Integrand size = 203, antiderivative size = 28 \[ \int \frac {1}{25} e^{16 x^6-32 x^7+16 x^8+e^{10} \left (x^2-2 x^3+x^4\right )+e^{15/2} \left (-8 x^3+16 x^4-8 x^5\right )+e^5 \left (24 x^4-48 x^5+24 x^6\right )+e^{5/2} \left (-32 x^5+64 x^6-32 x^7\right )} \left (1+96 x^6-224 x^7+128 x^8+e^{10} \left (2 x^2-6 x^3+4 x^4\right )+e^{15/2} \left (-24 x^3+64 x^4-40 x^5\right )+e^5 \left (96 x^4-240 x^5+144 x^6\right )+e^{5/2} \left (-160 x^5+384 x^6-224 x^7\right )\right ) \, dx=\frac {1}{25} e^{\left (e^{5/2}-2 x\right )^4 \left (-x+x^2\right )^2} x \]
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Leaf count is larger than twice the leaf count of optimal. \(295\) vs. \(2(28)=56\).
Time = 2.90 (sec) , antiderivative size = 295, normalized size of antiderivative = 10.54, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.010, Rules used = {12, 2326} \[ \int \frac {1}{25} e^{16 x^6-32 x^7+16 x^8+e^{10} \left (x^2-2 x^3+x^4\right )+e^{15/2} \left (-8 x^3+16 x^4-8 x^5\right )+e^5 \left (24 x^4-48 x^5+24 x^6\right )+e^{5/2} \left (-32 x^5+64 x^6-32 x^7\right )} \left (1+96 x^6-224 x^7+128 x^8+e^{10} \left (2 x^2-6 x^3+4 x^4\right )+e^{15/2} \left (-24 x^3+64 x^4-40 x^5\right )+e^5 \left (96 x^4-240 x^5+144 x^6\right )+e^{5/2} \left (-160 x^5+384 x^6-224 x^7\right )\right ) \, dx=\frac {\left (64 x^8-112 x^7+48 x^6-16 e^{5/2} \left (7 x^7-12 x^6+5 x^5\right )+24 e^5 \left (3 x^6-5 x^5+2 x^4\right )-4 e^{15/2} \left (5 x^5-8 x^4+3 x^3\right )+e^{10} \left (2 x^4-3 x^3+x^2\right )\right ) \exp \left (16 x^8-32 x^7+16 x^6-32 e^{5/2} \left (x^7-2 x^6+x^5\right )+24 e^5 \left (x^6-2 x^5+x^4\right )-8 e^{15/2} \left (x^5-2 x^4+x^3\right )+e^{10} \left (x^4-2 x^3+x^2\right )\right )}{25 \left (64 x^7-112 x^6+48 x^5+e^{10} \left (2 x^3-3 x^2+x\right )-16 e^{5/2} \left (7 x^6-12 x^5+5 x^4\right )+24 e^5 \left (3 x^5-5 x^4+2 x^3\right )-4 e^{15/2} \left (5 x^4-8 x^3+3 x^2\right )\right )} \]
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Rule 12
Rule 2326
Rubi steps \begin{align*} \text {integral}& = \frac {1}{25} \int \exp \left (16 x^6-32 x^7+16 x^8+e^{10} \left (x^2-2 x^3+x^4\right )+e^{15/2} \left (-8 x^3+16 x^4-8 x^5\right )+e^5 \left (24 x^4-48 x^5+24 x^6\right )+e^{5/2} \left (-32 x^5+64 x^6-32 x^7\right )\right ) \left (1+96 x^6-224 x^7+128 x^8+e^{10} \left (2 x^2-6 x^3+4 x^4\right )+e^{15/2} \left (-24 x^3+64 x^4-40 x^5\right )+e^5 \left (96 x^4-240 x^5+144 x^6\right )+e^{5/2} \left (-160 x^5+384 x^6-224 x^7\right )\right ) \, dx \\ & = \frac {\exp \left (16 x^6-32 x^7+16 x^8+e^{10} \left (x^2-2 x^3+x^4\right )-8 e^{15/2} \left (x^3-2 x^4+x^5\right )+24 e^5 \left (x^4-2 x^5+x^6\right )-32 e^{5/2} \left (x^5-2 x^6+x^7\right )\right ) \left (48 x^6-112 x^7+64 x^8+e^{10} \left (x^2-3 x^3+2 x^4\right )-4 e^{15/2} \left (3 x^3-8 x^4+5 x^5\right )+24 e^5 \left (2 x^4-5 x^5+3 x^6\right )-16 e^{5/2} \left (5 x^5-12 x^6+7 x^7\right )\right )}{25 \left (48 x^5-112 x^6+64 x^7+e^{10} \left (x-3 x^2+2 x^3\right )-4 e^{15/2} \left (3 x^2-8 x^3+5 x^4\right )+24 e^5 \left (2 x^3-5 x^4+3 x^5\right )-16 e^{5/2} \left (5 x^4-12 x^5+7 x^6\right )\right )} \\ \end{align*}
Time = 11.78 (sec) , antiderivative size = 27, normalized size of antiderivative = 0.96 \[ \int \frac {1}{25} e^{16 x^6-32 x^7+16 x^8+e^{10} \left (x^2-2 x^3+x^4\right )+e^{15/2} \left (-8 x^3+16 x^4-8 x^5\right )+e^5 \left (24 x^4-48 x^5+24 x^6\right )+e^{5/2} \left (-32 x^5+64 x^6-32 x^7\right )} \left (1+96 x^6-224 x^7+128 x^8+e^{10} \left (2 x^2-6 x^3+4 x^4\right )+e^{15/2} \left (-24 x^3+64 x^4-40 x^5\right )+e^5 \left (96 x^4-240 x^5+144 x^6\right )+e^{5/2} \left (-160 x^5+384 x^6-224 x^7\right )\right ) \, dx=\frac {1}{25} e^{\left (e^{5/2}-2 x\right )^4 (-1+x)^2 x^2} x \]
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Leaf count of result is larger than twice the leaf count of optimal. \(120\) vs. \(2(22)=44\).
Time = 0.02 (sec) , antiderivative size = 121, normalized size of antiderivative = 4.32
\[\frac {x \,{\mathrm e}^{x^{4} {\mathrm e}^{10}-8 \,{\mathrm e}^{\frac {15}{2}} x^{5}+24 x^{6} {\mathrm e}^{5}-32 \,{\mathrm e}^{\frac {5}{2}} x^{7}+16 x^{8}-2 x^{3} {\mathrm e}^{10}+16 \,{\mathrm e}^{\frac {15}{2}} x^{4}-48 x^{5} {\mathrm e}^{5}+64 \,{\mathrm e}^{\frac {5}{2}} x^{6}-32 x^{7}+x^{2} {\mathrm e}^{10}-8 \,{\mathrm e}^{\frac {15}{2}} x^{3}+24 x^{4} {\mathrm e}^{5}-32 \,{\mathrm e}^{\frac {5}{2}} x^{5}+16 x^{6}}}{25}\]
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Leaf count of result is larger than twice the leaf count of optimal. 83 vs. \(2 (24) = 48\).
Time = 0.32 (sec) , antiderivative size = 83, normalized size of antiderivative = 2.96 \[ \int \frac {1}{25} e^{16 x^6-32 x^7+16 x^8+e^{10} \left (x^2-2 x^3+x^4\right )+e^{15/2} \left (-8 x^3+16 x^4-8 x^5\right )+e^5 \left (24 x^4-48 x^5+24 x^6\right )+e^{5/2} \left (-32 x^5+64 x^6-32 x^7\right )} \left (1+96 x^6-224 x^7+128 x^8+e^{10} \left (2 x^2-6 x^3+4 x^4\right )+e^{15/2} \left (-24 x^3+64 x^4-40 x^5\right )+e^5 \left (96 x^4-240 x^5+144 x^6\right )+e^{5/2} \left (-160 x^5+384 x^6-224 x^7\right )\right ) \, dx=\frac {1}{25} \, x e^{\left (16 \, x^{8} - 32 \, x^{7} + 16 \, x^{6} + {\left (x^{4} - 2 \, x^{3} + x^{2}\right )} e^{10} - 8 \, {\left (x^{5} - 2 \, x^{4} + x^{3}\right )} e^{\frac {15}{2}} + 24 \, {\left (x^{6} - 2 \, x^{5} + x^{4}\right )} e^{5} - 32 \, {\left (x^{7} - 2 \, x^{6} + x^{5}\right )} e^{\frac {5}{2}}\right )} \]
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Leaf count of result is larger than twice the leaf count of optimal. 94 vs. \(2 (20) = 40\).
Time = 0.20 (sec) , antiderivative size = 94, normalized size of antiderivative = 3.36 \[ \int \frac {1}{25} e^{16 x^6-32 x^7+16 x^8+e^{10} \left (x^2-2 x^3+x^4\right )+e^{15/2} \left (-8 x^3+16 x^4-8 x^5\right )+e^5 \left (24 x^4-48 x^5+24 x^6\right )+e^{5/2} \left (-32 x^5+64 x^6-32 x^7\right )} \left (1+96 x^6-224 x^7+128 x^8+e^{10} \left (2 x^2-6 x^3+4 x^4\right )+e^{15/2} \left (-24 x^3+64 x^4-40 x^5\right )+e^5 \left (96 x^4-240 x^5+144 x^6\right )+e^{5/2} \left (-160 x^5+384 x^6-224 x^7\right )\right ) \, dx=\frac {x e^{16 x^{8} - 32 x^{7} + 16 x^{6} + \left (x^{4} - 2 x^{3} + x^{2}\right ) e^{10} + \left (- 8 x^{5} + 16 x^{4} - 8 x^{3}\right ) e^{\frac {15}{2}} + \left (24 x^{6} - 48 x^{5} + 24 x^{4}\right ) e^{5} + \left (- 32 x^{7} + 64 x^{6} - 32 x^{5}\right ) e^{\frac {5}{2}}}}{25} \]
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Leaf count of result is larger than twice the leaf count of optimal. 102 vs. \(2 (24) = 48\).
Time = 0.72 (sec) , antiderivative size = 102, normalized size of antiderivative = 3.64 \[ \int \frac {1}{25} e^{16 x^6-32 x^7+16 x^8+e^{10} \left (x^2-2 x^3+x^4\right )+e^{15/2} \left (-8 x^3+16 x^4-8 x^5\right )+e^5 \left (24 x^4-48 x^5+24 x^6\right )+e^{5/2} \left (-32 x^5+64 x^6-32 x^7\right )} \left (1+96 x^6-224 x^7+128 x^8+e^{10} \left (2 x^2-6 x^3+4 x^4\right )+e^{15/2} \left (-24 x^3+64 x^4-40 x^5\right )+e^5 \left (96 x^4-240 x^5+144 x^6\right )+e^{5/2} \left (-160 x^5+384 x^6-224 x^7\right )\right ) \, dx=\frac {1}{25} \, x e^{\left (16 \, x^{8} - 32 \, x^{7} e^{\frac {5}{2}} - 32 \, x^{7} + 24 \, x^{6} e^{5} + 64 \, x^{6} e^{\frac {5}{2}} + 16 \, x^{6} - 8 \, x^{5} e^{\frac {15}{2}} - 48 \, x^{5} e^{5} - 32 \, x^{5} e^{\frac {5}{2}} + x^{4} e^{10} + 16 \, x^{4} e^{\frac {15}{2}} + 24 \, x^{4} e^{5} - 2 \, x^{3} e^{10} - 8 \, x^{3} e^{\frac {15}{2}} + x^{2} e^{10}\right )} \]
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Leaf count of result is larger than twice the leaf count of optimal. 102 vs. \(2 (24) = 48\).
Time = 0.46 (sec) , antiderivative size = 102, normalized size of antiderivative = 3.64 \[ \int \frac {1}{25} e^{16 x^6-32 x^7+16 x^8+e^{10} \left (x^2-2 x^3+x^4\right )+e^{15/2} \left (-8 x^3+16 x^4-8 x^5\right )+e^5 \left (24 x^4-48 x^5+24 x^6\right )+e^{5/2} \left (-32 x^5+64 x^6-32 x^7\right )} \left (1+96 x^6-224 x^7+128 x^8+e^{10} \left (2 x^2-6 x^3+4 x^4\right )+e^{15/2} \left (-24 x^3+64 x^4-40 x^5\right )+e^5 \left (96 x^4-240 x^5+144 x^6\right )+e^{5/2} \left (-160 x^5+384 x^6-224 x^7\right )\right ) \, dx=\frac {1}{25} \, x e^{\left (16 \, x^{8} - 32 \, x^{7} e^{\frac {5}{2}} - 32 \, x^{7} + 24 \, x^{6} e^{5} + 64 \, x^{6} e^{\frac {5}{2}} + 16 \, x^{6} - 8 \, x^{5} e^{\frac {15}{2}} - 48 \, x^{5} e^{5} - 32 \, x^{5} e^{\frac {5}{2}} + x^{4} e^{10} + 16 \, x^{4} e^{\frac {15}{2}} + 24 \, x^{4} e^{5} - 2 \, x^{3} e^{10} - 8 \, x^{3} e^{\frac {15}{2}} + x^{2} e^{10}\right )} \]
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Time = 9.05 (sec) , antiderivative size = 115, normalized size of antiderivative = 4.11 \[ \int \frac {1}{25} e^{16 x^6-32 x^7+16 x^8+e^{10} \left (x^2-2 x^3+x^4\right )+e^{15/2} \left (-8 x^3+16 x^4-8 x^5\right )+e^5 \left (24 x^4-48 x^5+24 x^6\right )+e^{5/2} \left (-32 x^5+64 x^6-32 x^7\right )} \left (1+96 x^6-224 x^7+128 x^8+e^{10} \left (2 x^2-6 x^3+4 x^4\right )+e^{15/2} \left (-24 x^3+64 x^4-40 x^5\right )+e^5 \left (96 x^4-240 x^5+144 x^6\right )+e^{5/2} \left (-160 x^5+384 x^6-224 x^7\right )\right ) \, dx=\frac {x\,{\mathrm {e}}^{x^2\,{\mathrm {e}}^{10}}\,{\mathrm {e}}^{x^4\,{\mathrm {e}}^{10}}\,{\mathrm {e}}^{-2\,x^3\,{\mathrm {e}}^{10}}\,{\mathrm {e}}^{-8\,x^3\,{\mathrm {e}}^{15/2}}\,{\mathrm {e}}^{-8\,x^5\,{\mathrm {e}}^{15/2}}\,{\mathrm {e}}^{24\,x^4\,{\mathrm {e}}^5}\,{\mathrm {e}}^{24\,x^6\,{\mathrm {e}}^5}\,{\mathrm {e}}^{16\,x^4\,{\mathrm {e}}^{15/2}}\,{\mathrm {e}}^{-32\,x^5\,{\mathrm {e}}^{5/2}}\,{\mathrm {e}}^{-32\,x^7\,{\mathrm {e}}^{5/2}}\,{\mathrm {e}}^{-48\,x^5\,{\mathrm {e}}^5}\,{\mathrm {e}}^{64\,x^6\,{\mathrm {e}}^{5/2}}\,{\mathrm {e}}^{16\,x^6}\,{\mathrm {e}}^{16\,x^8}\,{\mathrm {e}}^{-32\,x^7}}{25} \]
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