | \(\frac {16 x^{6} {\mathrm e}^{4}-32 \,{\mathrm e}^{2} x^{7}+16 x^{8}+16 x^{5} {\mathrm e}^{4}-32 x^{6} {\mathrm e}^{2}+16 x^{7}+8 \,{\mathrm e}^{2} x^{5}-12 x^{6}+792 x^{5}+2500-800 x^{3} {\mathrm e}^{2}-200 x^{2} {\mathrm e}^{2}-200 x^{3}+9800 x^{2}+10000 x}{x^{4}}\) | \(93\) |
gosper | \(\frac {16 x^{6} {\mathrm e}^{4}-32 \,{\mathrm e}^{2} x^{7}+16 x^{8}+16 x^{5} {\mathrm e}^{4}-32 x^{6} {\mathrm e}^{2}+16 x^{7}+8 \,{\mathrm e}^{2} x^{5}-12 x^{6}+792 x^{5}+2500-800 x^{3} {\mathrm e}^{2}-200 x^{2} {\mathrm e}^{2}-200 x^{3}+9800 x^{2}+10000 x}{x^{4}}\) | \(94\) |
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Leaf count of result is larger than twice the leaf count of optimal. 81 vs. \(2 (23) = 46\).
Time = 0.26 (sec) , antiderivative size = 81, normalized size of antiderivative = 3.52 \[ \int \frac {-10000-30000 x-19600 x^2+200 x^3+792 x^5-24 x^6+48 x^7+64 x^8+e^4 \left (16 x^5+32 x^6\right )+e^2 \left (400 x^2+800 x^3+8 x^5-64 x^6-96 x^7\right )}{x^5} \, dx=\frac {4 \, {\left (4 \, x^{8} + 4 \, x^{7} - 3 \, x^{6} + 198 \, x^{5} - 50 \, x^{3} + 2450 \, x^{2} + 4 \, {\left (x^{6} + x^{5}\right )} e^{4} - 2 \, {\left (4 \, x^{7} + 4 \, x^{6} - x^{5} + 100 \, x^{3} + 25 \, x^{2}\right )} e^{2} + 2500 \, x + 625\right )}}{x^{4}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 73 vs. \(2 (19) = 38\).
Time = 0.25 (sec) , antiderivative size = 73, normalized size of antiderivative = 3.17 \[ \int \frac {-10000-30000 x-19600 x^2+200 x^3+792 x^5-24 x^6+48 x^7+64 x^8+e^4 \left (16 x^5+32 x^6\right )+e^2 \left (400 x^2+800 x^3+8 x^5-64 x^6-96 x^7\right )}{x^5} \, dx=16 x^{4} + x^{3} \cdot \left (16 - 32 e^{2}\right ) + x^{2} \left (- 32 e^{2} - 12 + 16 e^{4}\right ) + x \left (8 e^{2} + 792 + 16 e^{4}\right ) + \frac {x^{3} \left (- 800 e^{2} - 200\right ) + x^{2} \cdot \left (9800 - 200 e^{2}\right ) + 10000 x + 2500}{x^{4}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 73 vs. \(2 (23) = 46\).
Time = 0.18 (sec) , antiderivative size = 73, normalized size of antiderivative = 3.17 \[ \int \frac {-10000-30000 x-19600 x^2+200 x^3+792 x^5-24 x^6+48 x^7+64 x^8+e^4 \left (16 x^5+32 x^6\right )+e^2 \left (400 x^2+800 x^3+8 x^5-64 x^6-96 x^7\right )}{x^5} \, dx=16 \, x^{4} - 16 \, x^{3} {\left (2 \, e^{2} - 1\right )} + 4 \, x^{2} {\left (4 \, e^{4} - 8 \, e^{2} - 3\right )} + 8 \, x {\left (2 \, e^{4} + e^{2} + 99\right )} - \frac {100 \, {\left (2 \, x^{3} {\left (4 \, e^{2} + 1\right )} + 2 \, x^{2} {\left (e^{2} - 49\right )} - 100 \, x - 25\right )}}{x^{4}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 84 vs. \(2 (23) = 46\).
Time = 0.28 (sec) , antiderivative size = 84, normalized size of antiderivative = 3.65 \[ \int \frac {-10000-30000 x-19600 x^2+200 x^3+792 x^5-24 x^6+48 x^7+64 x^8+e^4 \left (16 x^5+32 x^6\right )+e^2 \left (400 x^2+800 x^3+8 x^5-64 x^6-96 x^7\right )}{x^5} \, dx=16 \, x^{4} - 32 \, x^{3} e^{2} + 16 \, x^{3} + 16 \, x^{2} e^{4} - 32 \, x^{2} e^{2} - 12 \, x^{2} + 16 \, x e^{4} + 8 \, x e^{2} + 792 \, x - \frac {100 \, {\left (8 \, x^{3} e^{2} + 2 \, x^{3} + 2 \, x^{2} e^{2} - 98 \, x^{2} - 100 \, x - 25\right )}}{x^{4}} \]
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Time = 11.36 (sec) , antiderivative size = 75, normalized size of antiderivative = 3.26 \[ \int \frac {-10000-30000 x-19600 x^2+200 x^3+792 x^5-24 x^6+48 x^7+64 x^8+e^4 \left (16 x^5+32 x^6\right )+e^2 \left (400 x^2+800 x^3+8 x^5-64 x^6-96 x^7\right )}{x^5} \, dx=\frac {\left (-800\,{\mathrm {e}}^2-200\right )\,x^3+\left (9800-200\,{\mathrm {e}}^2\right )\,x^2+10000\,x+2500}{x^4}-x^2\,\left (32\,{\mathrm {e}}^2-16\,{\mathrm {e}}^4+12\right )-x^3\,\left (32\,{\mathrm {e}}^2-16\right )+x\,\left (8\,{\mathrm {e}}^2+16\,{\mathrm {e}}^4+792\right )+16\,x^4 \]
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