Integrand size = 275, antiderivative size = 27 \[ \int \left (128 e^9 x+6144 e^{22/3} x^3+98304 e^{17/3} x^5+524288 e^4 x^7-256 e^{4+7 e^{16}} x^7+8 e^{4+8 e^{16}} x^7+e^{e^{16}} \left (-64 e^9 x-6144 e^{22/3} x^3-147456 e^{17/3} x^5-1048576 e^4 x^7\right )+e^{3 e^{16}} \left (-384 e^{22/3} x^3-30720 e^{17/3} x^5-458752 e^4 x^7\right )+e^{5 e^{16}} \left (-576 e^{17/3} x^5-28672 e^4 x^7\right )+e^{6 e^{16}} \left (24 e^{17/3} x^5+3584 e^4 x^7\right )+e^{4 e^{16}} \left (24 e^{22/3} x^3+5760 e^{17/3} x^5+143360 e^4 x^7\right )+e^{2 e^{16}} \left (8 e^9 x+2304 e^{22/3} x^3+92160 e^{17/3} x^5+917504 e^4 x^7\right )\right ) \, dx=e^4 \left (e^{5/3}+\left (4-e^{e^{16}}\right )^2 x^2\right )^4 \]
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Leaf count is larger than twice the leaf count of optimal. \(318\) vs. \(2(27)=54\).
Time = 0.08 (sec) , antiderivative size = 318, normalized size of antiderivative = 11.78, number of steps used = 9, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.004, Rules used = {6} \[ \int \left (128 e^9 x+6144 e^{22/3} x^3+98304 e^{17/3} x^5+524288 e^4 x^7-256 e^{4+7 e^{16}} x^7+8 e^{4+8 e^{16}} x^7+e^{e^{16}} \left (-64 e^9 x-6144 e^{22/3} x^3-147456 e^{17/3} x^5-1048576 e^4 x^7\right )+e^{3 e^{16}} \left (-384 e^{22/3} x^3-30720 e^{17/3} x^5-458752 e^4 x^7\right )+e^{5 e^{16}} \left (-576 e^{17/3} x^5-28672 e^4 x^7\right )+e^{6 e^{16}} \left (24 e^{17/3} x^5+3584 e^4 x^7\right )+e^{4 e^{16}} \left (24 e^{22/3} x^3+5760 e^{17/3} x^5+143360 e^4 x^7\right )+e^{2 e^{16}} \left (8 e^9 x+2304 e^{22/3} x^3+92160 e^{17/3} x^5+917504 e^4 x^7\right )\right ) \, dx=e^4 \left (65536-32 e^{7 e^{16}}+e^{8 e^{16}}\right ) x^8+448 e^{4+6 e^{16}} x^8-3584 e^{4+5 e^{16}} x^8+17920 e^{4+4 e^{16}} x^8-57344 e^{4+3 e^{16}} x^8+114688 e^{4+2 e^{16}} x^8-131072 e^{4+e^{16}} x^8+4 e^{\frac {17}{3}+6 e^{16}} x^6-96 e^{\frac {17}{3}+5 e^{16}} x^6+960 e^{\frac {17}{3}+4 e^{16}} x^6-5120 e^{\frac {17}{3}+3 e^{16}} x^6+15360 e^{\frac {17}{3}+2 e^{16}} x^6-24576 e^{\frac {17}{3}+e^{16}} x^6+16384 e^{17/3} x^6+6 e^{\frac {22}{3}+4 e^{16}} x^4-96 e^{\frac {22}{3}+3 e^{16}} x^4+576 e^{\frac {22}{3}+2 e^{16}} x^4-1536 e^{\frac {22}{3}+e^{16}} x^4+1536 e^{22/3} x^4+4 e^{9+2 e^{16}} x^2-32 e^{9+e^{16}} x^2+64 e^9 x^2 \]
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Rule 6
Rubi steps \begin{align*} \text {integral}& = \int \left (128 e^9 x+6144 e^{22/3} x^3+98304 e^{17/3} x^5+8 e^{4+8 e^{16}} x^7+\left (524288 e^4-256 e^{4+7 e^{16}}\right ) x^7+e^{e^{16}} \left (-64 e^9 x-6144 e^{22/3} x^3-147456 e^{17/3} x^5-1048576 e^4 x^7\right )+e^{3 e^{16}} \left (-384 e^{22/3} x^3-30720 e^{17/3} x^5-458752 e^4 x^7\right )+e^{5 e^{16}} \left (-576 e^{17/3} x^5-28672 e^4 x^7\right )+e^{6 e^{16}} \left (24 e^{17/3} x^5+3584 e^4 x^7\right )+e^{4 e^{16}} \left (24 e^{22/3} x^3+5760 e^{17/3} x^5+143360 e^4 x^7\right )+e^{2 e^{16}} \left (8 e^9 x+2304 e^{22/3} x^3+92160 e^{17/3} x^5+917504 e^4 x^7\right )\right ) \, dx \\ & = \int \left (128 e^9 x+6144 e^{22/3} x^3+98304 e^{17/3} x^5+\left (524288 e^4-256 e^{4+7 e^{16}}+8 e^{4+8 e^{16}}\right ) x^7+e^{e^{16}} \left (-64 e^9 x-6144 e^{22/3} x^3-147456 e^{17/3} x^5-1048576 e^4 x^7\right )+e^{3 e^{16}} \left (-384 e^{22/3} x^3-30720 e^{17/3} x^5-458752 e^4 x^7\right )+e^{5 e^{16}} \left (-576 e^{17/3} x^5-28672 e^4 x^7\right )+e^{6 e^{16}} \left (24 e^{17/3} x^5+3584 e^4 x^7\right )+e^{4 e^{16}} \left (24 e^{22/3} x^3+5760 e^{17/3} x^5+143360 e^4 x^7\right )+e^{2 e^{16}} \left (8 e^9 x+2304 e^{22/3} x^3+92160 e^{17/3} x^5+917504 e^4 x^7\right )\right ) \, dx \\ & = 64 e^9 x^2+1536 e^{22/3} x^4+16384 e^{17/3} x^6+e^4 \left (65536-32 e^{7 e^{16}}+e^{8 e^{16}}\right ) x^8+e^{e^{16}} \int \left (-64 e^9 x-6144 e^{22/3} x^3-147456 e^{17/3} x^5-1048576 e^4 x^7\right ) \, dx+e^{2 e^{16}} \int \left (8 e^9 x+2304 e^{22/3} x^3+92160 e^{17/3} x^5+917504 e^4 x^7\right ) \, dx+e^{3 e^{16}} \int \left (-384 e^{22/3} x^3-30720 e^{17/3} x^5-458752 e^4 x^7\right ) \, dx+e^{4 e^{16}} \int \left (24 e^{22/3} x^3+5760 e^{17/3} x^5+143360 e^4 x^7\right ) \, dx+e^{5 e^{16}} \int \left (-576 e^{17/3} x^5-28672 e^4 x^7\right ) \, dx+e^{6 e^{16}} \int \left (24 e^{17/3} x^5+3584 e^4 x^7\right ) \, dx \\ & = 64 e^9 x^2-32 e^{9+e^{16}} x^2+4 e^{9+2 e^{16}} x^2+1536 e^{22/3} x^4-1536 e^{\frac {22}{3}+e^{16}} x^4+576 e^{\frac {22}{3}+2 e^{16}} x^4-96 e^{\frac {22}{3}+3 e^{16}} x^4+6 e^{\frac {22}{3}+4 e^{16}} x^4+16384 e^{17/3} x^6-24576 e^{\frac {17}{3}+e^{16}} x^6+15360 e^{\frac {17}{3}+2 e^{16}} x^6-5120 e^{\frac {17}{3}+3 e^{16}} x^6+960 e^{\frac {17}{3}+4 e^{16}} x^6-96 e^{\frac {17}{3}+5 e^{16}} x^6+4 e^{\frac {17}{3}+6 e^{16}} x^6-131072 e^{4+e^{16}} x^8+114688 e^{4+2 e^{16}} x^8-57344 e^{4+3 e^{16}} x^8+17920 e^{4+4 e^{16}} x^8-3584 e^{4+5 e^{16}} x^8+448 e^{4+6 e^{16}} x^8+e^4 \left (65536-32 e^{7 e^{16}}+e^{8 e^{16}}\right ) x^8 \\ \end{align*}
Leaf count is larger than twice the leaf count of optimal. \(73\) vs. \(2(27)=54\).
Time = 0.04 (sec) , antiderivative size = 73, normalized size of antiderivative = 2.70 \[ \int \left (128 e^9 x+6144 e^{22/3} x^3+98304 e^{17/3} x^5+524288 e^4 x^7-256 e^{4+7 e^{16}} x^7+8 e^{4+8 e^{16}} x^7+e^{e^{16}} \left (-64 e^9 x-6144 e^{22/3} x^3-147456 e^{17/3} x^5-1048576 e^4 x^7\right )+e^{3 e^{16}} \left (-384 e^{22/3} x^3-30720 e^{17/3} x^5-458752 e^4 x^7\right )+e^{5 e^{16}} \left (-576 e^{17/3} x^5-28672 e^4 x^7\right )+e^{6 e^{16}} \left (24 e^{17/3} x^5+3584 e^4 x^7\right )+e^{4 e^{16}} \left (24 e^{22/3} x^3+5760 e^{17/3} x^5+143360 e^4 x^7\right )+e^{2 e^{16}} \left (8 e^9 x+2304 e^{22/3} x^3+92160 e^{17/3} x^5+917504 e^4 x^7\right )\right ) \, dx=e^4 \left (-4+e^{e^{16}}\right )^2 x^2 \left (4 e^5+6 e^{10/3} \left (-4+e^{e^{16}}\right )^2 x^2+4 e^{5/3} \left (-4+e^{e^{16}}\right )^4 x^4+\left (-4+e^{e^{16}}\right )^6 x^6\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. \(53\) vs. \(2(23)=46\).
Time = 0.59 (sec) , antiderivative size = 54, normalized size of antiderivative = 2.00
method | result | size |
default | \(\frac {{\mathrm e}^{4} \left ({\mathrm e}^{{\mathrm e}^{16}}-4\right )^{2} \left ({\mathrm e}^{2 \,{\mathrm e}^{16}} x^{2}-8 \,{\mathrm e}^{{\mathrm e}^{16}} x^{2}+16 x^{2}+{\mathrm e}^{\frac {5}{3}}\right )^{4}}{{\mathrm e}^{2 \,{\mathrm e}^{16}}-8 \,{\mathrm e}^{{\mathrm e}^{16}}+16}\) | \(54\) |
gosper | \(\left ({\mathrm e}^{2 \,{\mathrm e}^{16}}-8 \,{\mathrm e}^{{\mathrm e}^{16}}+16\right ) {\mathrm e}^{4} \left ({\mathrm e}^{6 \,{\mathrm e}^{16}} x^{6}-24 \,{\mathrm e}^{5 \,{\mathrm e}^{16}} x^{6}+240 \,{\mathrm e}^{4 \,{\mathrm e}^{16}} x^{6}+4 \,{\mathrm e}^{4 \,{\mathrm e}^{16}} {\mathrm e}^{\frac {5}{3}} x^{4}-1280 \,{\mathrm e}^{3 \,{\mathrm e}^{16}} x^{6}-64 \,{\mathrm e}^{3 \,{\mathrm e}^{16}} {\mathrm e}^{\frac {5}{3}} x^{4}+3840 \,{\mathrm e}^{2 \,{\mathrm e}^{16}} x^{6}+384 \,{\mathrm e}^{2 \,{\mathrm e}^{16}} {\mathrm e}^{\frac {5}{3}} x^{4}-6144 \,{\mathrm e}^{{\mathrm e}^{16}} x^{6}+6 \,{\mathrm e}^{2 \,{\mathrm e}^{16}} {\mathrm e}^{\frac {10}{3}} x^{2}-1024 \,{\mathrm e}^{{\mathrm e}^{16}} {\mathrm e}^{\frac {5}{3}} x^{4}+4096 x^{6}-48 \,{\mathrm e}^{{\mathrm e}^{16}} {\mathrm e}^{\frac {10}{3}} x^{2}+1024 \,{\mathrm e}^{\frac {5}{3}} x^{4}+96 \,{\mathrm e}^{\frac {10}{3}} x^{2}+4 \,{\mathrm e}^{5}\right ) x^{2}\) | \(178\) |
risch | \(x^{8} {\mathrm e}^{4+8 \,{\mathrm e}^{16}}-32 x^{8} {\mathrm e}^{4+7 \,{\mathrm e}^{16}}+4 \,{\mathrm e}^{6 \,{\mathrm e}^{16}+4} {\mathrm e}^{\frac {5}{3}} x^{6}+448 \,{\mathrm e}^{6 \,{\mathrm e}^{16}+4} x^{8}-96 \,{\mathrm e}^{5 \,{\mathrm e}^{16}+4} {\mathrm e}^{\frac {5}{3}} x^{6}-3584 \,{\mathrm e}^{5 \,{\mathrm e}^{16}+4} x^{8}+6 \,{\mathrm e}^{4 \,{\mathrm e}^{16}+4} {\mathrm e}^{\frac {10}{3}} x^{4}+960 \,{\mathrm e}^{4 \,{\mathrm e}^{16}+4} {\mathrm e}^{\frac {5}{3}} x^{6}+17920 \,{\mathrm e}^{4 \,{\mathrm e}^{16}+4} x^{8}-96 \,{\mathrm e}^{3 \,{\mathrm e}^{16}+4} {\mathrm e}^{\frac {10}{3}} x^{4}-5120 \,{\mathrm e}^{3 \,{\mathrm e}^{16}+4} {\mathrm e}^{\frac {5}{3}} x^{6}-57344 \,{\mathrm e}^{3 \,{\mathrm e}^{16}+4} x^{8}+4 \,{\mathrm e}^{2 \,{\mathrm e}^{16}+4} {\mathrm e}^{5} x^{2}+576 \,{\mathrm e}^{2 \,{\mathrm e}^{16}+4} {\mathrm e}^{\frac {10}{3}} x^{4}+15360 \,{\mathrm e}^{2 \,{\mathrm e}^{16}+4} {\mathrm e}^{\frac {5}{3}} x^{6}+114688 \,{\mathrm e}^{2 \,{\mathrm e}^{16}+4} x^{8}-32 \,{\mathrm e}^{{\mathrm e}^{16}+4} {\mathrm e}^{5} x^{2}-1536 \,{\mathrm e}^{{\mathrm e}^{16}+4} {\mathrm e}^{\frac {10}{3}} x^{4}-24576 \,{\mathrm e}^{{\mathrm e}^{16}+4} {\mathrm e}^{\frac {5}{3}} x^{6}-131072 \,{\mathrm e}^{{\mathrm e}^{16}+4} x^{8}+64 x^{2} {\mathrm e}^{9}+1536 \,{\mathrm e}^{\frac {22}{3}} x^{4}+16384 \,{\mathrm e}^{\frac {17}{3}} x^{6}+65536 x^{8} {\mathrm e}^{4}\) | \(285\) |
norman | \(\left (4 \,{\mathrm e}^{4} {\mathrm e}^{2 \,{\mathrm e}^{16}} {\mathrm e}^{5}-32 \,{\mathrm e}^{4} {\mathrm e}^{{\mathrm e}^{16}} {\mathrm e}^{5}+64 \,{\mathrm e}^{4} {\mathrm e}^{5}\right ) x^{2}+\left (6 \,{\mathrm e}^{4} {\mathrm e}^{4 \,{\mathrm e}^{16}} {\mathrm e}^{\frac {10}{3}}-96 \,{\mathrm e}^{4} {\mathrm e}^{3 \,{\mathrm e}^{16}} {\mathrm e}^{\frac {10}{3}}+576 \,{\mathrm e}^{4} {\mathrm e}^{2 \,{\mathrm e}^{16}} {\mathrm e}^{\frac {10}{3}}-1536 \,{\mathrm e}^{4} {\mathrm e}^{{\mathrm e}^{16}} {\mathrm e}^{\frac {10}{3}}+1536 \,{\mathrm e}^{4} {\mathrm e}^{\frac {10}{3}}\right ) x^{4}+\left (4 \,{\mathrm e}^{4} {\mathrm e}^{6 \,{\mathrm e}^{16}} {\mathrm e}^{\frac {5}{3}}-96 \,{\mathrm e}^{4} {\mathrm e}^{5 \,{\mathrm e}^{16}} {\mathrm e}^{\frac {5}{3}}+960 \,{\mathrm e}^{4} {\mathrm e}^{4 \,{\mathrm e}^{16}} {\mathrm e}^{\frac {5}{3}}-5120 \,{\mathrm e}^{4} {\mathrm e}^{3 \,{\mathrm e}^{16}} {\mathrm e}^{\frac {5}{3}}+15360 \,{\mathrm e}^{4} {\mathrm e}^{2 \,{\mathrm e}^{16}} {\mathrm e}^{\frac {5}{3}}-24576 \,{\mathrm e}^{4} {\mathrm e}^{{\mathrm e}^{16}} {\mathrm e}^{\frac {5}{3}}+16384 \,{\mathrm e}^{4} {\mathrm e}^{\frac {5}{3}}\right ) x^{6}+\left ({\mathrm e}^{4} {\mathrm e}^{8 \,{\mathrm e}^{16}}-32 \,{\mathrm e}^{4} {\mathrm e}^{7 \,{\mathrm e}^{16}}+448 \,{\mathrm e}^{4} {\mathrm e}^{6 \,{\mathrm e}^{16}}-3584 \,{\mathrm e}^{4} {\mathrm e}^{5 \,{\mathrm e}^{16}}+17920 \,{\mathrm e}^{4} {\mathrm e}^{4 \,{\mathrm e}^{16}}-57344 \,{\mathrm e}^{4} {\mathrm e}^{3 \,{\mathrm e}^{16}}+114688 \,{\mathrm e}^{4} {\mathrm e}^{2 \,{\mathrm e}^{16}}-131072 \,{\mathrm e}^{4} {\mathrm e}^{{\mathrm e}^{16}}+65536 \,{\mathrm e}^{4}\right ) x^{8}\) | \(303\) |
parallelrisch | \(15360 \,{\mathrm e}^{4} {\mathrm e}^{2 \,{\mathrm e}^{16}} {\mathrm e}^{\frac {5}{3}} x^{6}+576 \,{\mathrm e}^{4} {\mathrm e}^{2 \,{\mathrm e}^{16}} {\mathrm e}^{\frac {10}{3}} x^{4}-24576 \,{\mathrm e}^{4} {\mathrm e}^{{\mathrm e}^{16}} {\mathrm e}^{\frac {5}{3}} x^{6}+4 \,{\mathrm e}^{4} {\mathrm e}^{2 \,{\mathrm e}^{16}} {\mathrm e}^{5} x^{2}-1536 \,{\mathrm e}^{4} {\mathrm e}^{{\mathrm e}^{16}} {\mathrm e}^{\frac {10}{3}} x^{4}-32 \,{\mathrm e}^{4} {\mathrm e}^{{\mathrm e}^{16}} {\mathrm e}^{5} x^{2}+4 \,{\mathrm e}^{4} {\mathrm e}^{6 \,{\mathrm e}^{16}} {\mathrm e}^{\frac {5}{3}} x^{6}-96 \,{\mathrm e}^{4} {\mathrm e}^{5 \,{\mathrm e}^{16}} {\mathrm e}^{\frac {5}{3}} x^{6}+960 \,{\mathrm e}^{4} {\mathrm e}^{4 \,{\mathrm e}^{16}} {\mathrm e}^{\frac {5}{3}} x^{6}+6 \,{\mathrm e}^{4} {\mathrm e}^{4 \,{\mathrm e}^{16}} {\mathrm e}^{\frac {10}{3}} x^{4}-5120 \,{\mathrm e}^{4} {\mathrm e}^{3 \,{\mathrm e}^{16}} {\mathrm e}^{\frac {5}{3}} x^{6}-96 \,{\mathrm e}^{4} {\mathrm e}^{3 \,{\mathrm e}^{16}} {\mathrm e}^{\frac {10}{3}} x^{4}+65536 x^{8} {\mathrm e}^{4}+1536 \,{\mathrm e}^{4} {\mathrm e}^{\frac {10}{3}} x^{4}+64 x^{2} {\mathrm e}^{4} {\mathrm e}^{5}+{\mathrm e}^{4} {\mathrm e}^{8 \,{\mathrm e}^{16}} x^{8}-32 \,{\mathrm e}^{4} {\mathrm e}^{7 \,{\mathrm e}^{16}} x^{8}+448 \,{\mathrm e}^{4} {\mathrm e}^{6 \,{\mathrm e}^{16}} x^{8}-3584 \,{\mathrm e}^{4} {\mathrm e}^{5 \,{\mathrm e}^{16}} x^{8}+17920 \,{\mathrm e}^{4} {\mathrm e}^{4 \,{\mathrm e}^{16}} x^{8}-57344 \,{\mathrm e}^{4} {\mathrm e}^{3 \,{\mathrm e}^{16}} x^{8}+114688 \,{\mathrm e}^{4} {\mathrm e}^{2 \,{\mathrm e}^{16}} x^{8}-131072 \,{\mathrm e}^{4} {\mathrm e}^{{\mathrm e}^{16}} x^{8}+16384 \,{\mathrm e}^{4} {\mathrm e}^{\frac {5}{3}} x^{6}\) | \(355\) |
parts | \(15360 \,{\mathrm e}^{4} {\mathrm e}^{2 \,{\mathrm e}^{16}} {\mathrm e}^{\frac {5}{3}} x^{6}+576 \,{\mathrm e}^{4} {\mathrm e}^{2 \,{\mathrm e}^{16}} {\mathrm e}^{\frac {10}{3}} x^{4}-24576 \,{\mathrm e}^{4} {\mathrm e}^{{\mathrm e}^{16}} {\mathrm e}^{\frac {5}{3}} x^{6}+4 \,{\mathrm e}^{4} {\mathrm e}^{2 \,{\mathrm e}^{16}} {\mathrm e}^{5} x^{2}-1536 \,{\mathrm e}^{4} {\mathrm e}^{{\mathrm e}^{16}} {\mathrm e}^{\frac {10}{3}} x^{4}-32 \,{\mathrm e}^{4} {\mathrm e}^{{\mathrm e}^{16}} {\mathrm e}^{5} x^{2}+4 \,{\mathrm e}^{4} {\mathrm e}^{6 \,{\mathrm e}^{16}} {\mathrm e}^{\frac {5}{3}} x^{6}-96 \,{\mathrm e}^{4} {\mathrm e}^{5 \,{\mathrm e}^{16}} {\mathrm e}^{\frac {5}{3}} x^{6}+960 \,{\mathrm e}^{4} {\mathrm e}^{4 \,{\mathrm e}^{16}} {\mathrm e}^{\frac {5}{3}} x^{6}+6 \,{\mathrm e}^{4} {\mathrm e}^{4 \,{\mathrm e}^{16}} {\mathrm e}^{\frac {10}{3}} x^{4}-5120 \,{\mathrm e}^{4} {\mathrm e}^{3 \,{\mathrm e}^{16}} {\mathrm e}^{\frac {5}{3}} x^{6}-96 \,{\mathrm e}^{4} {\mathrm e}^{3 \,{\mathrm e}^{16}} {\mathrm e}^{\frac {10}{3}} x^{4}+65536 x^{8} {\mathrm e}^{4}+1536 \,{\mathrm e}^{4} {\mathrm e}^{\frac {10}{3}} x^{4}+64 x^{2} {\mathrm e}^{4} {\mathrm e}^{5}+{\mathrm e}^{4} {\mathrm e}^{8 \,{\mathrm e}^{16}} x^{8}-32 \,{\mathrm e}^{4} {\mathrm e}^{7 \,{\mathrm e}^{16}} x^{8}+448 \,{\mathrm e}^{4} {\mathrm e}^{6 \,{\mathrm e}^{16}} x^{8}-3584 \,{\mathrm e}^{4} {\mathrm e}^{5 \,{\mathrm e}^{16}} x^{8}+17920 \,{\mathrm e}^{4} {\mathrm e}^{4 \,{\mathrm e}^{16}} x^{8}-57344 \,{\mathrm e}^{4} {\mathrm e}^{3 \,{\mathrm e}^{16}} x^{8}+114688 \,{\mathrm e}^{4} {\mathrm e}^{2 \,{\mathrm e}^{16}} x^{8}-131072 \,{\mathrm e}^{4} {\mathrm e}^{{\mathrm e}^{16}} x^{8}+16384 \,{\mathrm e}^{4} {\mathrm e}^{\frac {5}{3}} x^{6}\) | \(355\) |
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Leaf count of result is larger than twice the leaf count of optimal. 221 vs. \(2 (19) = 38\).
Time = 0.25 (sec) , antiderivative size = 221, normalized size of antiderivative = 8.19 \[ \int \left (128 e^9 x+6144 e^{22/3} x^3+98304 e^{17/3} x^5+524288 e^4 x^7-256 e^{4+7 e^{16}} x^7+8 e^{4+8 e^{16}} x^7+e^{e^{16}} \left (-64 e^9 x-6144 e^{22/3} x^3-147456 e^{17/3} x^5-1048576 e^4 x^7\right )+e^{3 e^{16}} \left (-384 e^{22/3} x^3-30720 e^{17/3} x^5-458752 e^4 x^7\right )+e^{5 e^{16}} \left (-576 e^{17/3} x^5-28672 e^4 x^7\right )+e^{6 e^{16}} \left (24 e^{17/3} x^5+3584 e^4 x^7\right )+e^{4 e^{16}} \left (24 e^{22/3} x^3+5760 e^{17/3} x^5+143360 e^4 x^7\right )+e^{2 e^{16}} \left (8 e^9 x+2304 e^{22/3} x^3+92160 e^{17/3} x^5+917504 e^4 x^7\right )\right ) \, dx=65536 \, x^{8} e^{4} + x^{8} e^{\left (8 \, e^{16} + 4\right )} - 32 \, x^{8} e^{\left (7 \, e^{16} + 4\right )} + 16384 \, x^{6} e^{\frac {17}{3}} + 1536 \, x^{4} e^{\frac {22}{3}} + 64 \, x^{2} e^{9} + 4 \, {\left (112 \, x^{8} e^{4} + x^{6} e^{\frac {17}{3}}\right )} e^{\left (6 \, e^{16}\right )} - 32 \, {\left (112 \, x^{8} e^{4} + 3 \, x^{6} e^{\frac {17}{3}}\right )} e^{\left (5 \, e^{16}\right )} + 2 \, {\left (8960 \, x^{8} e^{4} + 480 \, x^{6} e^{\frac {17}{3}} + 3 \, x^{4} e^{\frac {22}{3}}\right )} e^{\left (4 \, e^{16}\right )} - 32 \, {\left (1792 \, x^{8} e^{4} + 160 \, x^{6} e^{\frac {17}{3}} + 3 \, x^{4} e^{\frac {22}{3}}\right )} e^{\left (3 \, e^{16}\right )} + 4 \, {\left (28672 \, x^{8} e^{4} + 3840 \, x^{6} e^{\frac {17}{3}} + 144 \, x^{4} e^{\frac {22}{3}} + x^{2} e^{9}\right )} e^{\left (2 \, e^{16}\right )} - 32 \, {\left (4096 \, x^{8} e^{4} + 768 \, x^{6} e^{\frac {17}{3}} + 48 \, x^{4} e^{\frac {22}{3}} + x^{2} e^{9}\right )} e^{\left (e^{16}\right )} \]
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Leaf count of result is larger than twice the leaf count of optimal. 282 vs. \(2 (20) = 40\).
Time = 0.06 (sec) , antiderivative size = 282, normalized size of antiderivative = 10.44 \[ \int \left (128 e^9 x+6144 e^{22/3} x^3+98304 e^{17/3} x^5+524288 e^4 x^7-256 e^{4+7 e^{16}} x^7+8 e^{4+8 e^{16}} x^7+e^{e^{16}} \left (-64 e^9 x-6144 e^{22/3} x^3-147456 e^{17/3} x^5-1048576 e^4 x^7\right )+e^{3 e^{16}} \left (-384 e^{22/3} x^3-30720 e^{17/3} x^5-458752 e^4 x^7\right )+e^{5 e^{16}} \left (-576 e^{17/3} x^5-28672 e^4 x^7\right )+e^{6 e^{16}} \left (24 e^{17/3} x^5+3584 e^4 x^7\right )+e^{4 e^{16}} \left (24 e^{22/3} x^3+5760 e^{17/3} x^5+143360 e^4 x^7\right )+e^{2 e^{16}} \left (8 e^9 x+2304 e^{22/3} x^3+92160 e^{17/3} x^5+917504 e^4 x^7\right )\right ) \, dx=x^{8} \cdot \left (65536 e^{4} + e^{4} e^{8 e^{16}} - 131072 e^{4} e^{e^{16}} - 57344 e^{4} e^{3 e^{16}} - 3584 e^{4} e^{5 e^{16}} - 32 e^{4} e^{7 e^{16}} + 448 e^{4} e^{6 e^{16}} + 17920 e^{4} e^{4 e^{16}} + 114688 e^{4} e^{2 e^{16}}\right ) + x^{6} \cdot \left (16384 e^{\frac {17}{3}} - 24576 e^{\frac {17}{3}} e^{e^{16}} - 5120 e^{\frac {17}{3}} e^{3 e^{16}} - 96 e^{\frac {17}{3}} e^{5 e^{16}} + 4 e^{\frac {17}{3}} e^{6 e^{16}} + 960 e^{\frac {17}{3}} e^{4 e^{16}} + 15360 e^{\frac {17}{3}} e^{2 e^{16}}\right ) + x^{4} \cdot \left (1536 e^{\frac {22}{3}} - 1536 e^{\frac {22}{3}} e^{e^{16}} - 96 e^{\frac {22}{3}} e^{3 e^{16}} + 6 e^{\frac {22}{3}} e^{4 e^{16}} + 576 e^{\frac {22}{3}} e^{2 e^{16}}\right ) + x^{2} \cdot \left (64 e^{9} - 32 e^{9} e^{e^{16}} + 4 e^{9} e^{2 e^{16}}\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. 221 vs. \(2 (19) = 38\).
Time = 0.20 (sec) , antiderivative size = 221, normalized size of antiderivative = 8.19 \[ \int \left (128 e^9 x+6144 e^{22/3} x^3+98304 e^{17/3} x^5+524288 e^4 x^7-256 e^{4+7 e^{16}} x^7+8 e^{4+8 e^{16}} x^7+e^{e^{16}} \left (-64 e^9 x-6144 e^{22/3} x^3-147456 e^{17/3} x^5-1048576 e^4 x^7\right )+e^{3 e^{16}} \left (-384 e^{22/3} x^3-30720 e^{17/3} x^5-458752 e^4 x^7\right )+e^{5 e^{16}} \left (-576 e^{17/3} x^5-28672 e^4 x^7\right )+e^{6 e^{16}} \left (24 e^{17/3} x^5+3584 e^4 x^7\right )+e^{4 e^{16}} \left (24 e^{22/3} x^3+5760 e^{17/3} x^5+143360 e^4 x^7\right )+e^{2 e^{16}} \left (8 e^9 x+2304 e^{22/3} x^3+92160 e^{17/3} x^5+917504 e^4 x^7\right )\right ) \, dx=65536 \, x^{8} e^{4} + x^{8} e^{\left (8 \, e^{16} + 4\right )} - 32 \, x^{8} e^{\left (7 \, e^{16} + 4\right )} + 16384 \, x^{6} e^{\frac {17}{3}} + 1536 \, x^{4} e^{\frac {22}{3}} + 64 \, x^{2} e^{9} + 4 \, {\left (112 \, x^{8} e^{4} + x^{6} e^{\frac {17}{3}}\right )} e^{\left (6 \, e^{16}\right )} - 32 \, {\left (112 \, x^{8} e^{4} + 3 \, x^{6} e^{\frac {17}{3}}\right )} e^{\left (5 \, e^{16}\right )} + 2 \, {\left (8960 \, x^{8} e^{4} + 480 \, x^{6} e^{\frac {17}{3}} + 3 \, x^{4} e^{\frac {22}{3}}\right )} e^{\left (4 \, e^{16}\right )} - 32 \, {\left (1792 \, x^{8} e^{4} + 160 \, x^{6} e^{\frac {17}{3}} + 3 \, x^{4} e^{\frac {22}{3}}\right )} e^{\left (3 \, e^{16}\right )} + 4 \, {\left (28672 \, x^{8} e^{4} + 3840 \, x^{6} e^{\frac {17}{3}} + 144 \, x^{4} e^{\frac {22}{3}} + x^{2} e^{9}\right )} e^{\left (2 \, e^{16}\right )} - 32 \, {\left (4096 \, x^{8} e^{4} + 768 \, x^{6} e^{\frac {17}{3}} + 48 \, x^{4} e^{\frac {22}{3}} + x^{2} e^{9}\right )} e^{\left (e^{16}\right )} \]
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Leaf count of result is larger than twice the leaf count of optimal. 221 vs. \(2 (19) = 38\).
Time = 0.26 (sec) , antiderivative size = 221, normalized size of antiderivative = 8.19 \[ \int \left (128 e^9 x+6144 e^{22/3} x^3+98304 e^{17/3} x^5+524288 e^4 x^7-256 e^{4+7 e^{16}} x^7+8 e^{4+8 e^{16}} x^7+e^{e^{16}} \left (-64 e^9 x-6144 e^{22/3} x^3-147456 e^{17/3} x^5-1048576 e^4 x^7\right )+e^{3 e^{16}} \left (-384 e^{22/3} x^3-30720 e^{17/3} x^5-458752 e^4 x^7\right )+e^{5 e^{16}} \left (-576 e^{17/3} x^5-28672 e^4 x^7\right )+e^{6 e^{16}} \left (24 e^{17/3} x^5+3584 e^4 x^7\right )+e^{4 e^{16}} \left (24 e^{22/3} x^3+5760 e^{17/3} x^5+143360 e^4 x^7\right )+e^{2 e^{16}} \left (8 e^9 x+2304 e^{22/3} x^3+92160 e^{17/3} x^5+917504 e^4 x^7\right )\right ) \, dx=65536 \, x^{8} e^{4} + x^{8} e^{\left (8 \, e^{16} + 4\right )} - 32 \, x^{8} e^{\left (7 \, e^{16} + 4\right )} + 16384 \, x^{6} e^{\frac {17}{3}} + 1536 \, x^{4} e^{\frac {22}{3}} + 64 \, x^{2} e^{9} + 4 \, {\left (112 \, x^{8} e^{4} + x^{6} e^{\frac {17}{3}}\right )} e^{\left (6 \, e^{16}\right )} - 32 \, {\left (112 \, x^{8} e^{4} + 3 \, x^{6} e^{\frac {17}{3}}\right )} e^{\left (5 \, e^{16}\right )} + 2 \, {\left (8960 \, x^{8} e^{4} + 480 \, x^{6} e^{\frac {17}{3}} + 3 \, x^{4} e^{\frac {22}{3}}\right )} e^{\left (4 \, e^{16}\right )} - 32 \, {\left (1792 \, x^{8} e^{4} + 160 \, x^{6} e^{\frac {17}{3}} + 3 \, x^{4} e^{\frac {22}{3}}\right )} e^{\left (3 \, e^{16}\right )} + 4 \, {\left (28672 \, x^{8} e^{4} + 3840 \, x^{6} e^{\frac {17}{3}} + 144 \, x^{4} e^{\frac {22}{3}} + x^{2} e^{9}\right )} e^{\left (2 \, e^{16}\right )} - 32 \, {\left (4096 \, x^{8} e^{4} + 768 \, x^{6} e^{\frac {17}{3}} + 48 \, x^{4} e^{\frac {22}{3}} + x^{2} e^{9}\right )} e^{\left (e^{16}\right )} \]
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Time = 9.02 (sec) , antiderivative size = 207, normalized size of antiderivative = 7.67 \[ \int \left (128 e^9 x+6144 e^{22/3} x^3+98304 e^{17/3} x^5+524288 e^4 x^7-256 e^{4+7 e^{16}} x^7+8 e^{4+8 e^{16}} x^7+e^{e^{16}} \left (-64 e^9 x-6144 e^{22/3} x^3-147456 e^{17/3} x^5-1048576 e^4 x^7\right )+e^{3 e^{16}} \left (-384 e^{22/3} x^3-30720 e^{17/3} x^5-458752 e^4 x^7\right )+e^{5 e^{16}} \left (-576 e^{17/3} x^5-28672 e^4 x^7\right )+e^{6 e^{16}} \left (24 e^{17/3} x^5+3584 e^4 x^7\right )+e^{4 e^{16}} \left (24 e^{22/3} x^3+5760 e^{17/3} x^5+143360 e^4 x^7\right )+e^{2 e^{16}} \left (8 e^9 x+2304 e^{22/3} x^3+92160 e^{17/3} x^5+917504 e^4 x^7\right )\right ) \, dx=\left (65536\,{\mathrm {e}}^4-131072\,{\mathrm {e}}^{{\mathrm {e}}^{16}+4}+114688\,{\mathrm {e}}^{2\,{\mathrm {e}}^{16}+4}-57344\,{\mathrm {e}}^{3\,{\mathrm {e}}^{16}+4}+17920\,{\mathrm {e}}^{4\,{\mathrm {e}}^{16}+4}-3584\,{\mathrm {e}}^{5\,{\mathrm {e}}^{16}+4}+448\,{\mathrm {e}}^{6\,{\mathrm {e}}^{16}+4}-32\,{\mathrm {e}}^{7\,{\mathrm {e}}^{16}+4}+{\mathrm {e}}^{8\,{\mathrm {e}}^{16}+4}\right )\,x^8+\left (16384\,{\mathrm {e}}^{17/3}-24576\,{\mathrm {e}}^{{\mathrm {e}}^{16}+\frac {17}{3}}+15360\,{\mathrm {e}}^{2\,{\mathrm {e}}^{16}+\frac {17}{3}}-5120\,{\mathrm {e}}^{3\,{\mathrm {e}}^{16}+\frac {17}{3}}+960\,{\mathrm {e}}^{4\,{\mathrm {e}}^{16}+\frac {17}{3}}-96\,{\mathrm {e}}^{5\,{\mathrm {e}}^{16}+\frac {17}{3}}+4\,{\mathrm {e}}^{6\,{\mathrm {e}}^{16}+\frac {17}{3}}\right )\,x^6+\left (1536\,{\mathrm {e}}^{22/3}-1536\,{\mathrm {e}}^{{\mathrm {e}}^{16}+\frac {22}{3}}+576\,{\mathrm {e}}^{2\,{\mathrm {e}}^{16}+\frac {22}{3}}-96\,{\mathrm {e}}^{3\,{\mathrm {e}}^{16}+\frac {22}{3}}+6\,{\mathrm {e}}^{4\,{\mathrm {e}}^{16}+\frac {22}{3}}\right )\,x^4+\left (64\,{\mathrm {e}}^9-32\,{\mathrm {e}}^{{\mathrm {e}}^{16}+9}+4\,{\mathrm {e}}^{2\,{\mathrm {e}}^{16}+9}\right )\,x^2 \]
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