Integrand size = 434, antiderivative size = 34 \[ \int \frac {-256 x^2-128 x^4-128 x^5+e^{\frac {20-x}{2}} \left (-128 x^2-128 x^3\right )+e^{\frac {20-x}{4}} \left (-64 x^2+240 x^3+256 x^4\right )+e^x \left (8 x+8 x^2+8 x^3+e^{\frac {20-x}{2}} (8+8 x)+e^{\frac {20-x}{4}} \left (4-15 x-16 x^2\right )\right )+\left (64 x^2-256 x^3-256 x^4+e^x \left (-4+e^{\frac {20-x}{4}} (-16-16 x)+16 x+16 x^2\right )+e^{\frac {20-x}{4}} \left (256 x^2+256 x^3\right )\right ) \log \left (e^{2 x}-32 e^x x^2+256 x^4\right )+\left (-128 x^2-128 x^3+e^x (8+8 x)\right ) \log ^2\left (e^{2 x}-32 e^x x^2+256 x^4\right )}{-64 e^{\frac {20-x}{2}} x^2+128 e^{\frac {20-x}{4}} x^3-64 x^4+e^x \left (4 e^{\frac {20-x}{2}}-8 e^{\frac {20-x}{4}} x+4 x^2\right )+\left (128 e^{\frac {20-x}{4}} x^2-128 x^3+e^x \left (-8 e^{\frac {20-x}{4}}+8 x\right )\right ) \log \left (e^{2 x}-32 e^x x^2+256 x^4\right )+\left (4 e^x-64 x^2\right ) \log ^2\left (e^{2 x}-32 e^x x^2+256 x^4\right )} \, dx=x \left (2+x-\frac {1}{-e^{5-\frac {x}{4}}+x+\log \left (\left (e^x-16 x^2\right )^2\right )}\right ) \]
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Timed out. \[ \int \frac {-256 x^2-128 x^4-128 x^5+e^{\frac {20-x}{2}} \left (-128 x^2-128 x^3\right )+e^{\frac {20-x}{4}} \left (-64 x^2+240 x^3+256 x^4\right )+e^x \left (8 x+8 x^2+8 x^3+e^{\frac {20-x}{2}} (8+8 x)+e^{\frac {20-x}{4}} \left (4-15 x-16 x^2\right )\right )+\left (64 x^2-256 x^3-256 x^4+e^x \left (-4+e^{\frac {20-x}{4}} (-16-16 x)+16 x+16 x^2\right )+e^{\frac {20-x}{4}} \left (256 x^2+256 x^3\right )\right ) \log \left (e^{2 x}-32 e^x x^2+256 x^4\right )+\left (-128 x^2-128 x^3+e^x (8+8 x)\right ) \log ^2\left (e^{2 x}-32 e^x x^2+256 x^4\right )}{-64 e^{\frac {20-x}{2}} x^2+128 e^{\frac {20-x}{4}} x^3-64 x^4+e^x \left (4 e^{\frac {20-x}{2}}-8 e^{\frac {20-x}{4}} x+4 x^2\right )+\left (128 e^{\frac {20-x}{4}} x^2-128 x^3+e^x \left (-8 e^{\frac {20-x}{4}}+8 x\right )\right ) \log \left (e^{2 x}-32 e^x x^2+256 x^4\right )+\left (4 e^x-64 x^2\right ) \log ^2\left (e^{2 x}-32 e^x x^2+256 x^4\right )} \, dx=\text {\$Aborted} \]
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Rubi steps Aborted
Time = 0.26 (sec) , antiderivative size = 51, normalized size of antiderivative = 1.50 \[ \int \frac {-256 x^2-128 x^4-128 x^5+e^{\frac {20-x}{2}} \left (-128 x^2-128 x^3\right )+e^{\frac {20-x}{4}} \left (-64 x^2+240 x^3+256 x^4\right )+e^x \left (8 x+8 x^2+8 x^3+e^{\frac {20-x}{2}} (8+8 x)+e^{\frac {20-x}{4}} \left (4-15 x-16 x^2\right )\right )+\left (64 x^2-256 x^3-256 x^4+e^x \left (-4+e^{\frac {20-x}{4}} (-16-16 x)+16 x+16 x^2\right )+e^{\frac {20-x}{4}} \left (256 x^2+256 x^3\right )\right ) \log \left (e^{2 x}-32 e^x x^2+256 x^4\right )+\left (-128 x^2-128 x^3+e^x (8+8 x)\right ) \log ^2\left (e^{2 x}-32 e^x x^2+256 x^4\right )}{-64 e^{\frac {20-x}{2}} x^2+128 e^{\frac {20-x}{4}} x^3-64 x^4+e^x \left (4 e^{\frac {20-x}{2}}-8 e^{\frac {20-x}{4}} x+4 x^2\right )+\left (128 e^{\frac {20-x}{4}} x^2-128 x^3+e^x \left (-8 e^{\frac {20-x}{4}}+8 x\right )\right ) \log \left (e^{2 x}-32 e^x x^2+256 x^4\right )+\left (4 e^x-64 x^2\right ) \log ^2\left (e^{2 x}-32 e^x x^2+256 x^4\right )} \, dx=x \left (2+x-\frac {e^{x/4}}{-e^5+e^{x/4} x+e^{x/4} \log \left (\left (e^x-16 x^2\right )^2\right )}\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. \(110\) vs. \(2(30)=60\).
Time = 4.15 (sec) , antiderivative size = 111, normalized size of antiderivative = 3.26
method | result | size |
parallelrisch | \(-\frac {-128 x^{3}+128 x^{2} {\mathrm e}^{-\frac {x}{4}+5}-128 \ln \left ({\mathrm e}^{2 x}-32 \,{\mathrm e}^{x} x^{2}+256 x^{4}\right ) x^{2}-256 x^{2}+256 x \,{\mathrm e}^{-\frac {x}{4}+5}-256 x \ln \left ({\mathrm e}^{2 x}-32 \,{\mathrm e}^{x} x^{2}+256 x^{4}\right )+128 x}{128 \left (\ln \left ({\mathrm e}^{2 x}-32 \,{\mathrm e}^{x} x^{2}+256 x^{4}\right )-{\mathrm e}^{-\frac {x}{4}+5}+x \right )}\) | \(111\) |
risch | \(x^{2}+2 x -\frac {2 x \,{\mathrm e}^{\frac {x}{4}}}{-i \pi {\operatorname {csgn}\left (i \left (\frac {{\mathrm e}^{x}}{16}-x^{2}\right )\right )}^{2} \operatorname {csgn}\left (i \left (\frac {{\mathrm e}^{x}}{16}-x^{2}\right )^{2}\right ) {\mathrm e}^{\frac {x}{4}}-2 i \pi \,\operatorname {csgn}\left (i \left (\frac {{\mathrm e}^{x}}{16}-x^{2}\right )\right ) {\operatorname {csgn}\left (i \left (\frac {{\mathrm e}^{x}}{16}-x^{2}\right )^{2}\right )}^{2} {\mathrm e}^{\frac {x}{4}}-i \pi {\operatorname {csgn}\left (i \left (\frac {{\mathrm e}^{x}}{16}-x^{2}\right )^{2}\right )}^{3} {\mathrm e}^{\frac {x}{4}}+2 x \,{\mathrm e}^{\frac {x}{4}}+4 \,{\mathrm e}^{\frac {x}{4}} \ln \left (-\frac {{\mathrm e}^{x}}{16}+x^{2}\right )-2 \,{\mathrm e}^{5}}\) | \(150\) |
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Leaf count of result is larger than twice the leaf count of optimal. 114 vs. \(2 (32) = 64\).
Time = 0.26 (sec) , antiderivative size = 114, normalized size of antiderivative = 3.35 \[ \int \frac {-256 x^2-128 x^4-128 x^5+e^{\frac {20-x}{2}} \left (-128 x^2-128 x^3\right )+e^{\frac {20-x}{4}} \left (-64 x^2+240 x^3+256 x^4\right )+e^x \left (8 x+8 x^2+8 x^3+e^{\frac {20-x}{2}} (8+8 x)+e^{\frac {20-x}{4}} \left (4-15 x-16 x^2\right )\right )+\left (64 x^2-256 x^3-256 x^4+e^x \left (-4+e^{\frac {20-x}{4}} (-16-16 x)+16 x+16 x^2\right )+e^{\frac {20-x}{4}} \left (256 x^2+256 x^3\right )\right ) \log \left (e^{2 x}-32 e^x x^2+256 x^4\right )+\left (-128 x^2-128 x^3+e^x (8+8 x)\right ) \log ^2\left (e^{2 x}-32 e^x x^2+256 x^4\right )}{-64 e^{\frac {20-x}{2}} x^2+128 e^{\frac {20-x}{4}} x^3-64 x^4+e^x \left (4 e^{\frac {20-x}{2}}-8 e^{\frac {20-x}{4}} x+4 x^2\right )+\left (128 e^{\frac {20-x}{4}} x^2-128 x^3+e^x \left (-8 e^{\frac {20-x}{4}}+8 x\right )\right ) \log \left (e^{2 x}-32 e^x x^2+256 x^4\right )+\left (4 e^x-64 x^2\right ) \log ^2\left (e^{2 x}-32 e^x x^2+256 x^4\right )} \, dx=\frac {x^{3} + 2 \, x^{2} - {\left (x^{2} + 2 \, x\right )} e^{\left (-\frac {1}{4} \, x + 5\right )} + {\left (x^{2} + 2 \, x\right )} \log \left ({\left (256 \, x^{4} e^{\left (-2 \, x + 40\right )} - 32 \, x^{2} e^{\left (-x + 40\right )} + e^{40}\right )} e^{\left (2 \, x - 40\right )}\right ) - x}{x - e^{\left (-\frac {1}{4} \, x + 5\right )} + \log \left ({\left (256 \, x^{4} e^{\left (-2 \, x + 40\right )} - 32 \, x^{2} e^{\left (-x + 40\right )} + e^{40}\right )} e^{\left (2 \, x - 40\right )}\right )} \]
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Leaf count of result is larger than twice the leaf count of optimal. 53 vs. \(2 (26) = 52\).
Time = 0.32 (sec) , antiderivative size = 53, normalized size of antiderivative = 1.56 \[ \int \frac {-256 x^2-128 x^4-128 x^5+e^{\frac {20-x}{2}} \left (-128 x^2-128 x^3\right )+e^{\frac {20-x}{4}} \left (-64 x^2+240 x^3+256 x^4\right )+e^x \left (8 x+8 x^2+8 x^3+e^{\frac {20-x}{2}} (8+8 x)+e^{\frac {20-x}{4}} \left (4-15 x-16 x^2\right )\right )+\left (64 x^2-256 x^3-256 x^4+e^x \left (-4+e^{\frac {20-x}{4}} (-16-16 x)+16 x+16 x^2\right )+e^{\frac {20-x}{4}} \left (256 x^2+256 x^3\right )\right ) \log \left (e^{2 x}-32 e^x x^2+256 x^4\right )+\left (-128 x^2-128 x^3+e^x (8+8 x)\right ) \log ^2\left (e^{2 x}-32 e^x x^2+256 x^4\right )}{-64 e^{\frac {20-x}{2}} x^2+128 e^{\frac {20-x}{4}} x^3-64 x^4+e^x \left (4 e^{\frac {20-x}{2}}-8 e^{\frac {20-x}{4}} x+4 x^2\right )+\left (128 e^{\frac {20-x}{4}} x^2-128 x^3+e^x \left (-8 e^{\frac {20-x}{4}}+8 x\right )\right ) \log \left (e^{2 x}-32 e^x x^2+256 x^4\right )+\left (4 e^x-64 x^2\right ) \log ^2\left (e^{2 x}-32 e^x x^2+256 x^4\right )} \, dx=x^{2} + 2 x - \frac {x \sqrt [4]{e^{x}}}{x \sqrt [4]{e^{x}} + \sqrt [4]{e^{x}} \log {\left (256 x^{4} - 32 x^{2} e^{x} + e^{2 x} \right )} - e^{5}} \]
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\[ \int \frac {-256 x^2-128 x^4-128 x^5+e^{\frac {20-x}{2}} \left (-128 x^2-128 x^3\right )+e^{\frac {20-x}{4}} \left (-64 x^2+240 x^3+256 x^4\right )+e^x \left (8 x+8 x^2+8 x^3+e^{\frac {20-x}{2}} (8+8 x)+e^{\frac {20-x}{4}} \left (4-15 x-16 x^2\right )\right )+\left (64 x^2-256 x^3-256 x^4+e^x \left (-4+e^{\frac {20-x}{4}} (-16-16 x)+16 x+16 x^2\right )+e^{\frac {20-x}{4}} \left (256 x^2+256 x^3\right )\right ) \log \left (e^{2 x}-32 e^x x^2+256 x^4\right )+\left (-128 x^2-128 x^3+e^x (8+8 x)\right ) \log ^2\left (e^{2 x}-32 e^x x^2+256 x^4\right )}{-64 e^{\frac {20-x}{2}} x^2+128 e^{\frac {20-x}{4}} x^3-64 x^4+e^x \left (4 e^{\frac {20-x}{2}}-8 e^{\frac {20-x}{4}} x+4 x^2\right )+\left (128 e^{\frac {20-x}{4}} x^2-128 x^3+e^x \left (-8 e^{\frac {20-x}{4}}+8 x\right )\right ) \log \left (e^{2 x}-32 e^x x^2+256 x^4\right )+\left (4 e^x-64 x^2\right ) \log ^2\left (e^{2 x}-32 e^x x^2+256 x^4\right )} \, dx=\int { \frac {128 \, x^{5} + 128 \, x^{4} + 8 \, {\left (16 \, x^{3} + 16 \, x^{2} - {\left (x + 1\right )} e^{x}\right )} \log \left (256 \, x^{4} - 32 \, x^{2} e^{x} + e^{\left (2 \, x\right )}\right )^{2} + 256 \, x^{2} - {\left (8 \, x^{3} + 8 \, x^{2} - {\left (16 \, x^{2} + 15 \, x - 4\right )} e^{\left (-\frac {1}{4} \, x + 5\right )} + 8 \, {\left (x + 1\right )} e^{\left (-\frac {1}{2} \, x + 10\right )} + 8 \, x\right )} e^{x} - 16 \, {\left (16 \, x^{4} + 15 \, x^{3} - 4 \, x^{2}\right )} e^{\left (-\frac {1}{4} \, x + 5\right )} + 128 \, {\left (x^{3} + x^{2}\right )} e^{\left (-\frac {1}{2} \, x + 10\right )} + 4 \, {\left (64 \, x^{4} + 64 \, x^{3} - 16 \, x^{2} - {\left (4 \, x^{2} - 4 \, {\left (x + 1\right )} e^{\left (-\frac {1}{4} \, x + 5\right )} + 4 \, x - 1\right )} e^{x} - 64 \, {\left (x^{3} + x^{2}\right )} e^{\left (-\frac {1}{4} \, x + 5\right )}\right )} \log \left (256 \, x^{4} - 32 \, x^{2} e^{x} + e^{\left (2 \, x\right )}\right )}{4 \, {\left (16 \, x^{4} - 32 \, x^{3} e^{\left (-\frac {1}{4} \, x + 5\right )} + 16 \, x^{2} e^{\left (-\frac {1}{2} \, x + 10\right )} + {\left (16 \, x^{2} - e^{x}\right )} \log \left (256 \, x^{4} - 32 \, x^{2} e^{x} + e^{\left (2 \, x\right )}\right )^{2} - {\left (x^{2} - 2 \, x e^{\left (-\frac {1}{4} \, x + 5\right )} + e^{\left (-\frac {1}{2} \, x + 10\right )}\right )} e^{x} + 2 \, {\left (16 \, x^{3} - 16 \, x^{2} e^{\left (-\frac {1}{4} \, x + 5\right )} - {\left (x - e^{\left (-\frac {1}{4} \, x + 5\right )}\right )} e^{x}\right )} \log \left (256 \, x^{4} - 32 \, x^{2} e^{x} + e^{\left (2 \, x\right )}\right )\right )}} \,d x } \]
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Leaf count of result is larger than twice the leaf count of optimal. 125 vs. \(2 (32) = 64\).
Time = 2.44 (sec) , antiderivative size = 125, normalized size of antiderivative = 3.68 \[ \int \frac {-256 x^2-128 x^4-128 x^5+e^{\frac {20-x}{2}} \left (-128 x^2-128 x^3\right )+e^{\frac {20-x}{4}} \left (-64 x^2+240 x^3+256 x^4\right )+e^x \left (8 x+8 x^2+8 x^3+e^{\frac {20-x}{2}} (8+8 x)+e^{\frac {20-x}{4}} \left (4-15 x-16 x^2\right )\right )+\left (64 x^2-256 x^3-256 x^4+e^x \left (-4+e^{\frac {20-x}{4}} (-16-16 x)+16 x+16 x^2\right )+e^{\frac {20-x}{4}} \left (256 x^2+256 x^3\right )\right ) \log \left (e^{2 x}-32 e^x x^2+256 x^4\right )+\left (-128 x^2-128 x^3+e^x (8+8 x)\right ) \log ^2\left (e^{2 x}-32 e^x x^2+256 x^4\right )}{-64 e^{\frac {20-x}{2}} x^2+128 e^{\frac {20-x}{4}} x^3-64 x^4+e^x \left (4 e^{\frac {20-x}{2}}-8 e^{\frac {20-x}{4}} x+4 x^2\right )+\left (128 e^{\frac {20-x}{4}} x^2-128 x^3+e^x \left (-8 e^{\frac {20-x}{4}}+8 x\right )\right ) \log \left (e^{2 x}-32 e^x x^2+256 x^4\right )+\left (4 e^x-64 x^2\right ) \log ^2\left (e^{2 x}-32 e^x x^2+256 x^4\right )} \, dx=\frac {x^{3} e^{\left (\frac {1}{4} \, x\right )} + x^{2} e^{\left (\frac {1}{4} \, x\right )} \log \left (256 \, x^{4} - 32 \, x^{2} e^{x} + e^{\left (2 \, x\right )}\right ) - x^{2} e^{5} + 2 \, x^{2} e^{\left (\frac {1}{4} \, x\right )} + 2 \, x e^{\left (\frac {1}{4} \, x\right )} \log \left (256 \, x^{4} - 32 \, x^{2} e^{x} + e^{\left (2 \, x\right )}\right ) - 2 \, x e^{5} - x e^{\left (\frac {1}{4} \, x\right )}}{x e^{\left (\frac {1}{4} \, x\right )} + e^{\left (\frac {1}{4} \, x\right )} \log \left (256 \, x^{4} - 32 \, x^{2} e^{x} + e^{\left (2 \, x\right )}\right ) - e^{5}} \]
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Timed out. \[ \int \frac {-256 x^2-128 x^4-128 x^5+e^{\frac {20-x}{2}} \left (-128 x^2-128 x^3\right )+e^{\frac {20-x}{4}} \left (-64 x^2+240 x^3+256 x^4\right )+e^x \left (8 x+8 x^2+8 x^3+e^{\frac {20-x}{2}} (8+8 x)+e^{\frac {20-x}{4}} \left (4-15 x-16 x^2\right )\right )+\left (64 x^2-256 x^3-256 x^4+e^x \left (-4+e^{\frac {20-x}{4}} (-16-16 x)+16 x+16 x^2\right )+e^{\frac {20-x}{4}} \left (256 x^2+256 x^3\right )\right ) \log \left (e^{2 x}-32 e^x x^2+256 x^4\right )+\left (-128 x^2-128 x^3+e^x (8+8 x)\right ) \log ^2\left (e^{2 x}-32 e^x x^2+256 x^4\right )}{-64 e^{\frac {20-x}{2}} x^2+128 e^{\frac {20-x}{4}} x^3-64 x^4+e^x \left (4 e^{\frac {20-x}{2}}-8 e^{\frac {20-x}{4}} x+4 x^2\right )+\left (128 e^{\frac {20-x}{4}} x^2-128 x^3+e^x \left (-8 e^{\frac {20-x}{4}}+8 x\right )\right ) \log \left (e^{2 x}-32 e^x x^2+256 x^4\right )+\left (4 e^x-64 x^2\right ) \log ^2\left (e^{2 x}-32 e^x x^2+256 x^4\right )} \, dx=-\int \frac {{\ln \left ({\mathrm {e}}^{2\,x}-32\,x^2\,{\mathrm {e}}^x+256\,x^4\right )}^2\,\left (128\,x^2-{\mathrm {e}}^x\,\left (8\,x+8\right )+128\,x^3\right )-\ln \left ({\mathrm {e}}^{2\,x}-32\,x^2\,{\mathrm {e}}^x+256\,x^4\right )\,\left ({\mathrm {e}}^{5-\frac {x}{4}}\,\left (256\,x^3+256\,x^2\right )+64\,x^2-256\,x^3-256\,x^4+{\mathrm {e}}^x\,\left (16\,x-{\mathrm {e}}^{5-\frac {x}{4}}\,\left (16\,x+16\right )+16\,x^2-4\right )\right )-{\mathrm {e}}^x\,\left (8\,x+{\mathrm {e}}^{10-\frac {x}{2}}\,\left (8\,x+8\right )-{\mathrm {e}}^{5-\frac {x}{4}}\,\left (16\,x^2+15\,x-4\right )+8\,x^2+8\,x^3\right )+{\mathrm {e}}^{10-\frac {x}{2}}\,\left (128\,x^3+128\,x^2\right )+256\,x^2+128\,x^4+128\,x^5-{\mathrm {e}}^{5-\frac {x}{4}}\,\left (256\,x^4+240\,x^3-64\,x^2\right )}{{\mathrm {e}}^x\,\left (4\,{\mathrm {e}}^{10-\frac {x}{2}}-8\,x\,{\mathrm {e}}^{5-\frac {x}{4}}+4\,x^2\right )+\ln \left ({\mathrm {e}}^{2\,x}-32\,x^2\,{\mathrm {e}}^x+256\,x^4\right )\,\left ({\mathrm {e}}^x\,\left (8\,x-8\,{\mathrm {e}}^{5-\frac {x}{4}}\right )+128\,x^2\,{\mathrm {e}}^{5-\frac {x}{4}}-128\,x^3\right )+128\,x^3\,{\mathrm {e}}^{5-\frac {x}{4}}-64\,x^2\,{\mathrm {e}}^{10-\frac {x}{2}}-64\,x^4+{\ln \left ({\mathrm {e}}^{2\,x}-32\,x^2\,{\mathrm {e}}^x+256\,x^4\right )}^2\,\left (4\,{\mathrm {e}}^x-64\,x^2\right )} \,d x \]
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