Integrand size = 637, antiderivative size = 38 \[ \int \frac {4+16 x-20 x^2-8 x^3+21 x^4+2 x^5-8 x^6+x^8+e^{16} \left (16-8 x^2+x^4\right )+e^{12} \left (-64 x+32 x^3-4 x^5\right )+e^8 \left (16+32 x+84 x^2-16 x^3-46 x^4+2 x^5+6 x^6\right )+e^4 \left (-32 x^2-56 x^3+16 x^4+30 x^5-2 x^6-4 x^7\right )+\left (32 x^2+56 x^3-16 x^4-30 x^5+2 x^6+4 x^7+e^{12} \left (-64+32 x^2-4 x^4\right )+e^8 \left (192 x-96 x^3+12 x^5\right )+e^4 \left (-32-64 x-168 x^2+32 x^3+92 x^4-4 x^5-12 x^6\right )\right ) \log (x)+\left (16+32 x+84 x^2-16 x^3-46 x^4+2 x^5+6 x^6+e^8 \left (96-48 x^2+6 x^4\right )+e^4 \left (-192 x+96 x^3-12 x^5\right )\right ) \log ^2(x)+\left (64 x-32 x^3+4 x^5+e^4 \left (-64+32 x^2-4 x^4\right )\right ) \log ^3(x)+\left (16-8 x^2+x^4\right ) \log ^4(x)}{4+12 x^2+5 x^4-6 x^6+x^8+e^{16} \left (16-8 x^2+x^4\right )+e^{12} \left (-64 x+32 x^3-4 x^5\right )+e^8 \left (16+84 x^2-46 x^4+6 x^6\right )+e^4 \left (-32 x-40 x^3+28 x^5-4 x^7\right )+\left (32 x+40 x^3-28 x^5+4 x^7+e^{12} \left (-64+32 x^2-4 x^4\right )+e^8 \left (192 x-96 x^3+12 x^5\right )+e^4 \left (-32-168 x^2+92 x^4-12 x^6\right )\right ) \log (x)+\left (16+84 x^2-46 x^4+6 x^6+e^8 \left (96-48 x^2+6 x^4\right )+e^4 \left (-192 x+96 x^3-12 x^5\right )\right ) \log ^2(x)+\left (64 x-32 x^3+4 x^5+e^4 \left (-64+32 x^2-4 x^4\right )\right ) \log ^3(x)+\left (16-8 x^2+x^4\right ) \log ^4(x)} \, dx=x+\frac {x^2}{\frac {x \left (-\frac {2}{x}+x\right )}{-4+x^2}+\left (e^4-x-\log (x)\right )^2} \]
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\[ \int \frac {4+16 x-20 x^2-8 x^3+21 x^4+2 x^5-8 x^6+x^8+e^{16} \left (16-8 x^2+x^4\right )+e^{12} \left (-64 x+32 x^3-4 x^5\right )+e^8 \left (16+32 x+84 x^2-16 x^3-46 x^4+2 x^5+6 x^6\right )+e^4 \left (-32 x^2-56 x^3+16 x^4+30 x^5-2 x^6-4 x^7\right )+\left (32 x^2+56 x^3-16 x^4-30 x^5+2 x^6+4 x^7+e^{12} \left (-64+32 x^2-4 x^4\right )+e^8 \left (192 x-96 x^3+12 x^5\right )+e^4 \left (-32-64 x-168 x^2+32 x^3+92 x^4-4 x^5-12 x^6\right )\right ) \log (x)+\left (16+32 x+84 x^2-16 x^3-46 x^4+2 x^5+6 x^6+e^8 \left (96-48 x^2+6 x^4\right )+e^4 \left (-192 x+96 x^3-12 x^5\right )\right ) \log ^2(x)+\left (64 x-32 x^3+4 x^5+e^4 \left (-64+32 x^2-4 x^4\right )\right ) \log ^3(x)+\left (16-8 x^2+x^4\right ) \log ^4(x)}{4+12 x^2+5 x^4-6 x^6+x^8+e^{16} \left (16-8 x^2+x^4\right )+e^{12} \left (-64 x+32 x^3-4 x^5\right )+e^8 \left (16+84 x^2-46 x^4+6 x^6\right )+e^4 \left (-32 x-40 x^3+28 x^5-4 x^7\right )+\left (32 x+40 x^3-28 x^5+4 x^7+e^{12} \left (-64+32 x^2-4 x^4\right )+e^8 \left (192 x-96 x^3+12 x^5\right )+e^4 \left (-32-168 x^2+92 x^4-12 x^6\right )\right ) \log (x)+\left (16+84 x^2-46 x^4+6 x^6+e^8 \left (96-48 x^2+6 x^4\right )+e^4 \left (-192 x+96 x^3-12 x^5\right )\right ) \log ^2(x)+\left (64 x-32 x^3+4 x^5+e^4 \left (-64+32 x^2-4 x^4\right )\right ) \log ^3(x)+\left (16-8 x^2+x^4\right ) \log ^4(x)} \, dx=\int \frac {4+16 x-20 x^2-8 x^3+21 x^4+2 x^5-8 x^6+x^8+e^{16} \left (16-8 x^2+x^4\right )+e^{12} \left (-64 x+32 x^3-4 x^5\right )+e^8 \left (16+32 x+84 x^2-16 x^3-46 x^4+2 x^5+6 x^6\right )+e^4 \left (-32 x^2-56 x^3+16 x^4+30 x^5-2 x^6-4 x^7\right )+\left (32 x^2+56 x^3-16 x^4-30 x^5+2 x^6+4 x^7+e^{12} \left (-64+32 x^2-4 x^4\right )+e^8 \left (192 x-96 x^3+12 x^5\right )+e^4 \left (-32-64 x-168 x^2+32 x^3+92 x^4-4 x^5-12 x^6\right )\right ) \log (x)+\left (16+32 x+84 x^2-16 x^3-46 x^4+2 x^5+6 x^6+e^8 \left (96-48 x^2+6 x^4\right )+e^4 \left (-192 x+96 x^3-12 x^5\right )\right ) \log ^2(x)+\left (64 x-32 x^3+4 x^5+e^4 \left (-64+32 x^2-4 x^4\right )\right ) \log ^3(x)+\left (16-8 x^2+x^4\right ) \log ^4(x)}{4+12 x^2+5 x^4-6 x^6+x^8+e^{16} \left (16-8 x^2+x^4\right )+e^{12} \left (-64 x+32 x^3-4 x^5\right )+e^8 \left (16+84 x^2-46 x^4+6 x^6\right )+e^4 \left (-32 x-40 x^3+28 x^5-4 x^7\right )+\left (32 x+40 x^3-28 x^5+4 x^7+e^{12} \left (-64+32 x^2-4 x^4\right )+e^8 \left (192 x-96 x^3+12 x^5\right )+e^4 \left (-32-168 x^2+92 x^4-12 x^6\right )\right ) \log (x)+\left (16+84 x^2-46 x^4+6 x^6+e^8 \left (96-48 x^2+6 x^4\right )+e^4 \left (-192 x+96 x^3-12 x^5\right )\right ) \log ^2(x)+\left (64 x-32 x^3+4 x^5+e^4 \left (-64+32 x^2-4 x^4\right )\right ) \log ^3(x)+\left (16-8 x^2+x^4\right ) \log ^4(x)} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {4+16 x-20 x^2-8 x^3+21 x^4+2 x^5-8 x^6+x^8+e^{16} \left (-4+x^2\right )^2-4 e^{12} x \left (-4+x^2\right )^2-2 e^4 x^2 \left (16+28 x-8 x^2-15 x^3+x^4+2 x^5\right )+2 e^8 \left (8+16 x+42 x^2-8 x^3-23 x^4+x^5+3 x^6\right )+2 \left (-4+x^2\right ) \left (-2 e^{12} \left (-4+x^2\right )+6 e^8 x \left (-4+x^2\right )+x^2 \left (-4-7 x+x^2+2 x^3\right )+e^4 \left (4+8 x+22 x^2-2 x^3-6 x^4\right )\right ) \log (x)+2 \left (-4+x^2\right ) \left (-2-4 x-11 x^2+x^3+3 x^4+3 e^8 \left (-4+x^2\right )-6 e^4 x \left (-4+x^2\right )\right ) \log ^2(x)-4 \left (e^4-x\right ) \left (-4+x^2\right )^2 \log ^3(x)+\left (-4+x^2\right )^2 \log ^4(x)}{\left (2+3 x^2-x^4-e^8 \left (-4+x^2\right )+2 e^4 x \left (-4+x^2\right )+2 \left (e^4-x\right ) \left (-4+x^2\right ) \log (x)-\left (-4+x^2\right ) \log ^2(x)\right )^2} \, dx \\ & = \int \left (1+\frac {2 x \left (16 e^4-16 \left (1-e^4\right ) x-14 \left (1+\frac {4 e^4}{7}\right ) x^2+8 \left (1-e^4\right ) x^3+8 \left (1+\frac {e^4}{8}\right ) x^4-\left (1-e^4\right ) x^5-x^6-16 \log (x)-16 x \log (x)+8 x^2 \log (x)+8 x^3 \log (x)-x^4 \log (x)-x^5 \log (x)\right )}{\left (2 \left (1+2 e^8\right )-8 e^4 x+3 \left (1-\frac {e^8}{3}\right ) x^2+2 e^4 x^3-x^4-8 e^4 \log (x)+8 x \log (x)+2 e^4 x^2 \log (x)-2 x^3 \log (x)+4 \log ^2(x)-x^2 \log ^2(x)\right )^2}+\frac {2 x \left (4-x^2\right )}{2 \left (1+2 e^8\right )-8 e^4 x+3 \left (1-\frac {e^8}{3}\right ) x^2+2 e^4 x^3-x^4-8 e^4 \log (x)+8 x \log (x)+2 e^4 x^2 \log (x)-2 x^3 \log (x)+4 \log ^2(x)-x^2 \log ^2(x)}\right ) \, dx \\ & = x+2 \int \frac {x \left (16 e^4-16 \left (1-e^4\right ) x-14 \left (1+\frac {4 e^4}{7}\right ) x^2+8 \left (1-e^4\right ) x^3+8 \left (1+\frac {e^4}{8}\right ) x^4-\left (1-e^4\right ) x^5-x^6-16 \log (x)-16 x \log (x)+8 x^2 \log (x)+8 x^3 \log (x)-x^4 \log (x)-x^5 \log (x)\right )}{\left (2 \left (1+2 e^8\right )-8 e^4 x+3 \left (1-\frac {e^8}{3}\right ) x^2+2 e^4 x^3-x^4-8 e^4 \log (x)+8 x \log (x)+2 e^4 x^2 \log (x)-2 x^3 \log (x)+4 \log ^2(x)-x^2 \log ^2(x)\right )^2} \, dx+2 \int \frac {x \left (4-x^2\right )}{2 \left (1+2 e^8\right )-8 e^4 x+3 \left (1-\frac {e^8}{3}\right ) x^2+2 e^4 x^3-x^4-8 e^4 \log (x)+8 x \log (x)+2 e^4 x^2 \log (x)-2 x^3 \log (x)+4 \log ^2(x)-x^2 \log ^2(x)} \, dx \\ & = x+2 \int \frac {x \left (e^4 (1+x) \left (-4+x^2\right )^2-x \left (16+14 x-8 x^2-8 x^3+x^4+x^5\right )-(1+x) \left (-4+x^2\right )^2 \log (x)\right )}{\left (2+3 x^2-x^4-e^8 \left (-4+x^2\right )+2 e^4 x \left (-4+x^2\right )+2 \left (e^4-x\right ) \left (-4+x^2\right ) \log (x)-\left (-4+x^2\right ) \log ^2(x)\right )^2} \, dx+2 \int \frac {x \left (4-x^2\right )}{2+3 x^2-x^4-e^8 \left (-4+x^2\right )+2 e^4 x \left (-4+x^2\right )+2 \left (e^4-x\right ) \left (-4+x^2\right ) \log (x)-\left (-4+x^2\right ) \log ^2(x)} \, dx \\ & = \text {Too large to display} \\ \end{align*}
Time = 0.25 (sec) , antiderivative size = 69, normalized size of antiderivative = 1.82 \[ \int \frac {4+16 x-20 x^2-8 x^3+21 x^4+2 x^5-8 x^6+x^8+e^{16} \left (16-8 x^2+x^4\right )+e^{12} \left (-64 x+32 x^3-4 x^5\right )+e^8 \left (16+32 x+84 x^2-16 x^3-46 x^4+2 x^5+6 x^6\right )+e^4 \left (-32 x^2-56 x^3+16 x^4+30 x^5-2 x^6-4 x^7\right )+\left (32 x^2+56 x^3-16 x^4-30 x^5+2 x^6+4 x^7+e^{12} \left (-64+32 x^2-4 x^4\right )+e^8 \left (192 x-96 x^3+12 x^5\right )+e^4 \left (-32-64 x-168 x^2+32 x^3+92 x^4-4 x^5-12 x^6\right )\right ) \log (x)+\left (16+32 x+84 x^2-16 x^3-46 x^4+2 x^5+6 x^6+e^8 \left (96-48 x^2+6 x^4\right )+e^4 \left (-192 x+96 x^3-12 x^5\right )\right ) \log ^2(x)+\left (64 x-32 x^3+4 x^5+e^4 \left (-64+32 x^2-4 x^4\right )\right ) \log ^3(x)+\left (16-8 x^2+x^4\right ) \log ^4(x)}{4+12 x^2+5 x^4-6 x^6+x^8+e^{16} \left (16-8 x^2+x^4\right )+e^{12} \left (-64 x+32 x^3-4 x^5\right )+e^8 \left (16+84 x^2-46 x^4+6 x^6\right )+e^4 \left (-32 x-40 x^3+28 x^5-4 x^7\right )+\left (32 x+40 x^3-28 x^5+4 x^7+e^{12} \left (-64+32 x^2-4 x^4\right )+e^8 \left (192 x-96 x^3+12 x^5\right )+e^4 \left (-32-168 x^2+92 x^4-12 x^6\right )\right ) \log (x)+\left (16+84 x^2-46 x^4+6 x^6+e^8 \left (96-48 x^2+6 x^4\right )+e^4 \left (-192 x+96 x^3-12 x^5\right )\right ) \log ^2(x)+\left (64 x-32 x^3+4 x^5+e^4 \left (-64+32 x^2-4 x^4\right )\right ) \log ^3(x)+\left (16-8 x^2+x^4\right ) \log ^4(x)} \, dx=x+\frac {x^2 \left (-4+x^2\right )}{-2-3 x^2+x^4+e^8 \left (-4+x^2\right )-2 e^4 x \left (-4+x^2\right )-2 \left (e^4-x\right ) \left (-4+x^2\right ) \log (x)+\left (-4+x^2\right ) \log ^2(x)} \]
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Leaf count of result is larger than twice the leaf count of optimal. \(86\) vs. \(2(37)=74\).
Time = 0.81 (sec) , antiderivative size = 87, normalized size of antiderivative = 2.29
method | result | size |
risch | \(x +\frac {x^{2} \left (x^{2}-4\right )}{x^{2} \ln \left (x \right )^{2}-2 x^{2} {\mathrm e}^{4} \ln \left (x \right )+2 x^{3} \ln \left (x \right )+x^{2} {\mathrm e}^{8}-2 x^{3} {\mathrm e}^{4}+x^{4}-4 \ln \left (x \right )^{2}+8 \,{\mathrm e}^{4} \ln \left (x \right )-8 x \ln \left (x \right )-4 \,{\mathrm e}^{8}+8 x \,{\mathrm e}^{4}-3 x^{2}-2}\) | \(87\) |
default | \(x -\frac {{\mathrm e}^{2 \ln \left (x \right )+8}-2 \ln \left (x \right ) {\mathrm e}^{2 \ln \left (x \right )+4}-2 \,{\mathrm e}^{3 \ln \left (x \right )+4}+x^{2} \ln \left (x \right )^{2}+2 x^{3} \ln \left (x \right )-4 \,{\mathrm e}^{8}+8 \,{\mathrm e}^{4} \ln \left (x \right )+8 \,{\mathrm e}^{\ln \left (x \right )+4}-4 \ln \left (x \right )^{2}-8 x \ln \left (x \right )+x^{2}-2}{{\mathrm e}^{2 \ln \left (x \right )+8}-2 \,{\mathrm e}^{3 \ln \left (x \right )+4}-2 \ln \left (x \right ) {\mathrm e}^{2 \ln \left (x \right )+4}+x^{4}+2 x^{3} \ln \left (x \right )+x^{2} \ln \left (x \right )^{2}-4 \,{\mathrm e}^{8}+8 \,{\mathrm e}^{\ln \left (x \right )+4}+8 \,{\mathrm e}^{4} \ln \left (x \right )-3 x^{2}-8 x \ln \left (x \right )-4 \ln \left (x \right )^{2}-2}\) | \(162\) |
parallelrisch | \(-\frac {2 x +4 x \,{\mathrm e}^{8}-{\mathrm e}^{8} x^{3}-8 x^{2} {\mathrm e}^{4}-2 x^{4} \ln \left (x \right )+4 x \ln \left (x \right )^{2}-8 x \,{\mathrm e}^{4} \ln \left (x \right )+2 x^{4} {\mathrm e}^{4}-x^{3} \ln \left (x \right )^{2}-x^{4}+3 x^{3}+4 x^{2}-x^{5}+8 x^{2} \ln \left (x \right )+2 \ln \left (x \right ) {\mathrm e}^{4} x^{3}}{x^{2} \ln \left (x \right )^{2}-2 x^{2} {\mathrm e}^{4} \ln \left (x \right )+2 x^{3} \ln \left (x \right )+x^{2} {\mathrm e}^{8}-2 x^{3} {\mathrm e}^{4}+x^{4}-4 \ln \left (x \right )^{2}+8 \,{\mathrm e}^{4} \ln \left (x \right )-8 x \ln \left (x \right )-4 \,{\mathrm e}^{8}+8 x \,{\mathrm e}^{4}-3 x^{2}-2}\) | \(182\) |
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Leaf count of result is larger than twice the leaf count of optimal. 141 vs. \(2 (35) = 70\).
Time = 0.28 (sec) , antiderivative size = 141, normalized size of antiderivative = 3.71 \[ \int \frac {4+16 x-20 x^2-8 x^3+21 x^4+2 x^5-8 x^6+x^8+e^{16} \left (16-8 x^2+x^4\right )+e^{12} \left (-64 x+32 x^3-4 x^5\right )+e^8 \left (16+32 x+84 x^2-16 x^3-46 x^4+2 x^5+6 x^6\right )+e^4 \left (-32 x^2-56 x^3+16 x^4+30 x^5-2 x^6-4 x^7\right )+\left (32 x^2+56 x^3-16 x^4-30 x^5+2 x^6+4 x^7+e^{12} \left (-64+32 x^2-4 x^4\right )+e^8 \left (192 x-96 x^3+12 x^5\right )+e^4 \left (-32-64 x-168 x^2+32 x^3+92 x^4-4 x^5-12 x^6\right )\right ) \log (x)+\left (16+32 x+84 x^2-16 x^3-46 x^4+2 x^5+6 x^6+e^8 \left (96-48 x^2+6 x^4\right )+e^4 \left (-192 x+96 x^3-12 x^5\right )\right ) \log ^2(x)+\left (64 x-32 x^3+4 x^5+e^4 \left (-64+32 x^2-4 x^4\right )\right ) \log ^3(x)+\left (16-8 x^2+x^4\right ) \log ^4(x)}{4+12 x^2+5 x^4-6 x^6+x^8+e^{16} \left (16-8 x^2+x^4\right )+e^{12} \left (-64 x+32 x^3-4 x^5\right )+e^8 \left (16+84 x^2-46 x^4+6 x^6\right )+e^4 \left (-32 x-40 x^3+28 x^5-4 x^7\right )+\left (32 x+40 x^3-28 x^5+4 x^7+e^{12} \left (-64+32 x^2-4 x^4\right )+e^8 \left (192 x-96 x^3+12 x^5\right )+e^4 \left (-32-168 x^2+92 x^4-12 x^6\right )\right ) \log (x)+\left (16+84 x^2-46 x^4+6 x^6+e^8 \left (96-48 x^2+6 x^4\right )+e^4 \left (-192 x+96 x^3-12 x^5\right )\right ) \log ^2(x)+\left (64 x-32 x^3+4 x^5+e^4 \left (-64+32 x^2-4 x^4\right )\right ) \log ^3(x)+\left (16-8 x^2+x^4\right ) \log ^4(x)} \, dx=\frac {x^{5} + x^{4} - 3 \, x^{3} + {\left (x^{3} - 4 \, x\right )} \log \left (x\right )^{2} - 4 \, x^{2} + {\left (x^{3} - 4 \, x\right )} e^{8} - 2 \, {\left (x^{4} - 4 \, x^{2}\right )} e^{4} + 2 \, {\left (x^{4} - 4 \, x^{2} - {\left (x^{3} - 4 \, x\right )} e^{4}\right )} \log \left (x\right ) - 2 \, x}{x^{4} + {\left (x^{2} - 4\right )} \log \left (x\right )^{2} - 3 \, x^{2} + {\left (x^{2} - 4\right )} e^{8} - 2 \, {\left (x^{3} - 4 \, x\right )} e^{4} + 2 \, {\left (x^{3} - {\left (x^{2} - 4\right )} e^{4} - 4 \, x\right )} \log \left (x\right ) - 2} \]
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Leaf count of result is larger than twice the leaf count of optimal. 82 vs. \(2 (26) = 52\).
Time = 0.48 (sec) , antiderivative size = 82, normalized size of antiderivative = 2.16 \[ \int \frac {4+16 x-20 x^2-8 x^3+21 x^4+2 x^5-8 x^6+x^8+e^{16} \left (16-8 x^2+x^4\right )+e^{12} \left (-64 x+32 x^3-4 x^5\right )+e^8 \left (16+32 x+84 x^2-16 x^3-46 x^4+2 x^5+6 x^6\right )+e^4 \left (-32 x^2-56 x^3+16 x^4+30 x^5-2 x^6-4 x^7\right )+\left (32 x^2+56 x^3-16 x^4-30 x^5+2 x^6+4 x^7+e^{12} \left (-64+32 x^2-4 x^4\right )+e^8 \left (192 x-96 x^3+12 x^5\right )+e^4 \left (-32-64 x-168 x^2+32 x^3+92 x^4-4 x^5-12 x^6\right )\right ) \log (x)+\left (16+32 x+84 x^2-16 x^3-46 x^4+2 x^5+6 x^6+e^8 \left (96-48 x^2+6 x^4\right )+e^4 \left (-192 x+96 x^3-12 x^5\right )\right ) \log ^2(x)+\left (64 x-32 x^3+4 x^5+e^4 \left (-64+32 x^2-4 x^4\right )\right ) \log ^3(x)+\left (16-8 x^2+x^4\right ) \log ^4(x)}{4+12 x^2+5 x^4-6 x^6+x^8+e^{16} \left (16-8 x^2+x^4\right )+e^{12} \left (-64 x+32 x^3-4 x^5\right )+e^8 \left (16+84 x^2-46 x^4+6 x^6\right )+e^4 \left (-32 x-40 x^3+28 x^5-4 x^7\right )+\left (32 x+40 x^3-28 x^5+4 x^7+e^{12} \left (-64+32 x^2-4 x^4\right )+e^8 \left (192 x-96 x^3+12 x^5\right )+e^4 \left (-32-168 x^2+92 x^4-12 x^6\right )\right ) \log (x)+\left (16+84 x^2-46 x^4+6 x^6+e^8 \left (96-48 x^2+6 x^4\right )+e^4 \left (-192 x+96 x^3-12 x^5\right )\right ) \log ^2(x)+\left (64 x-32 x^3+4 x^5+e^4 \left (-64+32 x^2-4 x^4\right )\right ) \log ^3(x)+\left (16-8 x^2+x^4\right ) \log ^4(x)} \, dx=x + \frac {x^{4} - 4 x^{2}}{x^{4} - 2 x^{3} e^{4} - 3 x^{2} + x^{2} e^{8} + 8 x e^{4} + \left (x^{2} - 4\right ) \log {\left (x \right )}^{2} + \left (2 x^{3} - 2 x^{2} e^{4} - 8 x + 8 e^{4}\right ) \log {\left (x \right )} - 4 e^{8} - 2} \]
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Leaf count of result is larger than twice the leaf count of optimal. 144 vs. \(2 (35) = 70\).
Time = 0.40 (sec) , antiderivative size = 144, normalized size of antiderivative = 3.79 \[ \int \frac {4+16 x-20 x^2-8 x^3+21 x^4+2 x^5-8 x^6+x^8+e^{16} \left (16-8 x^2+x^4\right )+e^{12} \left (-64 x+32 x^3-4 x^5\right )+e^8 \left (16+32 x+84 x^2-16 x^3-46 x^4+2 x^5+6 x^6\right )+e^4 \left (-32 x^2-56 x^3+16 x^4+30 x^5-2 x^6-4 x^7\right )+\left (32 x^2+56 x^3-16 x^4-30 x^5+2 x^6+4 x^7+e^{12} \left (-64+32 x^2-4 x^4\right )+e^8 \left (192 x-96 x^3+12 x^5\right )+e^4 \left (-32-64 x-168 x^2+32 x^3+92 x^4-4 x^5-12 x^6\right )\right ) \log (x)+\left (16+32 x+84 x^2-16 x^3-46 x^4+2 x^5+6 x^6+e^8 \left (96-48 x^2+6 x^4\right )+e^4 \left (-192 x+96 x^3-12 x^5\right )\right ) \log ^2(x)+\left (64 x-32 x^3+4 x^5+e^4 \left (-64+32 x^2-4 x^4\right )\right ) \log ^3(x)+\left (16-8 x^2+x^4\right ) \log ^4(x)}{4+12 x^2+5 x^4-6 x^6+x^8+e^{16} \left (16-8 x^2+x^4\right )+e^{12} \left (-64 x+32 x^3-4 x^5\right )+e^8 \left (16+84 x^2-46 x^4+6 x^6\right )+e^4 \left (-32 x-40 x^3+28 x^5-4 x^7\right )+\left (32 x+40 x^3-28 x^5+4 x^7+e^{12} \left (-64+32 x^2-4 x^4\right )+e^8 \left (192 x-96 x^3+12 x^5\right )+e^4 \left (-32-168 x^2+92 x^4-12 x^6\right )\right ) \log (x)+\left (16+84 x^2-46 x^4+6 x^6+e^8 \left (96-48 x^2+6 x^4\right )+e^4 \left (-192 x+96 x^3-12 x^5\right )\right ) \log ^2(x)+\left (64 x-32 x^3+4 x^5+e^4 \left (-64+32 x^2-4 x^4\right )\right ) \log ^3(x)+\left (16-8 x^2+x^4\right ) \log ^4(x)} \, dx=\frac {x^{5} - x^{4} {\left (2 \, e^{4} - 1\right )} + x^{3} {\left (e^{8} - 3\right )} + 4 \, x^{2} {\left (2 \, e^{4} - 1\right )} + {\left (x^{3} - 4 \, x\right )} \log \left (x\right )^{2} - 2 \, x {\left (2 \, e^{8} + 1\right )} + 2 \, {\left (x^{4} - x^{3} e^{4} - 4 \, x^{2} + 4 \, x e^{4}\right )} \log \left (x\right )}{x^{4} - 2 \, x^{3} e^{4} + x^{2} {\left (e^{8} - 3\right )} + {\left (x^{2} - 4\right )} \log \left (x\right )^{2} + 8 \, x e^{4} + 2 \, {\left (x^{3} - x^{2} e^{4} - 4 \, x + 4 \, e^{4}\right )} \log \left (x\right ) - 4 \, e^{8} - 2} \]
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Leaf count of result is larger than twice the leaf count of optimal. 168 vs. \(2 (35) = 70\).
Time = 1.65 (sec) , antiderivative size = 168, normalized size of antiderivative = 4.42 \[ \int \frac {4+16 x-20 x^2-8 x^3+21 x^4+2 x^5-8 x^6+x^8+e^{16} \left (16-8 x^2+x^4\right )+e^{12} \left (-64 x+32 x^3-4 x^5\right )+e^8 \left (16+32 x+84 x^2-16 x^3-46 x^4+2 x^5+6 x^6\right )+e^4 \left (-32 x^2-56 x^3+16 x^4+30 x^5-2 x^6-4 x^7\right )+\left (32 x^2+56 x^3-16 x^4-30 x^5+2 x^6+4 x^7+e^{12} \left (-64+32 x^2-4 x^4\right )+e^8 \left (192 x-96 x^3+12 x^5\right )+e^4 \left (-32-64 x-168 x^2+32 x^3+92 x^4-4 x^5-12 x^6\right )\right ) \log (x)+\left (16+32 x+84 x^2-16 x^3-46 x^4+2 x^5+6 x^6+e^8 \left (96-48 x^2+6 x^4\right )+e^4 \left (-192 x+96 x^3-12 x^5\right )\right ) \log ^2(x)+\left (64 x-32 x^3+4 x^5+e^4 \left (-64+32 x^2-4 x^4\right )\right ) \log ^3(x)+\left (16-8 x^2+x^4\right ) \log ^4(x)}{4+12 x^2+5 x^4-6 x^6+x^8+e^{16} \left (16-8 x^2+x^4\right )+e^{12} \left (-64 x+32 x^3-4 x^5\right )+e^8 \left (16+84 x^2-46 x^4+6 x^6\right )+e^4 \left (-32 x-40 x^3+28 x^5-4 x^7\right )+\left (32 x+40 x^3-28 x^5+4 x^7+e^{12} \left (-64+32 x^2-4 x^4\right )+e^8 \left (192 x-96 x^3+12 x^5\right )+e^4 \left (-32-168 x^2+92 x^4-12 x^6\right )\right ) \log (x)+\left (16+84 x^2-46 x^4+6 x^6+e^8 \left (96-48 x^2+6 x^4\right )+e^4 \left (-192 x+96 x^3-12 x^5\right )\right ) \log ^2(x)+\left (64 x-32 x^3+4 x^5+e^4 \left (-64+32 x^2-4 x^4\right )\right ) \log ^3(x)+\left (16-8 x^2+x^4\right ) \log ^4(x)} \, dx=\frac {x^{5} - 2 \, x^{4} e^{4} + 2 \, x^{4} \log \left (x\right ) - 2 \, x^{3} e^{4} \log \left (x\right ) + x^{3} \log \left (x\right )^{2} + 2 \, x^{4} + x^{3} e^{8} - 3 \, x^{3} + 8 \, x^{2} e^{4} - 8 \, x^{2} \log \left (x\right ) + 8 \, x e^{4} \log \left (x\right ) - 4 \, x \log \left (x\right )^{2} - 8 \, x^{2} - 4 \, x e^{8} - 2 \, x}{x^{4} - 2 \, x^{3} e^{4} + 2 \, x^{3} \log \left (x\right ) - 2 \, x^{2} e^{4} \log \left (x\right ) + x^{2} \log \left (x\right )^{2} + x^{2} e^{8} - 3 \, x^{2} + 8 \, x e^{4} - 8 \, x \log \left (x\right ) + 8 \, e^{4} \log \left (x\right ) - 4 \, \log \left (x\right )^{2} - 4 \, e^{8} - 2} \]
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Timed out. \[ \int \frac {4+16 x-20 x^2-8 x^3+21 x^4+2 x^5-8 x^6+x^8+e^{16} \left (16-8 x^2+x^4\right )+e^{12} \left (-64 x+32 x^3-4 x^5\right )+e^8 \left (16+32 x+84 x^2-16 x^3-46 x^4+2 x^5+6 x^6\right )+e^4 \left (-32 x^2-56 x^3+16 x^4+30 x^5-2 x^6-4 x^7\right )+\left (32 x^2+56 x^3-16 x^4-30 x^5+2 x^6+4 x^7+e^{12} \left (-64+32 x^2-4 x^4\right )+e^8 \left (192 x-96 x^3+12 x^5\right )+e^4 \left (-32-64 x-168 x^2+32 x^3+92 x^4-4 x^5-12 x^6\right )\right ) \log (x)+\left (16+32 x+84 x^2-16 x^3-46 x^4+2 x^5+6 x^6+e^8 \left (96-48 x^2+6 x^4\right )+e^4 \left (-192 x+96 x^3-12 x^5\right )\right ) \log ^2(x)+\left (64 x-32 x^3+4 x^5+e^4 \left (-64+32 x^2-4 x^4\right )\right ) \log ^3(x)+\left (16-8 x^2+x^4\right ) \log ^4(x)}{4+12 x^2+5 x^4-6 x^6+x^8+e^{16} \left (16-8 x^2+x^4\right )+e^{12} \left (-64 x+32 x^3-4 x^5\right )+e^8 \left (16+84 x^2-46 x^4+6 x^6\right )+e^4 \left (-32 x-40 x^3+28 x^5-4 x^7\right )+\left (32 x+40 x^3-28 x^5+4 x^7+e^{12} \left (-64+32 x^2-4 x^4\right )+e^8 \left (192 x-96 x^3+12 x^5\right )+e^4 \left (-32-168 x^2+92 x^4-12 x^6\right )\right ) \log (x)+\left (16+84 x^2-46 x^4+6 x^6+e^8 \left (96-48 x^2+6 x^4\right )+e^4 \left (-192 x+96 x^3-12 x^5\right )\right ) \log ^2(x)+\left (64 x-32 x^3+4 x^5+e^4 \left (-64+32 x^2-4 x^4\right )\right ) \log ^3(x)+\left (16-8 x^2+x^4\right ) \log ^4(x)} \, dx=\int \frac {16\,x+{\mathrm {e}}^8\,\left (6\,x^6+2\,x^5-46\,x^4-16\,x^3+84\,x^2+32\,x+16\right )+{\ln \left (x\right )}^4\,\left (x^4-8\,x^2+16\right )+{\mathrm {e}}^{16}\,\left (x^4-8\,x^2+16\right )-{\mathrm {e}}^{12}\,\left (4\,x^5-32\,x^3+64\,x\right )-{\mathrm {e}}^4\,\left (4\,x^7+2\,x^6-30\,x^5-16\,x^4+56\,x^3+32\,x^2\right )-20\,x^2-8\,x^3+21\,x^4+2\,x^5-8\,x^6+x^8+{\ln \left (x\right )}^3\,\left (64\,x-{\mathrm {e}}^4\,\left (4\,x^4-32\,x^2+64\right )-32\,x^3+4\,x^5\right )+{\ln \left (x\right )}^2\,\left (32\,x-{\mathrm {e}}^4\,\left (12\,x^5-96\,x^3+192\,x\right )+{\mathrm {e}}^8\,\left (6\,x^4-48\,x^2+96\right )+84\,x^2-16\,x^3-46\,x^4+2\,x^5+6\,x^6+16\right )+\ln \left (x\right )\,\left ({\mathrm {e}}^8\,\left (12\,x^5-96\,x^3+192\,x\right )-{\mathrm {e}}^4\,\left (12\,x^6+4\,x^5-92\,x^4-32\,x^3+168\,x^2+64\,x+32\right )-{\mathrm {e}}^{12}\,\left (4\,x^4-32\,x^2+64\right )+32\,x^2+56\,x^3-16\,x^4-30\,x^5+2\,x^6+4\,x^7\right )+4}{{\ln \left (x\right )}^4\,\left (x^4-8\,x^2+16\right )+{\mathrm {e}}^{16}\,\left (x^4-8\,x^2+16\right )-{\mathrm {e}}^{12}\,\left (4\,x^5-32\,x^3+64\,x\right )-{\mathrm {e}}^4\,\left (4\,x^7-28\,x^5+40\,x^3+32\,x\right )+{\ln \left (x\right )}^2\,\left ({\mathrm {e}}^8\,\left (6\,x^4-48\,x^2+96\right )-{\mathrm {e}}^4\,\left (12\,x^5-96\,x^3+192\,x\right )+84\,x^2-46\,x^4+6\,x^6+16\right )+{\mathrm {e}}^8\,\left (6\,x^6-46\,x^4+84\,x^2+16\right )+12\,x^2+5\,x^4-6\,x^6+x^8+{\ln \left (x\right )}^3\,\left (64\,x-{\mathrm {e}}^4\,\left (4\,x^4-32\,x^2+64\right )-32\,x^3+4\,x^5\right )+\ln \left (x\right )\,\left (32\,x+{\mathrm {e}}^8\,\left (12\,x^5-96\,x^3+192\,x\right )-{\mathrm {e}}^{12}\,\left (4\,x^4-32\,x^2+64\right )-{\mathrm {e}}^4\,\left (12\,x^6-92\,x^4+168\,x^2+32\right )+40\,x^3-28\,x^5+4\,x^7\right )+4} \,d x \]
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