Integrand size = 145, antiderivative size = 31 \[ \int \frac {3 e^{3+x} x^4-6 e^{2+2 x} x^4+12 x \log \left (x^2\right )-6 x \log ^2\left (x^2\right )}{144 x^4-24 e^{3+x} x^4+e^{6+2 x} x^4+e^{4+4 x} x^4+e^{2+2 x} \left (24 x^4-2 e^{3+x} x^4\right )+\left (-24 x^2+2 e^{3+x} x^2-2 e^{2+2 x} x^2\right ) \log ^2\left (x^2\right )+\log ^4\left (x^2\right )} \, dx=\frac {3}{12-e^{3+x}+e^{2+2 x}-\frac {\log ^2\left (x^2\right )}{x^2}} \]
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\[ \int \frac {3 e^{3+x} x^4-6 e^{2+2 x} x^4+12 x \log \left (x^2\right )-6 x \log ^2\left (x^2\right )}{144 x^4-24 e^{3+x} x^4+e^{6+2 x} x^4+e^{4+4 x} x^4+e^{2+2 x} \left (24 x^4-2 e^{3+x} x^4\right )+\left (-24 x^2+2 e^{3+x} x^2-2 e^{2+2 x} x^2\right ) \log ^2\left (x^2\right )+\log ^4\left (x^2\right )} \, dx=\int \frac {3 e^{3+x} x^4-6 e^{2+2 x} x^4+12 x \log \left (x^2\right )-6 x \log ^2\left (x^2\right )}{144 x^4-24 e^{3+x} x^4+e^{6+2 x} x^4+e^{4+4 x} x^4+e^{2+2 x} \left (24 x^4-2 e^{3+x} x^4\right )+\left (-24 x^2+2 e^{3+x} x^2-2 e^{2+2 x} x^2\right ) \log ^2\left (x^2\right )+\log ^4\left (x^2\right )} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {3 x \left (-e^{2+x} \left (-e+2 e^x\right ) x^3+4 \log \left (x^2\right )-2 \log ^2\left (x^2\right )\right )}{\left (\left (12-e^{3+x}+e^{2+2 x}\right ) x^2-\log ^2\left (x^2\right )\right )^2} \, dx \\ & = 3 \int \frac {x \left (-e^{2+x} \left (-e+2 e^x\right ) x^3+4 \log \left (x^2\right )-2 \log ^2\left (x^2\right )\right )}{\left (\left (12-e^{3+x}+e^{2+2 x}\right ) x^2-\log ^2\left (x^2\right )\right )^2} \, dx \\ & = 3 \int \left (-\frac {2 x^2}{12 x^2-e^{3+x} x^2+e^{2+2 x} x^2-\log ^2\left (x^2\right )}-\frac {x \left (-24 x^3+e^{3+x} x^3-4 \log \left (x^2\right )+2 \log ^2\left (x^2\right )+2 x \log ^2\left (x^2\right )\right )}{\left (12 x^2-e^{3+x} x^2+e^{2+2 x} x^2-\log ^2\left (x^2\right )\right )^2}\right ) \, dx \\ & = -\left (3 \int \frac {x \left (-24 x^3+e^{3+x} x^3-4 \log \left (x^2\right )+2 \log ^2\left (x^2\right )+2 x \log ^2\left (x^2\right )\right )}{\left (12 x^2-e^{3+x} x^2+e^{2+2 x} x^2-\log ^2\left (x^2\right )\right )^2} \, dx\right )-6 \int \frac {x^2}{12 x^2-e^{3+x} x^2+e^{2+2 x} x^2-\log ^2\left (x^2\right )} \, dx \\ & = -\left (3 \int \left (-\frac {24 x^4}{\left (12 x^2-e^{3+x} x^2+e^{2+2 x} x^2-\log ^2\left (x^2\right )\right )^2}+\frac {e^{3+x} x^4}{\left (12 x^2-e^{3+x} x^2+e^{2+2 x} x^2-\log ^2\left (x^2\right )\right )^2}-\frac {4 x \log \left (x^2\right )}{\left (12 x^2-e^{3+x} x^2+e^{2+2 x} x^2-\log ^2\left (x^2\right )\right )^2}+\frac {2 x \log ^2\left (x^2\right )}{\left (12 x^2-e^{3+x} x^2+e^{2+2 x} x^2-\log ^2\left (x^2\right )\right )^2}+\frac {2 x^2 \log ^2\left (x^2\right )}{\left (12 x^2-e^{3+x} x^2+e^{2+2 x} x^2-\log ^2\left (x^2\right )\right )^2}\right ) \, dx\right )-6 \int \frac {x^2}{12 x^2-e^{3+x} x^2+e^{2+2 x} x^2-\log ^2\left (x^2\right )} \, dx \\ & = -\left (3 \int \frac {e^{3+x} x^4}{\left (12 x^2-e^{3+x} x^2+e^{2+2 x} x^2-\log ^2\left (x^2\right )\right )^2} \, dx\right )-6 \int \frac {x \log ^2\left (x^2\right )}{\left (12 x^2-e^{3+x} x^2+e^{2+2 x} x^2-\log ^2\left (x^2\right )\right )^2} \, dx-6 \int \frac {x^2 \log ^2\left (x^2\right )}{\left (12 x^2-e^{3+x} x^2+e^{2+2 x} x^2-\log ^2\left (x^2\right )\right )^2} \, dx-6 \int \frac {x^2}{12 x^2-e^{3+x} x^2+e^{2+2 x} x^2-\log ^2\left (x^2\right )} \, dx+12 \int \frac {x \log \left (x^2\right )}{\left (12 x^2-e^{3+x} x^2+e^{2+2 x} x^2-\log ^2\left (x^2\right )\right )^2} \, dx+72 \int \frac {x^4}{\left (12 x^2-e^{3+x} x^2+e^{2+2 x} x^2-\log ^2\left (x^2\right )\right )^2} \, dx \\ \end{align*}
Time = 0.68 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.16 \[ \int \frac {3 e^{3+x} x^4-6 e^{2+2 x} x^4+12 x \log \left (x^2\right )-6 x \log ^2\left (x^2\right )}{144 x^4-24 e^{3+x} x^4+e^{6+2 x} x^4+e^{4+4 x} x^4+e^{2+2 x} \left (24 x^4-2 e^{3+x} x^4\right )+\left (-24 x^2+2 e^{3+x} x^2-2 e^{2+2 x} x^2\right ) \log ^2\left (x^2\right )+\log ^4\left (x^2\right )} \, dx=\frac {3 x^2}{\left (12-e^{3+x}+e^{2+2 x}\right ) x^2-\log ^2\left (x^2\right )} \]
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Time = 2.32 (sec) , antiderivative size = 41, normalized size of antiderivative = 1.32
method | result | size |
parallelrisch | \(\frac {3 x^{2}}{x^{2} {\mathrm e}^{2+2 x}-x^{2} {\mathrm e}^{3+x}+12 x^{2}-\ln \left (x^{2}\right )^{2}}\) | \(41\) |
risch | \(-\frac {12 x^{2}}{-\operatorname {csgn}\left (i x^{2}\right )^{2} \operatorname {csgn}\left (i x \right )^{4} \pi ^{2}+4 \operatorname {csgn}\left (i x^{2}\right )^{3} \operatorname {csgn}\left (i x \right )^{3} \pi ^{2}-6 \operatorname {csgn}\left (i x^{2}\right )^{4} \operatorname {csgn}\left (i x \right )^{2} \pi ^{2}+4 \operatorname {csgn}\left (i x^{2}\right )^{5} \operatorname {csgn}\left (i x \right ) \pi ^{2}-\operatorname {csgn}\left (i x^{2}\right )^{6} \pi ^{2}-8 i \ln \left (x \right ) \pi \operatorname {csgn}\left (i x \right )^{2} \operatorname {csgn}\left (i x^{2}\right )+16 i \ln \left (x \right ) \pi \,\operatorname {csgn}\left (i x \right ) \operatorname {csgn}\left (i x^{2}\right )^{2}-8 i \ln \left (x \right ) \pi \operatorname {csgn}\left (i x^{2}\right )^{3}+4 x^{2} {\mathrm e}^{3+x}-4 x^{2} {\mathrm e}^{2+2 x}-48 x^{2}+16 \ln \left (x \right )^{2}}\) | \(191\) |
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Time = 0.25 (sec) , antiderivative size = 46, normalized size of antiderivative = 1.48 \[ \int \frac {3 e^{3+x} x^4-6 e^{2+2 x} x^4+12 x \log \left (x^2\right )-6 x \log ^2\left (x^2\right )}{144 x^4-24 e^{3+x} x^4+e^{6+2 x} x^4+e^{4+4 x} x^4+e^{2+2 x} \left (24 x^4-2 e^{3+x} x^4\right )+\left (-24 x^2+2 e^{3+x} x^2-2 e^{2+2 x} x^2\right ) \log ^2\left (x^2\right )+\log ^4\left (x^2\right )} \, dx=\frac {3 \, x^{2} e^{4}}{12 \, x^{2} e^{4} + x^{2} e^{\left (2 \, x + 6\right )} - x^{2} e^{\left (x + 7\right )} - e^{4} \log \left (x^{2}\right )^{2}} \]
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Time = 0.19 (sec) , antiderivative size = 48, normalized size of antiderivative = 1.55 \[ \int \frac {3 e^{3+x} x^4-6 e^{2+2 x} x^4+12 x \log \left (x^2\right )-6 x \log ^2\left (x^2\right )}{144 x^4-24 e^{3+x} x^4+e^{6+2 x} x^4+e^{4+4 x} x^4+e^{2+2 x} \left (24 x^4-2 e^{3+x} x^4\right )+\left (-24 x^2+2 e^{3+x} x^2-2 e^{2+2 x} x^2\right ) \log ^2\left (x^2\right )+\log ^4\left (x^2\right )} \, dx=\frac {3 x^{2} e^{4}}{- x^{2} e^{4} e^{x + 3} + x^{2} e^{2 x + 6} + 12 x^{2} e^{4} - e^{4} \log {\left (x^{2} \right )}^{2}} \]
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Time = 0.29 (sec) , antiderivative size = 38, normalized size of antiderivative = 1.23 \[ \int \frac {3 e^{3+x} x^4-6 e^{2+2 x} x^4+12 x \log \left (x^2\right )-6 x \log ^2\left (x^2\right )}{144 x^4-24 e^{3+x} x^4+e^{6+2 x} x^4+e^{4+4 x} x^4+e^{2+2 x} \left (24 x^4-2 e^{3+x} x^4\right )+\left (-24 x^2+2 e^{3+x} x^2-2 e^{2+2 x} x^2\right ) \log ^2\left (x^2\right )+\log ^4\left (x^2\right )} \, dx=\frac {3 \, x^{2}}{x^{2} e^{\left (2 \, x + 2\right )} - x^{2} e^{\left (x + 3\right )} + 12 \, x^{2} - 4 \, \log \left (x\right )^{2}} \]
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Timed out. \[ \int \frac {3 e^{3+x} x^4-6 e^{2+2 x} x^4+12 x \log \left (x^2\right )-6 x \log ^2\left (x^2\right )}{144 x^4-24 e^{3+x} x^4+e^{6+2 x} x^4+e^{4+4 x} x^4+e^{2+2 x} \left (24 x^4-2 e^{3+x} x^4\right )+\left (-24 x^2+2 e^{3+x} x^2-2 e^{2+2 x} x^2\right ) \log ^2\left (x^2\right )+\log ^4\left (x^2\right )} \, dx=\text {Timed out} \]
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Timed out. \[ \int \frac {3 e^{3+x} x^4-6 e^{2+2 x} x^4+12 x \log \left (x^2\right )-6 x \log ^2\left (x^2\right )}{144 x^4-24 e^{3+x} x^4+e^{6+2 x} x^4+e^{4+4 x} x^4+e^{2+2 x} \left (24 x^4-2 e^{3+x} x^4\right )+\left (-24 x^2+2 e^{3+x} x^2-2 e^{2+2 x} x^2\right ) \log ^2\left (x^2\right )+\log ^4\left (x^2\right )} \, dx=\int \frac {12\,x\,\ln \left (x^2\right )+3\,x^4\,{\mathrm {e}}^{x+3}-6\,x\,{\ln \left (x^2\right )}^2-6\,x^4\,{\mathrm {e}}^{2\,x+2}}{{\ln \left (x^2\right )}^4-24\,x^4\,{\mathrm {e}}^{x+3}-{\mathrm {e}}^{2\,x+2}\,\left (2\,x^4\,{\mathrm {e}}^{x+3}-24\,x^4\right )+x^4\,{\mathrm {e}}^{2\,x+6}+x^4\,{\mathrm {e}}^{4\,x+4}+144\,x^4-{\ln \left (x^2\right )}^2\,\left (2\,x^2\,{\mathrm {e}}^{2\,x+2}-2\,x^2\,{\mathrm {e}}^{x+3}+24\,x^2\right )} \,d x \]
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