Integrand size = 132, antiderivative size = 24 \[ \int \frac {e^{\frac {65536 x+16384 x^2-261121 x^3-65536 x^4-8196 x^5-512 x^6-16 x^7}{65536+16384 x+2048 x^2+128 x^3+4 x^4}} \left (8388608+3145728 x-100467072 x^2-37765136 x^3-7081471 x^4-786624 x^5-55300 x^6-2304 x^7-48 x^8\right )}{8388608+3145728 x+589824 x^2+65536 x^3+4608 x^4+192 x^5+4 x^6} \, dx=e^{x-x^3 \left (2+\frac {1}{x^2+(16+x)^2}\right )^2} \]
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\[ \int \frac {e^{\frac {65536 x+16384 x^2-261121 x^3-65536 x^4-8196 x^5-512 x^6-16 x^7}{65536+16384 x+2048 x^2+128 x^3+4 x^4}} \left (8388608+3145728 x-100467072 x^2-37765136 x^3-7081471 x^4-786624 x^5-55300 x^6-2304 x^7-48 x^8\right )}{8388608+3145728 x+589824 x^2+65536 x^3+4608 x^4+192 x^5+4 x^6} \, dx=\int \frac {\exp \left (\frac {65536 x+16384 x^2-261121 x^3-65536 x^4-8196 x^5-512 x^6-16 x^7}{65536+16384 x+2048 x^2+128 x^3+4 x^4}\right ) \left (8388608+3145728 x-100467072 x^2-37765136 x^3-7081471 x^4-786624 x^5-55300 x^6-2304 x^7-48 x^8\right )}{8388608+3145728 x+589824 x^2+65536 x^3+4608 x^4+192 x^5+4 x^6} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {\exp \left (-\frac {x \left (-65536-16384 x+261121 x^2+65536 x^3+8196 x^4+512 x^5+16 x^6\right )}{4 \left (128+16 x+x^2\right )^2}\right ) \left (8388608+3145728 x-100467072 x^2-37765136 x^3-7081471 x^4-786624 x^5-55300 x^6-2304 x^7-48 x^8\right )}{4 \left (128+16 x+x^2\right )^3} \, dx \\ & = \frac {1}{4} \int \frac {\exp \left (-\frac {x \left (-65536-16384 x+261121 x^2+65536 x^3+8196 x^4+512 x^5+16 x^6\right )}{4 \left (128+16 x+x^2\right )^2}\right ) \left (8388608+3145728 x-100467072 x^2-37765136 x^3-7081471 x^4-786624 x^5-55300 x^6-2304 x^7-48 x^8\right )}{\left (128+16 x+x^2\right )^3} \, dx \\ & = \frac {1}{4} \int \left (-4 \exp \left (-\frac {x \left (-65536-16384 x+261121 x^2+65536 x^3+8196 x^4+512 x^5+16 x^6\right )}{4 \left (128+16 x+x^2\right )^2}\right )-48 \exp \left (-\frac {x \left (-65536-16384 x+261121 x^2+65536 x^3+8196 x^4+512 x^5+16 x^6\right )}{4 \left (128+16 x+x^2\right )^2}\right ) x^2+\frac {4096 \exp \left (-\frac {x \left (-65536-16384 x+261121 x^2+65536 x^3+8196 x^4+512 x^5+16 x^6\right )}{4 \left (128+16 x+x^2\right )^2}\right ) x}{\left (128+16 x+x^2\right )^3}+\frac {16 \exp \left (-\frac {x \left (-65536-16384 x+261121 x^2+65536 x^3+8196 x^4+512 x^5+16 x^6\right )}{4 \left (128+16 x+x^2\right )^2}\right ) (-8+1021 x)}{\left (128+16 x+x^2\right )^2}+\frac {1025 \exp \left (-\frac {x \left (-65536-16384 x+261121 x^2+65536 x^3+8196 x^4+512 x^5+16 x^6\right )}{4 \left (128+16 x+x^2\right )^2}\right )}{128+16 x+x^2}\right ) \, dx \\ & = 4 \int \frac {\exp \left (-\frac {x \left (-65536-16384 x+261121 x^2+65536 x^3+8196 x^4+512 x^5+16 x^6\right )}{4 \left (128+16 x+x^2\right )^2}\right ) (-8+1021 x)}{\left (128+16 x+x^2\right )^2} \, dx-12 \int \exp \left (-\frac {x \left (-65536-16384 x+261121 x^2+65536 x^3+8196 x^4+512 x^5+16 x^6\right )}{4 \left (128+16 x+x^2\right )^2}\right ) x^2 \, dx+\frac {1025}{4} \int \frac {\exp \left (-\frac {x \left (-65536-16384 x+261121 x^2+65536 x^3+8196 x^4+512 x^5+16 x^6\right )}{4 \left (128+16 x+x^2\right )^2}\right )}{128+16 x+x^2} \, dx+1024 \int \frac {\exp \left (-\frac {x \left (-65536-16384 x+261121 x^2+65536 x^3+8196 x^4+512 x^5+16 x^6\right )}{4 \left (128+16 x+x^2\right )^2}\right ) x}{\left (128+16 x+x^2\right )^3} \, dx-\int \exp \left (-\frac {x \left (-65536-16384 x+261121 x^2+65536 x^3+8196 x^4+512 x^5+16 x^6\right )}{4 \left (128+16 x+x^2\right )^2}\right ) \, dx \\ & = 4 \int \left (-\frac {8 \exp \left (-\frac {x \left (-65536-16384 x+261121 x^2+65536 x^3+8196 x^4+512 x^5+16 x^6\right )}{4 \left (128+16 x+x^2\right )^2}\right )}{\left (128+16 x+x^2\right )^2}+\frac {1021 \exp \left (-\frac {x \left (-65536-16384 x+261121 x^2+65536 x^3+8196 x^4+512 x^5+16 x^6\right )}{4 \left (128+16 x+x^2\right )^2}\right ) x}{\left (128+16 x+x^2\right )^2}\right ) \, dx-12 \int \exp \left (-\frac {x \left (-65536-16384 x+261121 x^2+65536 x^3+8196 x^4+512 x^5+16 x^6\right )}{4 \left (128+16 x+x^2\right )^2}\right ) x^2 \, dx+\frac {1025}{4} \int \left (\frac {i \exp \left (-\frac {x \left (-65536-16384 x+261121 x^2+65536 x^3+8196 x^4+512 x^5+16 x^6\right )}{4 \left (128+16 x+x^2\right )^2}\right )}{8 ((-16+16 i)-2 x)}+\frac {i \exp \left (-\frac {x \left (-65536-16384 x+261121 x^2+65536 x^3+8196 x^4+512 x^5+16 x^6\right )}{4 \left (128+16 x+x^2\right )^2}\right )}{8 ((16+16 i)+2 x)}\right ) \, dx+1024 \int \left (\frac {\left (\frac {1}{64}+\frac {i}{64}\right ) \exp \left (-\frac {x \left (-65536-16384 x+261121 x^2+65536 x^3+8196 x^4+512 x^5+16 x^6\right )}{4 \left (128+16 x+x^2\right )^2}\right )}{((-16+16 i)-2 x)^3}+\frac {\left (\frac {3}{2048}-\frac {i}{2048}\right ) \exp \left (-\frac {x \left (-65536-16384 x+261121 x^2+65536 x^3+8196 x^4+512 x^5+16 x^6\right )}{4 \left (128+16 x+x^2\right )^2}\right )}{((-16+16 i)-2 x)^2}-\frac {3 i \exp \left (-\frac {x \left (-65536-16384 x+261121 x^2+65536 x^3+8196 x^4+512 x^5+16 x^6\right )}{4 \left (128+16 x+x^2\right )^2}\right )}{32768 ((-16+16 i)-2 x)}-\frac {\left (\frac {1}{64}-\frac {i}{64}\right ) \exp \left (-\frac {x \left (-65536-16384 x+261121 x^2+65536 x^3+8196 x^4+512 x^5+16 x^6\right )}{4 \left (128+16 x+x^2\right )^2}\right )}{((16+16 i)+2 x)^3}+\frac {\left (\frac {3}{2048}+\frac {i}{2048}\right ) \exp \left (-\frac {x \left (-65536-16384 x+261121 x^2+65536 x^3+8196 x^4+512 x^5+16 x^6\right )}{4 \left (128+16 x+x^2\right )^2}\right )}{((16+16 i)+2 x)^2}-\frac {3 i \exp \left (-\frac {x \left (-65536-16384 x+261121 x^2+65536 x^3+8196 x^4+512 x^5+16 x^6\right )}{4 \left (128+16 x+x^2\right )^2}\right )}{32768 ((16+16 i)+2 x)}\right ) \, dx-\int \exp \left (-\frac {x \left (-65536-16384 x+261121 x^2+65536 x^3+8196 x^4+512 x^5+16 x^6\right )}{4 \left (128+16 x+x^2\right )^2}\right ) \, dx \\ & = (-16+16 i) \int \frac {\exp \left (-\frac {x \left (-65536-16384 x+261121 x^2+65536 x^3+8196 x^4+512 x^5+16 x^6\right )}{4 \left (128+16 x+x^2\right )^2}\right )}{((16+16 i)+2 x)^3} \, dx-\frac {3}{32} i \int \frac {\exp \left (-\frac {x \left (-65536-16384 x+261121 x^2+65536 x^3+8196 x^4+512 x^5+16 x^6\right )}{4 \left (128+16 x+x^2\right )^2}\right )}{(-16+16 i)-2 x} \, dx-\frac {3}{32} i \int \frac {\exp \left (-\frac {x \left (-65536-16384 x+261121 x^2+65536 x^3+8196 x^4+512 x^5+16 x^6\right )}{4 \left (128+16 x+x^2\right )^2}\right )}{(16+16 i)+2 x} \, dx+\frac {1025}{32} i \int \frac {\exp \left (-\frac {x \left (-65536-16384 x+261121 x^2+65536 x^3+8196 x^4+512 x^5+16 x^6\right )}{4 \left (128+16 x+x^2\right )^2}\right )}{(-16+16 i)-2 x} \, dx+\frac {1025}{32} i \int \frac {\exp \left (-\frac {x \left (-65536-16384 x+261121 x^2+65536 x^3+8196 x^4+512 x^5+16 x^6\right )}{4 \left (128+16 x+x^2\right )^2}\right )}{(16+16 i)+2 x} \, dx+\left (\frac {3}{2}-\frac {i}{2}\right ) \int \frac {\exp \left (-\frac {x \left (-65536-16384 x+261121 x^2+65536 x^3+8196 x^4+512 x^5+16 x^6\right )}{4 \left (128+16 x+x^2\right )^2}\right )}{((-16+16 i)-2 x)^2} \, dx+\left (\frac {3}{2}+\frac {i}{2}\right ) \int \frac {\exp \left (-\frac {x \left (-65536-16384 x+261121 x^2+65536 x^3+8196 x^4+512 x^5+16 x^6\right )}{4 \left (128+16 x+x^2\right )^2}\right )}{((16+16 i)+2 x)^2} \, dx-12 \int \exp \left (-\frac {x \left (-65536-16384 x+261121 x^2+65536 x^3+8196 x^4+512 x^5+16 x^6\right )}{4 \left (128+16 x+x^2\right )^2}\right ) x^2 \, dx+(16+16 i) \int \frac {\exp \left (-\frac {x \left (-65536-16384 x+261121 x^2+65536 x^3+8196 x^4+512 x^5+16 x^6\right )}{4 \left (128+16 x+x^2\right )^2}\right )}{((-16+16 i)-2 x)^3} \, dx-32 \int \frac {\exp \left (-\frac {x \left (-65536-16384 x+261121 x^2+65536 x^3+8196 x^4+512 x^5+16 x^6\right )}{4 \left (128+16 x+x^2\right )^2}\right )}{\left (128+16 x+x^2\right )^2} \, dx+4084 \int \frac {\exp \left (-\frac {x \left (-65536-16384 x+261121 x^2+65536 x^3+8196 x^4+512 x^5+16 x^6\right )}{4 \left (128+16 x+x^2\right )^2}\right ) x}{\left (128+16 x+x^2\right )^2} \, dx-\int \exp \left (-\frac {x \left (-65536-16384 x+261121 x^2+65536 x^3+8196 x^4+512 x^5+16 x^6\right )}{4 \left (128+16 x+x^2\right )^2}\right ) \, dx \\ & = (-16+16 i) \int \frac {e^{-\frac {x \left (-65536-16384 x+261121 x^2+65536 x^3+8196 x^4+512 x^5+16 x^6\right )}{4 \left (128+16 x+x^2\right )^2}}}{((16+16 i)+2 x)^3} \, dx-\frac {3}{32} i \int \frac {e^{-\frac {x \left (-65536-16384 x+261121 x^2+65536 x^3+8196 x^4+512 x^5+16 x^6\right )}{4 \left (128+16 x+x^2\right )^2}}}{(-16+16 i)-2 x} \, dx-\frac {3}{32} i \int \frac {e^{-\frac {x \left (-65536-16384 x+261121 x^2+65536 x^3+8196 x^4+512 x^5+16 x^6\right )}{4 \left (128+16 x+x^2\right )^2}}}{(16+16 i)+2 x} \, dx+\frac {1025}{32} i \int \frac {e^{-\frac {x \left (-65536-16384 x+261121 x^2+65536 x^3+8196 x^4+512 x^5+16 x^6\right )}{4 \left (128+16 x+x^2\right )^2}}}{(-16+16 i)-2 x} \, dx+\frac {1025}{32} i \int \frac {e^{-\frac {x \left (-65536-16384 x+261121 x^2+65536 x^3+8196 x^4+512 x^5+16 x^6\right )}{4 \left (128+16 x+x^2\right )^2}}}{(16+16 i)+2 x} \, dx+\left (\frac {3}{2}-\frac {i}{2}\right ) \int \frac {e^{-\frac {x \left (-65536-16384 x+261121 x^2+65536 x^3+8196 x^4+512 x^5+16 x^6\right )}{4 \left (128+16 x+x^2\right )^2}}}{((-16+16 i)-2 x)^2} \, dx+\left (\frac {3}{2}+\frac {i}{2}\right ) \int \frac {e^{-\frac {x \left (-65536-16384 x+261121 x^2+65536 x^3+8196 x^4+512 x^5+16 x^6\right )}{4 \left (128+16 x+x^2\right )^2}}}{((16+16 i)+2 x)^2} \, dx-12 \int e^{-\frac {x \left (-65536-16384 x+261121 x^2+65536 x^3+8196 x^4+512 x^5+16 x^6\right )}{4 \left (128+16 x+x^2\right )^2}} x^2 \, dx+(16+16 i) \int \frac {e^{-\frac {x \left (-65536-16384 x+261121 x^2+65536 x^3+8196 x^4+512 x^5+16 x^6\right )}{4 \left (128+16 x+x^2\right )^2}}}{((-16+16 i)-2 x)^3} \, dx-32 \int \left (-\frac {e^{-\frac {x \left (-65536-16384 x+261121 x^2+65536 x^3+8196 x^4+512 x^5+16 x^6\right )}{4 \left (128+16 x+x^2\right )^2}}}{64 ((-16+16 i)-2 x)^2}+\frac {i e^{-\frac {x \left (-65536-16384 x+261121 x^2+65536 x^3+8196 x^4+512 x^5+16 x^6\right )}{4 \left (128+16 x+x^2\right )^2}}}{1024 ((-16+16 i)-2 x)}-\frac {e^{-\frac {x \left (-65536-16384 x+261121 x^2+65536 x^3+8196 x^4+512 x^5+16 x^6\right )}{4 \left (128+16 x+x^2\right )^2}}}{64 ((16+16 i)+2 x)^2}+\frac {i e^{-\frac {x \left (-65536-16384 x+261121 x^2+65536 x^3+8196 x^4+512 x^5+16 x^6\right )}{4 \left (128+16 x+x^2\right )^2}}}{1024 ((16+16 i)+2 x)}\right ) \, dx+4084 \int \left (\frac {\left (\frac {1}{8}-\frac {i}{8}\right ) e^{-\frac {x \left (-65536-16384 x+261121 x^2+65536 x^3+8196 x^4+512 x^5+16 x^6\right )}{4 \left (128+16 x+x^2\right )^2}}}{((-16+16 i)-2 x)^2}-\frac {i e^{-\frac {x \left (-65536-16384 x+261121 x^2+65536 x^3+8196 x^4+512 x^5+16 x^6\right )}{4 \left (128+16 x+x^2\right )^2}}}{128 ((-16+16 i)-2 x)}+\frac {\left (\frac {1}{8}+\frac {i}{8}\right ) e^{-\frac {x \left (-65536-16384 x+261121 x^2+65536 x^3+8196 x^4+512 x^5+16 x^6\right )}{4 \left (128+16 x+x^2\right )^2}}}{((16+16 i)+2 x)^2}-\frac {i e^{-\frac {x \left (-65536-16384 x+261121 x^2+65536 x^3+8196 x^4+512 x^5+16 x^6\right )}{4 \left (128+16 x+x^2\right )^2}}}{128 ((16+16 i)+2 x)}\right ) \, dx-\int e^{-\frac {x \left (-65536-16384 x+261121 x^2+65536 x^3+8196 x^4+512 x^5+16 x^6\right )}{4 \left (128+16 x+x^2\right )^2}} \, dx \\ & = \text {Too large to display} \\ \end{align*}
Time = 0.08 (sec) , antiderivative size = 46, normalized size of antiderivative = 1.92 \[ \int \frac {e^{\frac {65536 x+16384 x^2-261121 x^3-65536 x^4-8196 x^5-512 x^6-16 x^7}{65536+16384 x+2048 x^2+128 x^3+4 x^4}} \left (8388608+3145728 x-100467072 x^2-37765136 x^3-7081471 x^4-786624 x^5-55300 x^6-2304 x^7-48 x^8\right )}{8388608+3145728 x+589824 x^2+65536 x^3+4608 x^4+192 x^5+4 x^6} \, dx=e^{32-x-4 x^3-\frac {32 (16+x)}{\left (128+16 x+x^2\right )^2}+\frac {-16368-1025 x}{4 \left (128+16 x+x^2\right )}} \]
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Time = 15.86 (sec) , antiderivative size = 45, normalized size of antiderivative = 1.88
method | result | size |
risch | \({\mathrm e}^{-\frac {x \left (4 x^{3}+62 x^{2}+481 x -256\right ) \left (4 x^{3}+66 x^{2}+545 x +256\right )}{4 \left (x^{2}+16 x +128\right )^{2}}}\) | \(45\) |
gosper | \({\mathrm e}^{-\frac {x \left (16 x^{6}+512 x^{5}+8196 x^{4}+65536 x^{3}+261121 x^{2}-16384 x -65536\right )}{4 \left (x^{4}+32 x^{3}+512 x^{2}+4096 x +16384\right )}}\) | \(55\) |
parallelrisch | \({\mathrm e}^{\frac {-16 x^{7}-512 x^{6}-8196 x^{5}-65536 x^{4}-261121 x^{3}+16384 x^{2}+65536 x}{4 x^{4}+128 x^{3}+2048 x^{2}+16384 x +65536}}\) | \(58\) |
norman | \(\frac {x^{4} {\mathrm e}^{\frac {-16 x^{7}-512 x^{6}-8196 x^{5}-65536 x^{4}-261121 x^{3}+16384 x^{2}+65536 x}{4 x^{4}+128 x^{3}+2048 x^{2}+16384 x +65536}}+4096 x \,{\mathrm e}^{\frac {-16 x^{7}-512 x^{6}-8196 x^{5}-65536 x^{4}-261121 x^{3}+16384 x^{2}+65536 x}{4 x^{4}+128 x^{3}+2048 x^{2}+16384 x +65536}}+512 x^{2} {\mathrm e}^{\frac {-16 x^{7}-512 x^{6}-8196 x^{5}-65536 x^{4}-261121 x^{3}+16384 x^{2}+65536 x}{4 x^{4}+128 x^{3}+2048 x^{2}+16384 x +65536}}+32 x^{3} {\mathrm e}^{\frac {-16 x^{7}-512 x^{6}-8196 x^{5}-65536 x^{4}-261121 x^{3}+16384 x^{2}+65536 x}{4 x^{4}+128 x^{3}+2048 x^{2}+16384 x +65536}}+16384 \,{\mathrm e}^{\frac {-16 x^{7}-512 x^{6}-8196 x^{5}-65536 x^{4}-261121 x^{3}+16384 x^{2}+65536 x}{4 x^{4}+128 x^{3}+2048 x^{2}+16384 x +65536}}}{\left (x^{2}+16 x +128\right )^{2}}\) | \(322\) |
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Leaf count of result is larger than twice the leaf count of optimal. 57 vs. \(2 (23) = 46\).
Time = 0.27 (sec) , antiderivative size = 57, normalized size of antiderivative = 2.38 \[ \int \frac {e^{\frac {65536 x+16384 x^2-261121 x^3-65536 x^4-8196 x^5-512 x^6-16 x^7}{65536+16384 x+2048 x^2+128 x^3+4 x^4}} \left (8388608+3145728 x-100467072 x^2-37765136 x^3-7081471 x^4-786624 x^5-55300 x^6-2304 x^7-48 x^8\right )}{8388608+3145728 x+589824 x^2+65536 x^3+4608 x^4+192 x^5+4 x^6} \, dx=e^{\left (-\frac {16 \, x^{7} + 512 \, x^{6} + 8196 \, x^{5} + 65536 \, x^{4} + 261121 \, x^{3} - 16384 \, x^{2} - 65536 \, x}{4 \, {\left (x^{4} + 32 \, x^{3} + 512 \, x^{2} + 4096 \, x + 16384\right )}}\right )} \]
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Leaf count of result is larger than twice the leaf count of optimal. 54 vs. \(2 (19) = 38\).
Time = 0.25 (sec) , antiderivative size = 54, normalized size of antiderivative = 2.25 \[ \int \frac {e^{\frac {65536 x+16384 x^2-261121 x^3-65536 x^4-8196 x^5-512 x^6-16 x^7}{65536+16384 x+2048 x^2+128 x^3+4 x^4}} \left (8388608+3145728 x-100467072 x^2-37765136 x^3-7081471 x^4-786624 x^5-55300 x^6-2304 x^7-48 x^8\right )}{8388608+3145728 x+589824 x^2+65536 x^3+4608 x^4+192 x^5+4 x^6} \, dx=e^{\frac {- 16 x^{7} - 512 x^{6} - 8196 x^{5} - 65536 x^{4} - 261121 x^{3} + 16384 x^{2} + 65536 x}{4 x^{4} + 128 x^{3} + 2048 x^{2} + 16384 x + 65536}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 81 vs. \(2 (23) = 46\).
Time = 0.66 (sec) , antiderivative size = 81, normalized size of antiderivative = 3.38 \[ \int \frac {e^{\frac {65536 x+16384 x^2-261121 x^3-65536 x^4-8196 x^5-512 x^6-16 x^7}{65536+16384 x+2048 x^2+128 x^3+4 x^4}} \left (8388608+3145728 x-100467072 x^2-37765136 x^3-7081471 x^4-786624 x^5-55300 x^6-2304 x^7-48 x^8\right )}{8388608+3145728 x+589824 x^2+65536 x^3+4608 x^4+192 x^5+4 x^6} \, dx=e^{\left (-4 \, x^{3} - x - \frac {32 \, x}{x^{4} + 32 \, x^{3} + 512 \, x^{2} + 4096 \, x + 16384} - \frac {1025 \, x}{4 \, {\left (x^{2} + 16 \, x + 128\right )}} - \frac {512}{x^{4} + 32 \, x^{3} + 512 \, x^{2} + 4096 \, x + 16384} - \frac {4092}{x^{2} + 16 \, x + 128} + 32\right )} \]
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Leaf count of result is larger than twice the leaf count of optimal. 175 vs. \(2 (23) = 46\).
Time = 0.29 (sec) , antiderivative size = 175, normalized size of antiderivative = 7.29 \[ \int \frac {e^{\frac {65536 x+16384 x^2-261121 x^3-65536 x^4-8196 x^5-512 x^6-16 x^7}{65536+16384 x+2048 x^2+128 x^3+4 x^4}} \left (8388608+3145728 x-100467072 x^2-37765136 x^3-7081471 x^4-786624 x^5-55300 x^6-2304 x^7-48 x^8\right )}{8388608+3145728 x+589824 x^2+65536 x^3+4608 x^4+192 x^5+4 x^6} \, dx=e^{\left (-\frac {4 \, x^{7}}{x^{4} + 32 \, x^{3} + 512 \, x^{2} + 4096 \, x + 16384} - \frac {128 \, x^{6}}{x^{4} + 32 \, x^{3} + 512 \, x^{2} + 4096 \, x + 16384} - \frac {2049 \, x^{5}}{x^{4} + 32 \, x^{3} + 512 \, x^{2} + 4096 \, x + 16384} - \frac {16384 \, x^{4}}{x^{4} + 32 \, x^{3} + 512 \, x^{2} + 4096 \, x + 16384} - \frac {261121 \, x^{3}}{4 \, {\left (x^{4} + 32 \, x^{3} + 512 \, x^{2} + 4096 \, x + 16384\right )}} + \frac {4096 \, x^{2}}{x^{4} + 32 \, x^{3} + 512 \, x^{2} + 4096 \, x + 16384} + \frac {16384 \, x}{x^{4} + 32 \, x^{3} + 512 \, x^{2} + 4096 \, x + 16384}\right )} \]
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Time = 15.91 (sec) , antiderivative size = 183, normalized size of antiderivative = 7.62 \[ \int \frac {e^{\frac {65536 x+16384 x^2-261121 x^3-65536 x^4-8196 x^5-512 x^6-16 x^7}{65536+16384 x+2048 x^2+128 x^3+4 x^4}} \left (8388608+3145728 x-100467072 x^2-37765136 x^3-7081471 x^4-786624 x^5-55300 x^6-2304 x^7-48 x^8\right )}{8388608+3145728 x+589824 x^2+65536 x^3+4608 x^4+192 x^5+4 x^6} \, dx={\mathrm {e}}^{\frac {16384\,x}{x^4+32\,x^3+512\,x^2+4096\,x+16384}}\,{\mathrm {e}}^{-\frac {4\,x^7}{x^4+32\,x^3+512\,x^2+4096\,x+16384}}\,{\mathrm {e}}^{-\frac {128\,x^6}{x^4+32\,x^3+512\,x^2+4096\,x+16384}}\,{\mathrm {e}}^{-\frac {2049\,x^5}{x^4+32\,x^3+512\,x^2+4096\,x+16384}}\,{\mathrm {e}}^{\frac {4096\,x^2}{x^4+32\,x^3+512\,x^2+4096\,x+16384}}\,{\mathrm {e}}^{-\frac {16384\,x^4}{x^4+32\,x^3+512\,x^2+4096\,x+16384}}\,{\mathrm {e}}^{-\frac {261121\,x^3}{4\,x^4+128\,x^3+2048\,x^2+16384\,x+65536}} \]
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