Integrand size = 267, antiderivative size = 33 \[ \int \frac {128 x^2+32 x^3-2 x^5+e^4 \left (-64 x^2-32 x^3+4 x^4-2 x^5\right )+e^{14} \left (32+8 x+e^4 \left (-16-8 x+x^2\right )\right )+e^7 \left (128 x+32 x^2-2 x^4+e^4 \left (-64 x-32 x^2+4 x^3-x^4\right )\right )+\left (-64 x^2-32 x^3+4 x^4-2 x^5+e^{14} \left (-16-8 x+x^2\right )+e^7 \left (-64 x-32 x^2+4 x^3-x^4\right )\right ) \log \left (\frac {-32 x-16 x^2+2 x^3-x^4+e^7 \left (-16-8 x+x^2\right )}{e^7 x^2+2 x^3}\right )}{-64 x^2-32 x^3+4 x^4-2 x^5+e^{14} \left (-16-8 x+x^2\right )+e^7 \left (-64 x-32 x^2+4 x^3-x^4\right )} \, dx=x \left (e^4+\log \left (2-\frac {x}{2+\frac {e^7}{x}}-\frac {(4+x)^2}{x^2}\right )\right ) \]
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\[ \int \frac {128 x^2+32 x^3-2 x^5+e^4 \left (-64 x^2-32 x^3+4 x^4-2 x^5\right )+e^{14} \left (32+8 x+e^4 \left (-16-8 x+x^2\right )\right )+e^7 \left (128 x+32 x^2-2 x^4+e^4 \left (-64 x-32 x^2+4 x^3-x^4\right )\right )+\left (-64 x^2-32 x^3+4 x^4-2 x^5+e^{14} \left (-16-8 x+x^2\right )+e^7 \left (-64 x-32 x^2+4 x^3-x^4\right )\right ) \log \left (\frac {-32 x-16 x^2+2 x^3-x^4+e^7 \left (-16-8 x+x^2\right )}{e^7 x^2+2 x^3}\right )}{-64 x^2-32 x^3+4 x^4-2 x^5+e^{14} \left (-16-8 x+x^2\right )+e^7 \left (-64 x-32 x^2+4 x^3-x^4\right )} \, dx=\int \frac {128 x^2+32 x^3-2 x^5+e^4 \left (-64 x^2-32 x^3+4 x^4-2 x^5\right )+e^{14} \left (32+8 x+e^4 \left (-16-8 x+x^2\right )\right )+e^7 \left (128 x+32 x^2-2 x^4+e^4 \left (-64 x-32 x^2+4 x^3-x^4\right )\right )+\left (-64 x^2-32 x^3+4 x^4-2 x^5+e^{14} \left (-16-8 x+x^2\right )+e^7 \left (-64 x-32 x^2+4 x^3-x^4\right )\right ) \log \left (\frac {-32 x-16 x^2+2 x^3-x^4+e^7 \left (-16-8 x+x^2\right )}{e^7 x^2+2 x^3}\right )}{-64 x^2-32 x^3+4 x^4-2 x^5+e^{14} \left (-16-8 x+x^2\right )+e^7 \left (-64 x-32 x^2+4 x^3-x^4\right )} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {128 x^2}{\left (-e^7-2 x\right ) \left (16 e^7+8 \left (4+e^7\right ) x+\left (16-e^7\right ) x^2-2 x^3+x^4\right )}+\frac {32 x^3}{\left (-e^7-2 x\right ) \left (16 e^7+8 \left (4+e^7\right ) x+\left (16-e^7\right ) x^2-2 x^3+x^4\right )}+\frac {2 x^5}{\left (e^7+2 x\right ) \left (16 e^7+8 \left (4+e^7\right ) x+\left (16-e^7\right ) x^2-2 x^3+x^4\right )}+\frac {e^{14} \left (-16 \left (2-e^4\right )-8 \left (1-e^4\right ) x-e^4 x^2\right )}{\left (e^7+2 x\right ) \left (16 e^7+8 \left (4+e^7\right ) x+\left (16-e^7\right ) x^2-2 x^3+x^4\right )}+\frac {2 e^4 x^2 \left (32+16 x-2 x^2+x^3\right )}{\left (e^7+2 x\right ) \left (16 e^7+8 \left (4+e^7\right ) x+\left (16-e^7\right ) x^2-2 x^3+x^4\right )}+\frac {e^7 x \left (-64 \left (2-e^4\right )-32 \left (1-e^4\right ) x-4 e^4 x^2+\left (2+e^4\right ) x^3\right )}{\left (e^7+2 x\right ) \left (16 e^7+8 \left (4+e^7\right ) x+\left (16-e^7\right ) x^2-2 x^3+x^4\right )}+\log \left (\frac {-16 e^7-8 \left (4+e^7\right ) x-\left (16-e^7\right ) x^2+2 x^3-x^4}{x^2 \left (e^7+2 x\right )}\right )\right ) \, dx \\ & = 2 \int \frac {x^5}{\left (e^7+2 x\right ) \left (16 e^7+8 \left (4+e^7\right ) x+\left (16-e^7\right ) x^2-2 x^3+x^4\right )} \, dx+32 \int \frac {x^3}{\left (-e^7-2 x\right ) \left (16 e^7+8 \left (4+e^7\right ) x+\left (16-e^7\right ) x^2-2 x^3+x^4\right )} \, dx+128 \int \frac {x^2}{\left (-e^7-2 x\right ) \left (16 e^7+8 \left (4+e^7\right ) x+\left (16-e^7\right ) x^2-2 x^3+x^4\right )} \, dx+\left (2 e^4\right ) \int \frac {x^2 \left (32+16 x-2 x^2+x^3\right )}{\left (e^7+2 x\right ) \left (16 e^7+8 \left (4+e^7\right ) x+\left (16-e^7\right ) x^2-2 x^3+x^4\right )} \, dx+e^7 \int \frac {x \left (-64 \left (2-e^4\right )-32 \left (1-e^4\right ) x-4 e^4 x^2+\left (2+e^4\right ) x^3\right )}{\left (e^7+2 x\right ) \left (16 e^7+8 \left (4+e^7\right ) x+\left (16-e^7\right ) x^2-2 x^3+x^4\right )} \, dx+e^{14} \int \frac {-16 \left (2-e^4\right )-8 \left (1-e^4\right ) x-e^4 x^2}{\left (e^7+2 x\right ) \left (16 e^7+8 \left (4+e^7\right ) x+\left (16-e^7\right ) x^2-2 x^3+x^4\right )} \, dx+\int \log \left (\frac {-16 e^7-8 \left (4+e^7\right ) x-\left (16-e^7\right ) x^2+2 x^3-x^4}{x^2 \left (e^7+2 x\right )}\right ) \, dx \\ & = x \log \left (-\frac {16 e^7+8 \left (4+e^7\right ) x+\left (16-e^7\right ) x^2-2 x^3+x^4}{x^2 \left (e^7+2 x\right )}\right )+2 \int \left (\frac {1}{2}-\frac {e^7}{2 \left (e^7+2 x\right )}+\frac {x \left (-16-8 x+x^2\right )}{16 e^7+8 \left (4+e^7\right ) x+\left (16-e^7\right ) x^2-2 x^3+x^4}\right ) \, dx+32 \int \left (\frac {2}{e^7 \left (e^7+2 x\right )}+\frac {-32-16 x+2 x^2-x^3}{e^7 \left (16 e^7+8 \left (4+e^7\right ) x+\left (16-e^7\right ) x^2-2 x^3+x^4\right )}\right ) \, dx+128 \int \left (-\frac {4}{e^{14} \left (e^7+2 x\right )}+\frac {64+32 x-\left (4+e^7\right ) x^2+2 x^3}{e^{14} \left (16 e^7+8 \left (4+e^7\right ) x+\left (16-e^7\right ) x^2-2 x^3+x^4\right )}\right ) \, dx+\left (2 e^4\right ) \int \left (\frac {1}{2}+\frac {256-64 e^7-4 e^{14}-e^{21}}{2 e^{14} \left (e^7+2 x\right )}+\frac {-32 \left (64-16 e^7-e^{14}\right )-256 \left (4-e^7\right ) x+2 \left (64-5 e^{14}\right ) x^2-\left (64-16 e^7-e^{14}\right ) x^3}{e^{14} \left (16 e^7+8 \left (4+e^7\right ) x+\left (16-e^7\right ) x^2-2 x^3+x^4\right )}\right ) \, dx+e^7 \int \left (\frac {1024-512 e^4-128 e^7+128 e^{11}+8 e^{18}+2 e^{21}+e^{25}}{e^{21} \left (e^7+2 x\right )}+\frac {-16 \left (1024-512 e^4-128 e^7+128 e^{11}+8 e^{18}+2 e^{21}+e^{25}\right )-8 \left (1024-512 e^4-128 e^7+128 e^{11}+16 e^{14}+2 e^{21}+e^{25}\right ) x+\left (1024-512 e^4+128 e^7-32 e^{14}+40 e^{18}+2 e^{21}+e^{25}\right ) x^2-4 \left (128-64 e^4-16 e^7+16 e^{11}+e^{18}\right ) x^3}{e^{21} \left (16 e^7+8 \left (4+e^7\right ) x+\left (16-e^7\right ) x^2-2 x^3+x^4\right )}\right ) \, dx+e^{14} \int \left (-\frac {4 \left (128-64 e^4-16 e^7+16 e^{11}+e^{18}\right )}{e^{28} \left (e^7+2 x\right )}+\frac {16 \left (512-256 e^4-64 e^7+64 e^{11}+4 e^{18}-2 e^{21}+e^{25}\right )+8 \left (512-256 e^4-64 e^7+64 e^{11}+8 e^{14}-e^{21}+e^{25}\right ) x-\left (512-256 e^4+64 e^7-16 e^{14}+20 e^{18}+e^{25}\right ) x^2+2 \left (128-64 e^4-16 e^7+16 e^{11}+e^{18}\right ) x^3}{e^{28} \left (16 e^7+8 \left (4+e^7\right ) x+\left (16-e^7\right ) x^2-2 x^3+x^4\right )}\right ) \, dx-\int \frac {2 \left (-4 e^{14} (4+x)-e^7 x \left (64+16 x-x^3\right )-x^2 \left (64+16 x-x^3\right )\right )}{\left (e^7+2 x\right ) \left (16 e^7+8 \left (4+e^7\right ) x+\left (16-e^7\right ) x^2-2 x^3+x^4\right )} \, dx \\ & = x+e^4 x-\frac {256 \log \left (e^7+2 x\right )}{e^{14}}+\frac {32 \log \left (e^7+2 x\right )}{e^7}-\frac {1}{2} e^7 \log \left (e^7+2 x\right )-\frac {2 \left (128-64 e^4-16 e^7+16 e^{11}+e^{18}\right ) \log \left (e^7+2 x\right )}{e^{14}}+\frac {\left (256-64 e^7-4 e^{14}-e^{21}\right ) \log \left (e^7+2 x\right )}{2 e^{10}}+\frac {\left (1024-512 e^4-128 e^7+128 e^{11}+8 e^{18}+2 e^{21}+e^{25}\right ) \log \left (e^7+2 x\right )}{2 e^{14}}+x \log \left (-\frac {16 e^7+8 \left (4+e^7\right ) x+\left (16-e^7\right ) x^2-2 x^3+x^4}{x^2 \left (e^7+2 x\right )}\right )+2 \int \frac {x \left (-16-8 x+x^2\right )}{16 e^7+8 \left (4+e^7\right ) x+\left (16-e^7\right ) x^2-2 x^3+x^4} \, dx-2 \int \frac {-4 e^{14} (4+x)-e^7 x \left (64+16 x-x^3\right )-x^2 \left (64+16 x-x^3\right )}{\left (e^7+2 x\right ) \left (16 e^7+8 \left (4+e^7\right ) x+\left (16-e^7\right ) x^2-2 x^3+x^4\right )} \, dx+\frac {\int \frac {-16 \left (1024-512 e^4-128 e^7+128 e^{11}+8 e^{18}+2 e^{21}+e^{25}\right )-8 \left (1024-512 e^4-128 e^7+128 e^{11}+16 e^{14}+2 e^{21}+e^{25}\right ) x+\left (1024-512 e^4+128 e^7-32 e^{14}+40 e^{18}+2 e^{21}+e^{25}\right ) x^2-4 \left (128-64 e^4-16 e^7+16 e^{11}+e^{18}\right ) x^3}{16 e^7+8 \left (4+e^7\right ) x+\left (16-e^7\right ) x^2-2 x^3+x^4} \, dx}{e^{14}}+\frac {\int \frac {16 \left (512-256 e^4-64 e^7+64 e^{11}+4 e^{18}-2 e^{21}+e^{25}\right )+8 \left (512-256 e^4-64 e^7+64 e^{11}+8 e^{14}-e^{21}+e^{25}\right ) x-\left (512-256 e^4+64 e^7-16 e^{14}+20 e^{18}+e^{25}\right ) x^2+2 \left (128-64 e^4-16 e^7+16 e^{11}+e^{18}\right ) x^3}{16 e^7+8 \left (4+e^7\right ) x+\left (16-e^7\right ) x^2-2 x^3+x^4} \, dx}{e^{14}}+\frac {128 \int \frac {64+32 x-\left (4+e^7\right ) x^2+2 x^3}{16 e^7+8 \left (4+e^7\right ) x+\left (16-e^7\right ) x^2-2 x^3+x^4} \, dx}{e^{14}}+\frac {2 \int \frac {-32 \left (64-16 e^7-e^{14}\right )-256 \left (4-e^7\right ) x+2 \left (64-5 e^{14}\right ) x^2-\left (64-16 e^7-e^{14}\right ) x^3}{16 e^7+8 \left (4+e^7\right ) x+\left (16-e^7\right ) x^2-2 x^3+x^4} \, dx}{e^{10}}+\frac {32 \int \frac {-32-16 x+2 x^2-x^3}{16 e^7+8 \left (4+e^7\right ) x+\left (16-e^7\right ) x^2-2 x^3+x^4} \, dx}{e^7} \\ & = x+e^4 x-\frac {256 \log \left (e^7+2 x\right )}{e^{14}}+\frac {32 \log \left (e^7+2 x\right )}{e^7}-\frac {1}{2} e^7 \log \left (e^7+2 x\right )-\frac {2 \left (128-64 e^4-16 e^7+16 e^{11}+e^{18}\right ) \log \left (e^7+2 x\right )}{e^{14}}+\frac {\left (256-64 e^7-4 e^{14}-e^{21}\right ) \log \left (e^7+2 x\right )}{2 e^{10}}+\frac {\left (1024-512 e^4-128 e^7+128 e^{11}+8 e^{18}+2 e^{21}+e^{25}\right ) \log \left (e^7+2 x\right )}{2 e^{14}}+\frac {1}{2} \log \left (16 e^7+8 \left (4+e^7\right ) x+\left (16-e^7\right ) x^2-2 x^3+x^4\right )+\frac {64 \log \left (16 e^7+8 \left (4+e^7\right ) x+\left (16-e^7\right ) x^2-2 x^3+x^4\right )}{e^{14}}-\frac {8 \log \left (16 e^7+8 \left (4+e^7\right ) x+\left (16-e^7\right ) x^2-2 x^3+x^4\right )}{e^7}-\frac {\left (64-16 e^7-e^{14}\right ) \log \left (16 e^7+8 \left (4+e^7\right ) x+\left (16-e^7\right ) x^2-2 x^3+x^4\right )}{2 e^{10}}-\frac {\left (128-64 e^4-16 e^7+16 e^{11}+e^{18}\right ) \log \left (16 e^7+8 \left (4+e^7\right ) x+\left (16-e^7\right ) x^2-2 x^3+x^4\right )}{2 e^{14}}+x \log \left (-\frac {16 e^7+8 \left (4+e^7\right ) x+\left (16-e^7\right ) x^2-2 x^3+x^4}{x^2 \left (e^7+2 x\right )}\right )+\frac {1}{2} \int \frac {-8 \left (4+e^7\right )-2 \left (48-e^7\right ) x-26 x^2}{16 e^7+8 \left (4+e^7\right ) x+\left (16-e^7\right ) x^2-2 x^3+x^4} \, dx-2 \int \left (\frac {1}{2}+\frac {e^7}{2 \left (e^7+2 x\right )}+\frac {-32 e^7-12 \left (4+e^7\right ) x-\left (16-e^7\right ) x^2+x^3}{16 e^7+8 \left (4+e^7\right ) x+\left (16-e^7\right ) x^2-2 x^3+x^4}\right ) \, dx+\frac {\int \frac {16 \left (1536-768 e^4-320 e^7+256 e^{11}+16 e^{14}-4 e^{18}-8 e^{21}+3 e^{25}\right )+4 \left (2048-1024 e^4-128 e^7+192 e^{11}+48 e^{14}-8 e^{21}+9 e^{25}\right ) x-4 \left (128-64 e^4+112 e^7-48 e^{11}-16 e^{14}+17 e^{18}+e^{25}\right ) x^2}{16 e^7+8 \left (4+e^7\right ) x+\left (16-e^7\right ) x^2-2 x^3+x^4} \, dx}{4 e^{14}}+\frac {\int \frac {-32 \left (1536-768 e^4-320 e^7+256 e^{11}+16 e^{14}-4 e^{18}+4 e^{21}+e^{25}\right )-8 \left (2048-1024 e^4-128 e^7+192 e^{11}+48 e^{14}+8 e^{21}+5 e^{25}\right ) x+4 \left (256-128 e^4+224 e^7-96 e^{11}-32 e^{14}+34 e^{18}+2 e^{21}+e^{25}\right ) x^2}{16 e^7+8 \left (4+e^7\right ) x+\left (16-e^7\right ) x^2-2 x^3+x^4} \, dx}{4 e^{14}}+\frac {32 \int \frac {16 \left (12-e^7\right )+4 \left (16+e^7\right ) x-4 \left (1+e^7\right ) x^2}{16 e^7+8 \left (4+e^7\right ) x+\left (16-e^7\right ) x^2-2 x^3+x^4} \, dx}{e^{14}}+\frac {\int \frac {-8 \left (768-256 e^7+4 e^{14}+e^{21}\right )-2 \left (1024-192 e^7-e^{21}\right ) x+2 \left (64+48 e^7-17 e^{14}\right ) x^2}{16 e^7+8 \left (4+e^7\right ) x+\left (16-e^7\right ) x^2-2 x^3+x^4} \, dx}{2 e^{10}}+\frac {8 \int \frac {-8 \left (12-e^7\right )-2 \left (16+e^7\right ) x+2 x^2}{16 e^7+8 \left (4+e^7\right ) x+\left (16-e^7\right ) x^2-2 x^3+x^4} \, dx}{e^7} \\ & = \text {Too large to display} \\ \end{align*}
Time = 0.23 (sec) , antiderivative size = 51, normalized size of antiderivative = 1.55 \[ \int \frac {128 x^2+32 x^3-2 x^5+e^4 \left (-64 x^2-32 x^3+4 x^4-2 x^5\right )+e^{14} \left (32+8 x+e^4 \left (-16-8 x+x^2\right )\right )+e^7 \left (128 x+32 x^2-2 x^4+e^4 \left (-64 x-32 x^2+4 x^3-x^4\right )\right )+\left (-64 x^2-32 x^3+4 x^4-2 x^5+e^{14} \left (-16-8 x+x^2\right )+e^7 \left (-64 x-32 x^2+4 x^3-x^4\right )\right ) \log \left (\frac {-32 x-16 x^2+2 x^3-x^4+e^7 \left (-16-8 x+x^2\right )}{e^7 x^2+2 x^3}\right )}{-64 x^2-32 x^3+4 x^4-2 x^5+e^{14} \left (-16-8 x+x^2\right )+e^7 \left (-64 x-32 x^2+4 x^3-x^4\right )} \, dx=e^4 x+x \log \left (\frac {e^7 \left (-16-8 x+x^2\right )-x \left (32+16 x-2 x^2+x^3\right )}{x^2 \left (e^7+2 x\right )}\right ) \]
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Time = 1.38 (sec) , antiderivative size = 54, normalized size of antiderivative = 1.64
method | result | size |
norman | \(x \,{\mathrm e}^{4}+x \ln \left (\frac {\left (x^{2}-8 x -16\right ) {\mathrm e}^{7}-x^{4}+2 x^{3}-16 x^{2}-32 x}{x^{2} {\mathrm e}^{7}+2 x^{3}}\right )\) | \(54\) |
risch | \(x \,{\mathrm e}^{4}+x \ln \left (\frac {\left (x^{2}-8 x -16\right ) {\mathrm e}^{7}-x^{4}+2 x^{3}-16 x^{2}-32 x}{x^{2} {\mathrm e}^{7}+2 x^{3}}\right )\) | \(54\) |
parallelrisch | \(\frac {\left (256 \,{\mathrm e}^{28} {\mathrm e}^{4} x +256 \,{\mathrm e}^{28} x \ln \left (\frac {\left (x^{2}-8 x -16\right ) {\mathrm e}^{7}-x^{4}+2 x^{3}-16 x^{2}-32 x}{x^{2} \left ({\mathrm e}^{7}+2 x \right )}\right )\right ) {\mathrm e}^{-28}}{256}\) | \(67\) |
default | \(x \,{\mathrm e}^{4}+\frac {\left (\munderset {\textit {\_R} =\operatorname {RootOf}\left (2 \textit {\_Z}^{5}+\left ({\mathrm e}^{7}-4\right ) \textit {\_Z}^{4}+\left (-4 \,{\mathrm e}^{7}+32\right ) \textit {\_Z}^{3}+\left (32 \,{\mathrm e}^{7}-{\mathrm e}^{14}+64\right ) \textit {\_Z}^{2}+\left (64 \,{\mathrm e}^{7}+8 \,{\mathrm e}^{14}\right ) \textit {\_Z} +16 \,{\mathrm e}^{14}\right )}{\sum }\frac {\left (\left ({\mathrm e}^{7}+4\right ) \textit {\_R}^{4}+4 \left ({\mathrm e}^{7}-16\right ) \textit {\_R}^{3}+\left (-64 \,{\mathrm e}^{7}+{\mathrm e}^{14}-192\right ) \textit {\_R}^{2}+16 \left (-12 \,{\mathrm e}^{7}-{\mathrm e}^{14}\right ) \textit {\_R} -48 \,{\mathrm e}^{14}\right ) \ln \left (x -\textit {\_R} \right )}{2 \textit {\_R}^{3} {\mathrm e}^{7}+5 \textit {\_R}^{4}-{\mathrm e}^{14} \textit {\_R} -6 \textit {\_R}^{2} {\mathrm e}^{7}-8 \textit {\_R}^{3}+4 \,{\mathrm e}^{14}+32 \textit {\_R} \,{\mathrm e}^{7}+48 \textit {\_R}^{2}+32 \,{\mathrm e}^{7}+64 \textit {\_R}}\right )}{2}+x \ln \left (\frac {-x^{4}+x^{2} {\mathrm e}^{7}+2 x^{3}-8 x \,{\mathrm e}^{7}-16 x^{2}-16 \,{\mathrm e}^{7}-32 x}{x^{2} \left ({\mathrm e}^{7}+2 x \right )}\right )-\frac {\left ({\mathrm e}^{35}-4 \,{\mathrm e}^{28}-128 \,{\mathrm e}^{21}+4 \left ({\mathrm e}^{14}\right )^{2}+128 \,{\mathrm e}^{7} {\mathrm e}^{14}\right ) {\mathrm e}^{-28} \ln \left ({\mathrm e}^{7}+2 x \right )}{2}+{\mathrm e}^{-28} \left (\munderset {\textit {\_R} =\operatorname {RootOf}\left (\textit {\_Z}^{4}-2 \textit {\_Z}^{3}+\left (-{\mathrm e}^{7}+16\right ) \textit {\_Z}^{2}+\left (8 \,{\mathrm e}^{7}+32\right ) \textit {\_Z} +16 \,{\mathrm e}^{7}\right )}{\sum }\frac {\left ({\mathrm e}^{28} \textit {\_R}^{3}+\left (-16 \,{\mathrm e}^{28}+{\mathrm e}^{35}\right ) \textit {\_R}^{2}+12 \left (-4 \,{\mathrm e}^{28}-{\mathrm e}^{35}\right ) \textit {\_R} -32 \,{\mathrm e}^{35}\right ) \ln \left (x -\textit {\_R} \right )}{-16-2 \textit {\_R}^{3}+\textit {\_R} \,{\mathrm e}^{7}+3 \textit {\_R}^{2}-4 \,{\mathrm e}^{7}-16 \textit {\_R}}\right )\) | \(378\) |
parts | \(x \,{\mathrm e}^{4}+\frac {\left (\munderset {\textit {\_R} =\operatorname {RootOf}\left (2 \textit {\_Z}^{5}+\left ({\mathrm e}^{7}-4\right ) \textit {\_Z}^{4}+\left (-4 \,{\mathrm e}^{7}+32\right ) \textit {\_Z}^{3}+\left (32 \,{\mathrm e}^{7}-{\mathrm e}^{14}+64\right ) \textit {\_Z}^{2}+\left (64 \,{\mathrm e}^{7}+8 \,{\mathrm e}^{14}\right ) \textit {\_Z} +16 \,{\mathrm e}^{14}\right )}{\sum }\frac {\left (\left ({\mathrm e}^{7}+4\right ) \textit {\_R}^{4}+4 \left ({\mathrm e}^{7}-16\right ) \textit {\_R}^{3}+\left (-64 \,{\mathrm e}^{7}+{\mathrm e}^{14}-192\right ) \textit {\_R}^{2}+16 \left (-12 \,{\mathrm e}^{7}-{\mathrm e}^{14}\right ) \textit {\_R} -48 \,{\mathrm e}^{14}\right ) \ln \left (x -\textit {\_R} \right )}{2 \textit {\_R}^{3} {\mathrm e}^{7}+5 \textit {\_R}^{4}-{\mathrm e}^{14} \textit {\_R} -6 \textit {\_R}^{2} {\mathrm e}^{7}-8 \textit {\_R}^{3}+4 \,{\mathrm e}^{14}+32 \textit {\_R} \,{\mathrm e}^{7}+48 \textit {\_R}^{2}+32 \,{\mathrm e}^{7}+64 \textit {\_R}}\right )}{2}+x \ln \left (\frac {-x^{4}+x^{2} {\mathrm e}^{7}+2 x^{3}-8 x \,{\mathrm e}^{7}-16 x^{2}-16 \,{\mathrm e}^{7}-32 x}{x^{2} \left ({\mathrm e}^{7}+2 x \right )}\right )-\frac {\left ({\mathrm e}^{35}-4 \,{\mathrm e}^{28}-128 \,{\mathrm e}^{21}+4 \left ({\mathrm e}^{14}\right )^{2}+128 \,{\mathrm e}^{7} {\mathrm e}^{14}\right ) {\mathrm e}^{-28} \ln \left ({\mathrm e}^{7}+2 x \right )}{2}+{\mathrm e}^{-28} \left (\munderset {\textit {\_R} =\operatorname {RootOf}\left (\textit {\_Z}^{4}-2 \textit {\_Z}^{3}+\left (-{\mathrm e}^{7}+16\right ) \textit {\_Z}^{2}+\left (8 \,{\mathrm e}^{7}+32\right ) \textit {\_Z} +16 \,{\mathrm e}^{7}\right )}{\sum }\frac {\left ({\mathrm e}^{28} \textit {\_R}^{3}+\left (-16 \,{\mathrm e}^{28}+{\mathrm e}^{35}\right ) \textit {\_R}^{2}+12 \left (-4 \,{\mathrm e}^{28}-{\mathrm e}^{35}\right ) \textit {\_R} -32 \,{\mathrm e}^{35}\right ) \ln \left (x -\textit {\_R} \right )}{-16-2 \textit {\_R}^{3}+\textit {\_R} \,{\mathrm e}^{7}+3 \textit {\_R}^{2}-4 \,{\mathrm e}^{7}-16 \textit {\_R}}\right )\) | \(378\) |
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Time = 0.25 (sec) , antiderivative size = 53, normalized size of antiderivative = 1.61 \[ \int \frac {128 x^2+32 x^3-2 x^5+e^4 \left (-64 x^2-32 x^3+4 x^4-2 x^5\right )+e^{14} \left (32+8 x+e^4 \left (-16-8 x+x^2\right )\right )+e^7 \left (128 x+32 x^2-2 x^4+e^4 \left (-64 x-32 x^2+4 x^3-x^4\right )\right )+\left (-64 x^2-32 x^3+4 x^4-2 x^5+e^{14} \left (-16-8 x+x^2\right )+e^7 \left (-64 x-32 x^2+4 x^3-x^4\right )\right ) \log \left (\frac {-32 x-16 x^2+2 x^3-x^4+e^7 \left (-16-8 x+x^2\right )}{e^7 x^2+2 x^3}\right )}{-64 x^2-32 x^3+4 x^4-2 x^5+e^{14} \left (-16-8 x+x^2\right )+e^7 \left (-64 x-32 x^2+4 x^3-x^4\right )} \, dx=x e^{4} + x \log \left (-\frac {x^{4} - 2 \, x^{3} + 16 \, x^{2} - {\left (x^{2} - 8 \, x - 16\right )} e^{7} + 32 \, x}{2 \, x^{3} + x^{2} e^{7}}\right ) \]
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Time = 0.25 (sec) , antiderivative size = 48, normalized size of antiderivative = 1.45 \[ \int \frac {128 x^2+32 x^3-2 x^5+e^4 \left (-64 x^2-32 x^3+4 x^4-2 x^5\right )+e^{14} \left (32+8 x+e^4 \left (-16-8 x+x^2\right )\right )+e^7 \left (128 x+32 x^2-2 x^4+e^4 \left (-64 x-32 x^2+4 x^3-x^4\right )\right )+\left (-64 x^2-32 x^3+4 x^4-2 x^5+e^{14} \left (-16-8 x+x^2\right )+e^7 \left (-64 x-32 x^2+4 x^3-x^4\right )\right ) \log \left (\frac {-32 x-16 x^2+2 x^3-x^4+e^7 \left (-16-8 x+x^2\right )}{e^7 x^2+2 x^3}\right )}{-64 x^2-32 x^3+4 x^4-2 x^5+e^{14} \left (-16-8 x+x^2\right )+e^7 \left (-64 x-32 x^2+4 x^3-x^4\right )} \, dx=x \log {\left (\frac {- x^{4} + 2 x^{3} - 16 x^{2} - 32 x + \left (x^{2} - 8 x - 16\right ) e^{7}}{2 x^{3} + x^{2} e^{7}} \right )} + x e^{4} \]
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Time = 0.23 (sec) , antiderivative size = 53, normalized size of antiderivative = 1.61 \[ \int \frac {128 x^2+32 x^3-2 x^5+e^4 \left (-64 x^2-32 x^3+4 x^4-2 x^5\right )+e^{14} \left (32+8 x+e^4 \left (-16-8 x+x^2\right )\right )+e^7 \left (128 x+32 x^2-2 x^4+e^4 \left (-64 x-32 x^2+4 x^3-x^4\right )\right )+\left (-64 x^2-32 x^3+4 x^4-2 x^5+e^{14} \left (-16-8 x+x^2\right )+e^7 \left (-64 x-32 x^2+4 x^3-x^4\right )\right ) \log \left (\frac {-32 x-16 x^2+2 x^3-x^4+e^7 \left (-16-8 x+x^2\right )}{e^7 x^2+2 x^3}\right )}{-64 x^2-32 x^3+4 x^4-2 x^5+e^{14} \left (-16-8 x+x^2\right )+e^7 \left (-64 x-32 x^2+4 x^3-x^4\right )} \, dx=x e^{4} + x \log \left (-x^{4} + 2 \, x^{3} + x^{2} {\left (e^{7} - 16\right )} - 8 \, x {\left (e^{7} + 4\right )} - 16 \, e^{7}\right ) - x \log \left (2 \, x + e^{7}\right ) - 2 \, x \log \left (x\right ) \]
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Time = 1.14 (sec) , antiderivative size = 57, normalized size of antiderivative = 1.73 \[ \int \frac {128 x^2+32 x^3-2 x^5+e^4 \left (-64 x^2-32 x^3+4 x^4-2 x^5\right )+e^{14} \left (32+8 x+e^4 \left (-16-8 x+x^2\right )\right )+e^7 \left (128 x+32 x^2-2 x^4+e^4 \left (-64 x-32 x^2+4 x^3-x^4\right )\right )+\left (-64 x^2-32 x^3+4 x^4-2 x^5+e^{14} \left (-16-8 x+x^2\right )+e^7 \left (-64 x-32 x^2+4 x^3-x^4\right )\right ) \log \left (\frac {-32 x-16 x^2+2 x^3-x^4+e^7 \left (-16-8 x+x^2\right )}{e^7 x^2+2 x^3}\right )}{-64 x^2-32 x^3+4 x^4-2 x^5+e^{14} \left (-16-8 x+x^2\right )+e^7 \left (-64 x-32 x^2+4 x^3-x^4\right )} \, dx=x e^{4} + x \log \left (-\frac {x^{4} - 2 \, x^{3} - x^{2} e^{7} + 16 \, x^{2} + 8 \, x e^{7} + 32 \, x + 16 \, e^{7}}{2 \, x^{3} + x^{2} e^{7}}\right ) \]
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Time = 13.06 (sec) , antiderivative size = 52, normalized size of antiderivative = 1.58 \[ \int \frac {128 x^2+32 x^3-2 x^5+e^4 \left (-64 x^2-32 x^3+4 x^4-2 x^5\right )+e^{14} \left (32+8 x+e^4 \left (-16-8 x+x^2\right )\right )+e^7 \left (128 x+32 x^2-2 x^4+e^4 \left (-64 x-32 x^2+4 x^3-x^4\right )\right )+\left (-64 x^2-32 x^3+4 x^4-2 x^5+e^{14} \left (-16-8 x+x^2\right )+e^7 \left (-64 x-32 x^2+4 x^3-x^4\right )\right ) \log \left (\frac {-32 x-16 x^2+2 x^3-x^4+e^7 \left (-16-8 x+x^2\right )}{e^7 x^2+2 x^3}\right )}{-64 x^2-32 x^3+4 x^4-2 x^5+e^{14} \left (-16-8 x+x^2\right )+e^7 \left (-64 x-32 x^2+4 x^3-x^4\right )} \, dx=x\,\left (\ln \left (-\frac {32\,x+{\mathrm {e}}^7\,\left (-x^2+8\,x+16\right )+16\,x^2-2\,x^3+x^4}{2\,x^3+{\mathrm {e}}^7\,x^2}\right )+{\mathrm {e}}^4\right ) \]
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