Integrand size = 81, antiderivative size = 32 \[ \int \frac {e^{\frac {6 x+(-2-x) \log \left (\frac {x}{-10+8 x^2}\right )}{12+6 x}} \left (20-40 x+21 x^2+64 x^3+4 x^4\right ) \log (3)}{-120 x-120 x^2+66 x^3+96 x^4+24 x^5} \, dx=\frac {\sqrt [6]{2} e^{\frac {x}{2+x}} \log (3)}{\sqrt [6]{\frac {x}{-5+4 x^2}}} \]
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\[ \int \frac {e^{\frac {6 x+(-2-x) \log \left (\frac {x}{-10+8 x^2}\right )}{12+6 x}} \left (20-40 x+21 x^2+64 x^3+4 x^4\right ) \log (3)}{-120 x-120 x^2+66 x^3+96 x^4+24 x^5} \, dx=\int \frac {\exp \left (\frac {6 x+(-2-x) \log \left (\frac {x}{-10+8 x^2}\right )}{12+6 x}\right ) \left (20-40 x+21 x^2+64 x^3+4 x^4\right ) \log (3)}{-120 x-120 x^2+66 x^3+96 x^4+24 x^5} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \log (3) \int \frac {\exp \left (\frac {6 x+(-2-x) \log \left (\frac {x}{-10+8 x^2}\right )}{12+6 x}\right ) \left (20-40 x+21 x^2+64 x^3+4 x^4\right )}{-120 x-120 x^2+66 x^3+96 x^4+24 x^5} \, dx \\ & = \log (3) \int \frac {e^{\frac {x}{2+x}} \left (\frac {x}{-10+8 x^2}\right )^{5/6} \left (20-40 x+21 x^2+64 x^3+4 x^4\right )}{3 x^2 (2+x)^2} \, dx \\ & = \frac {1}{3} \log (3) \int \frac {e^{\frac {x}{2+x}} \left (\frac {x}{-10+8 x^2}\right )^{5/6} \left (20-40 x+21 x^2+64 x^3+4 x^4\right )}{x^2 (2+x)^2} \, dx \\ & = \frac {\left (\left (\frac {x}{-10+8 x^2}\right )^{5/6} \left (-10+8 x^2\right )^{5/6} \log (3)\right ) \int \frac {e^{\frac {x}{2+x}} \left (20-40 x+21 x^2+64 x^3+4 x^4\right )}{x^{7/6} (2+x)^2 \left (-10+8 x^2\right )^{5/6}} \, dx}{3 x^{5/6}} \\ & = \frac {\left (2 \left (\frac {x}{-10+8 x^2}\right )^{5/6} \left (-10+8 x^2\right )^{5/6} \log (3)\right ) \text {Subst}\left (\int \frac {e^{\frac {x^6}{2+x^6}} \left (20-40 x^6+21 x^{12}+64 x^{18}+4 x^{24}\right )}{x^2 \left (2+x^6\right )^2 \left (-10+8 x^{12}\right )^{5/6}} \, dx,x,\sqrt [6]{x}\right )}{x^{5/6}} \\ & = \frac {\left (2 \left (\frac {x}{-10+8 x^2}\right )^{5/6} \left (-10+8 x^2\right )^{5/6} \log (3)\right ) \text {Subst}\left (\int \left (\frac {5 e^{\frac {x^6}{2+x^6}}}{x^2 \left (-10+8 x^{12}\right )^{5/6}}+\frac {48 e^{\frac {x^6}{2+x^6}} x^4}{\left (-10+8 x^{12}\right )^{5/6}}+\frac {4 e^{\frac {x^6}{2+x^6}} x^{10}}{\left (-10+8 x^{12}\right )^{5/6}}+\frac {132 e^{\frac {x^6}{2+x^6}} x^4}{\left (2+x^6\right )^2 \left (-10+8 x^{12}\right )^{5/6}}-\frac {192 e^{\frac {x^6}{2+x^6}} x^4}{\left (2+x^6\right ) \left (-10+8 x^{12}\right )^{5/6}}\right ) \, dx,x,\sqrt [6]{x}\right )}{x^{5/6}} \\ & = \frac {\left (8 \left (\frac {x}{-10+8 x^2}\right )^{5/6} \left (-10+8 x^2\right )^{5/6} \log (3)\right ) \text {Subst}\left (\int \frac {e^{\frac {x^6}{2+x^6}} x^{10}}{\left (-10+8 x^{12}\right )^{5/6}} \, dx,x,\sqrt [6]{x}\right )}{x^{5/6}}+\frac {\left (10 \left (\frac {x}{-10+8 x^2}\right )^{5/6} \left (-10+8 x^2\right )^{5/6} \log (3)\right ) \text {Subst}\left (\int \frac {e^{\frac {x^6}{2+x^6}}}{x^2 \left (-10+8 x^{12}\right )^{5/6}} \, dx,x,\sqrt [6]{x}\right )}{x^{5/6}}+\frac {\left (96 \left (\frac {x}{-10+8 x^2}\right )^{5/6} \left (-10+8 x^2\right )^{5/6} \log (3)\right ) \text {Subst}\left (\int \frac {e^{\frac {x^6}{2+x^6}} x^4}{\left (-10+8 x^{12}\right )^{5/6}} \, dx,x,\sqrt [6]{x}\right )}{x^{5/6}}+\frac {\left (264 \left (\frac {x}{-10+8 x^2}\right )^{5/6} \left (-10+8 x^2\right )^{5/6} \log (3)\right ) \text {Subst}\left (\int \frac {e^{\frac {x^6}{2+x^6}} x^4}{\left (2+x^6\right )^2 \left (-10+8 x^{12}\right )^{5/6}} \, dx,x,\sqrt [6]{x}\right )}{x^{5/6}}-\frac {\left (384 \left (\frac {x}{-10+8 x^2}\right )^{5/6} \left (-10+8 x^2\right )^{5/6} \log (3)\right ) \text {Subst}\left (\int \frac {e^{\frac {x^6}{2+x^6}} x^4}{\left (2+x^6\right ) \left (-10+8 x^{12}\right )^{5/6}} \, dx,x,\sqrt [6]{x}\right )}{x^{5/6}} \\ & = \frac {\left (8 \left (\frac {x}{-10+8 x^2}\right )^{5/6} \left (-10+8 x^2\right )^{5/6} \log (3)\right ) \text {Subst}\left (\int \frac {e^{\frac {x^6}{2+x^6}} x^{10}}{\left (-10+8 x^{12}\right )^{5/6}} \, dx,x,\sqrt [6]{x}\right )}{x^{5/6}}+\frac {\left (10 \left (\frac {x}{-10+8 x^2}\right )^{5/6} \left (-10+8 x^2\right )^{5/6} \log (3)\right ) \text {Subst}\left (\int \frac {e^{\frac {x^6}{2+x^6}}}{x^2 \left (-10+8 x^{12}\right )^{5/6}} \, dx,x,\sqrt [6]{x}\right )}{x^{5/6}}+\frac {\left (96 \left (\frac {x}{-10+8 x^2}\right )^{5/6} \left (-10+8 x^2\right )^{5/6} \log (3)\right ) \text {Subst}\left (\int \frac {e^{\frac {x^6}{2+x^6}} x^4}{\left (-10+8 x^{12}\right )^{5/6}} \, dx,x,\sqrt [6]{x}\right )}{x^{5/6}}+\frac {\left (264 \left (\frac {x}{-10+8 x^2}\right )^{5/6} \left (-10+8 x^2\right )^{5/6} \log (3)\right ) \text {Subst}\left (\int \left (-\frac {i e^{\frac {x^6}{2+x^6}} x}{4 \sqrt {2} \left (i \sqrt {2}-x^3\right )^2 \left (-10+8 x^{12}\right )^{5/6}}+\frac {i e^{\frac {x^6}{2+x^6}} x}{4 \sqrt {2} \left (i \sqrt {2}+x^3\right )^2 \left (-10+8 x^{12}\right )^{5/6}}\right ) \, dx,x,\sqrt [6]{x}\right )}{x^{5/6}}-\frac {\left (384 \left (\frac {x}{-10+8 x^2}\right )^{5/6} \left (-10+8 x^2\right )^{5/6} \log (3)\right ) \text {Subst}\left (\int \left (\frac {e^{\frac {x^6}{2+x^6}} x}{2 \left (-i \sqrt {2}+x^3\right ) \left (-10+8 x^{12}\right )^{5/6}}+\frac {e^{\frac {x^6}{2+x^6}} x}{2 \left (i \sqrt {2}+x^3\right ) \left (-10+8 x^{12}\right )^{5/6}}\right ) \, dx,x,\sqrt [6]{x}\right )}{x^{5/6}} \\ & = \frac {\left (8 \left (\frac {x}{-10+8 x^2}\right )^{5/6} \left (-10+8 x^2\right )^{5/6} \log (3)\right ) \text {Subst}\left (\int \frac {e^{\frac {x^6}{2+x^6}} x^{10}}{\left (-10+8 x^{12}\right )^{5/6}} \, dx,x,\sqrt [6]{x}\right )}{x^{5/6}}+\frac {\left (10 \left (\frac {x}{-10+8 x^2}\right )^{5/6} \left (-10+8 x^2\right )^{5/6} \log (3)\right ) \text {Subst}\left (\int \frac {e^{\frac {x^6}{2+x^6}}}{x^2 \left (-10+8 x^{12}\right )^{5/6}} \, dx,x,\sqrt [6]{x}\right )}{x^{5/6}}+\frac {\left (96 \left (\frac {x}{-10+8 x^2}\right )^{5/6} \left (-10+8 x^2\right )^{5/6} \log (3)\right ) \text {Subst}\left (\int \frac {e^{\frac {x^6}{2+x^6}} x^4}{\left (-10+8 x^{12}\right )^{5/6}} \, dx,x,\sqrt [6]{x}\right )}{x^{5/6}}-\frac {\left (192 \left (\frac {x}{-10+8 x^2}\right )^{5/6} \left (-10+8 x^2\right )^{5/6} \log (3)\right ) \text {Subst}\left (\int \frac {e^{\frac {x^6}{2+x^6}} x}{\left (-i \sqrt {2}+x^3\right ) \left (-10+8 x^{12}\right )^{5/6}} \, dx,x,\sqrt [6]{x}\right )}{x^{5/6}}-\frac {\left (192 \left (\frac {x}{-10+8 x^2}\right )^{5/6} \left (-10+8 x^2\right )^{5/6} \log (3)\right ) \text {Subst}\left (\int \frac {e^{\frac {x^6}{2+x^6}} x}{\left (i \sqrt {2}+x^3\right ) \left (-10+8 x^{12}\right )^{5/6}} \, dx,x,\sqrt [6]{x}\right )}{x^{5/6}}-\frac {\left (33 i \sqrt {2} \left (\frac {x}{-10+8 x^2}\right )^{5/6} \left (-10+8 x^2\right )^{5/6} \log (3)\right ) \text {Subst}\left (\int \frac {e^{\frac {x^6}{2+x^6}} x}{\left (i \sqrt {2}-x^3\right )^2 \left (-10+8 x^{12}\right )^{5/6}} \, dx,x,\sqrt [6]{x}\right )}{x^{5/6}}+\frac {\left (33 i \sqrt {2} \left (\frac {x}{-10+8 x^2}\right )^{5/6} \left (-10+8 x^2\right )^{5/6} \log (3)\right ) \text {Subst}\left (\int \frac {e^{\frac {x^6}{2+x^6}} x}{\left (i \sqrt {2}+x^3\right )^2 \left (-10+8 x^{12}\right )^{5/6}} \, dx,x,\sqrt [6]{x}\right )}{x^{5/6}} \\ & = \frac {\left (8 \left (\frac {x}{-10+8 x^2}\right )^{5/6} \left (-10+8 x^2\right )^{5/6} \log (3)\right ) \text {Subst}\left (\int \frac {e^{\frac {x^6}{2+x^6}} x^{10}}{\left (-10+8 x^{12}\right )^{5/6}} \, dx,x,\sqrt [6]{x}\right )}{x^{5/6}}+\frac {\left (10 \left (\frac {x}{-10+8 x^2}\right )^{5/6} \left (-10+8 x^2\right )^{5/6} \log (3)\right ) \text {Subst}\left (\int \frac {e^{\frac {x^6}{2+x^6}}}{x^2 \left (-10+8 x^{12}\right )^{5/6}} \, dx,x,\sqrt [6]{x}\right )}{x^{5/6}}+\frac {\left (96 \left (\frac {x}{-10+8 x^2}\right )^{5/6} \left (-10+8 x^2\right )^{5/6} \log (3)\right ) \text {Subst}\left (\int \frac {e^{\frac {x^6}{2+x^6}} x^4}{\left (-10+8 x^{12}\right )^{5/6}} \, dx,x,\sqrt [6]{x}\right )}{x^{5/6}}-\frac {\left (192 \left (\frac {x}{-10+8 x^2}\right )^{5/6} \left (-10+8 x^2\right )^{5/6} \log (3)\right ) \text {Subst}\left (\int \left (\frac {(-1)^{5/6} e^{\frac {x^6}{2+x^6}}}{3 \sqrt [6]{2} \left (\sqrt [6]{-2}-x\right ) \left (-10+8 x^{12}\right )^{5/6}}-\frac {i e^{\frac {x^6}{2+x^6}}}{3 \sqrt [6]{2} \left (\sqrt [6]{-2}+\sqrt [3]{-1} x\right ) \left (-10+8 x^{12}\right )^{5/6}}+\frac {\sqrt [6]{-\frac {1}{2}} e^{\frac {x^6}{2+x^6}}}{3 \left (\sqrt [6]{-2}-(-1)^{2/3} x\right ) \left (-10+8 x^{12}\right )^{5/6}}\right ) \, dx,x,\sqrt [6]{x}\right )}{x^{5/6}}-\frac {\left (192 \left (\frac {x}{-10+8 x^2}\right )^{5/6} \left (-10+8 x^2\right )^{5/6} \log (3)\right ) \text {Subst}\left (\int \left (\frac {(-1)^{5/6} e^{\frac {x^6}{2+x^6}}}{3 \sqrt [6]{2} \left (\sqrt [6]{-2}+x\right ) \left (-10+8 x^{12}\right )^{5/6}}-\frac {i e^{\frac {x^6}{2+x^6}}}{3 \sqrt [6]{2} \left (\sqrt [6]{-2}-\sqrt [3]{-1} x\right ) \left (-10+8 x^{12}\right )^{5/6}}+\frac {\sqrt [6]{-\frac {1}{2}} e^{\frac {x^6}{2+x^6}}}{3 \left (\sqrt [6]{-2}+(-1)^{2/3} x\right ) \left (-10+8 x^{12}\right )^{5/6}}\right ) \, dx,x,\sqrt [6]{x}\right )}{x^{5/6}}-\frac {\left (33 i \sqrt {2} \left (\frac {x}{-10+8 x^2}\right )^{5/6} \left (-10+8 x^2\right )^{5/6} \log (3)\right ) \text {Subst}\left (\int \frac {e^{\frac {x^6}{2+x^6}} x}{\left (i \sqrt {2}-x^3\right )^2 \left (-10+8 x^{12}\right )^{5/6}} \, dx,x,\sqrt [6]{x}\right )}{x^{5/6}}+\frac {\left (33 i \sqrt {2} \left (\frac {x}{-10+8 x^2}\right )^{5/6} \left (-10+8 x^2\right )^{5/6} \log (3)\right ) \text {Subst}\left (\int \frac {e^{\frac {x^6}{2+x^6}} x}{\left (i \sqrt {2}+x^3\right )^2 \left (-10+8 x^{12}\right )^{5/6}} \, dx,x,\sqrt [6]{x}\right )}{x^{5/6}} \\ & = \frac {\left (8 \left (\frac {x}{-10+8 x^2}\right )^{5/6} \left (-10+8 x^2\right )^{5/6} \log (3)\right ) \text {Subst}\left (\int \frac {e^{\frac {x^6}{2+x^6}} x^{10}}{\left (-10+8 x^{12}\right )^{5/6}} \, dx,x,\sqrt [6]{x}\right )}{x^{5/6}}+\frac {\left (10 \left (\frac {x}{-10+8 x^2}\right )^{5/6} \left (-10+8 x^2\right )^{5/6} \log (3)\right ) \text {Subst}\left (\int \frac {e^{\frac {x^6}{2+x^6}}}{x^2 \left (-10+8 x^{12}\right )^{5/6}} \, dx,x,\sqrt [6]{x}\right )}{x^{5/6}}+\frac {\left (96 \left (\frac {x}{-10+8 x^2}\right )^{5/6} \left (-10+8 x^2\right )^{5/6} \log (3)\right ) \text {Subst}\left (\int \frac {e^{\frac {x^6}{2+x^6}} x^4}{\left (-10+8 x^{12}\right )^{5/6}} \, dx,x,\sqrt [6]{x}\right )}{x^{5/6}}-\frac {\left (32 (-2)^{5/6} \left (\frac {x}{-10+8 x^2}\right )^{5/6} \left (-10+8 x^2\right )^{5/6} \log (3)\right ) \text {Subst}\left (\int \frac {e^{\frac {x^6}{2+x^6}}}{\left (\sqrt [6]{-2}-x\right ) \left (-10+8 x^{12}\right )^{5/6}} \, dx,x,\sqrt [6]{x}\right )}{x^{5/6}}-\frac {\left (32 (-2)^{5/6} \left (\frac {x}{-10+8 x^2}\right )^{5/6} \left (-10+8 x^2\right )^{5/6} \log (3)\right ) \text {Subst}\left (\int \frac {e^{\frac {x^6}{2+x^6}}}{\left (\sqrt [6]{-2}+x\right ) \left (-10+8 x^{12}\right )^{5/6}} \, dx,x,\sqrt [6]{x}\right )}{x^{5/6}}-\frac {\left (33 i \sqrt {2} \left (\frac {x}{-10+8 x^2}\right )^{5/6} \left (-10+8 x^2\right )^{5/6} \log (3)\right ) \text {Subst}\left (\int \frac {e^{\frac {x^6}{2+x^6}} x}{\left (i \sqrt {2}-x^3\right )^2 \left (-10+8 x^{12}\right )^{5/6}} \, dx,x,\sqrt [6]{x}\right )}{x^{5/6}}+\frac {\left (33 i \sqrt {2} \left (\frac {x}{-10+8 x^2}\right )^{5/6} \left (-10+8 x^2\right )^{5/6} \log (3)\right ) \text {Subst}\left (\int \frac {e^{\frac {x^6}{2+x^6}} x}{\left (i \sqrt {2}+x^3\right )^2 \left (-10+8 x^{12}\right )^{5/6}} \, dx,x,\sqrt [6]{x}\right )}{x^{5/6}}+\frac {\left (32 i 2^{5/6} \left (\frac {x}{-10+8 x^2}\right )^{5/6} \left (-10+8 x^2\right )^{5/6} \log (3)\right ) \text {Subst}\left (\int \frac {e^{\frac {x^6}{2+x^6}}}{\left (\sqrt [6]{-2}-\sqrt [3]{-1} x\right ) \left (-10+8 x^{12}\right )^{5/6}} \, dx,x,\sqrt [6]{x}\right )}{x^{5/6}}+\frac {\left (32 i 2^{5/6} \left (\frac {x}{-10+8 x^2}\right )^{5/6} \left (-10+8 x^2\right )^{5/6} \log (3)\right ) \text {Subst}\left (\int \frac {e^{\frac {x^6}{2+x^6}}}{\left (\sqrt [6]{-2}+\sqrt [3]{-1} x\right ) \left (-10+8 x^{12}\right )^{5/6}} \, dx,x,\sqrt [6]{x}\right )}{x^{5/6}}-\frac {\left (32 \sqrt [6]{-1} 2^{5/6} \left (\frac {x}{-10+8 x^2}\right )^{5/6} \left (-10+8 x^2\right )^{5/6} \log (3)\right ) \text {Subst}\left (\int \frac {e^{\frac {x^6}{2+x^6}}}{\left (\sqrt [6]{-2}-(-1)^{2/3} x\right ) \left (-10+8 x^{12}\right )^{5/6}} \, dx,x,\sqrt [6]{x}\right )}{x^{5/6}}-\frac {\left (32 \sqrt [6]{-1} 2^{5/6} \left (\frac {x}{-10+8 x^2}\right )^{5/6} \left (-10+8 x^2\right )^{5/6} \log (3)\right ) \text {Subst}\left (\int \frac {e^{\frac {x^6}{2+x^6}}}{\left (\sqrt [6]{-2}+(-1)^{2/3} x\right ) \left (-10+8 x^{12}\right )^{5/6}} \, dx,x,\sqrt [6]{x}\right )}{x^{5/6}} \\ \end{align*}
\[ \int \frac {e^{\frac {6 x+(-2-x) \log \left (\frac {x}{-10+8 x^2}\right )}{12+6 x}} \left (20-40 x+21 x^2+64 x^3+4 x^4\right ) \log (3)}{-120 x-120 x^2+66 x^3+96 x^4+24 x^5} \, dx=\int \frac {e^{\frac {6 x+(-2-x) \log \left (\frac {x}{-10+8 x^2}\right )}{12+6 x}} \left (20-40 x+21 x^2+64 x^3+4 x^4\right ) \log (3)}{-120 x-120 x^2+66 x^3+96 x^4+24 x^5} \, dx \]
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Time = 1.94 (sec) , antiderivative size = 35, normalized size of antiderivative = 1.09
method | result | size |
default | \(\ln \left (3\right ) {\mathrm e}^{\frac {\left (-2-x \right ) \ln \left (\frac {x}{8 x^{2}-10}\right )+6 x}{6 x +12}}\) | \(35\) |
parallelrisch | \(\ln \left (3\right ) {\mathrm e}^{\frac {\left (-2-x \right ) \ln \left (\frac {x}{8 x^{2}-10}\right )+6 x}{6 x +12}}\) | \(35\) |
risch | \(\ln \left (3\right ) {\mathrm e}^{-\frac {\ln \left (\frac {x}{8 x^{2}-10}\right ) x +2 \ln \left (\frac {x}{8 x^{2}-10}\right )-6 x}{6 \left (2+x \right )}}\) | \(44\) |
gosper | \(\ln \left (3\right ) {\mathrm e}^{-\frac {\ln \left (\frac {x}{8 x^{2}-10}\right ) x +2 \ln \left (\frac {x}{8 x^{2}-10}\right )-6 x}{6 \left (2+x \right )}}\) | \(46\) |
norman | \(\frac {x \ln \left (3\right ) {\mathrm e}^{\frac {\left (-2-x \right ) \ln \left (\frac {x}{8 x^{2}-10}\right )+6 x}{6 x +12}}+2 \ln \left (3\right ) {\mathrm e}^{\frac {\left (-2-x \right ) \ln \left (\frac {x}{8 x^{2}-10}\right )+6 x}{6 x +12}}}{2+x}\) | \(78\) |
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Time = 0.26 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.00 \[ \int \frac {e^{\frac {6 x+(-2-x) \log \left (\frac {x}{-10+8 x^2}\right )}{12+6 x}} \left (20-40 x+21 x^2+64 x^3+4 x^4\right ) \log (3)}{-120 x-120 x^2+66 x^3+96 x^4+24 x^5} \, dx=e^{\left (-\frac {{\left (x + 2\right )} \log \left (\frac {x}{2 \, {\left (4 \, x^{2} - 5\right )}}\right ) - 6 \, x}{6 \, {\left (x + 2\right )}}\right )} \log \left (3\right ) \]
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Time = 0.50 (sec) , antiderivative size = 27, normalized size of antiderivative = 0.84 \[ \int \frac {e^{\frac {6 x+(-2-x) \log \left (\frac {x}{-10+8 x^2}\right )}{12+6 x}} \left (20-40 x+21 x^2+64 x^3+4 x^4\right ) \log (3)}{-120 x-120 x^2+66 x^3+96 x^4+24 x^5} \, dx=e^{\frac {6 x + \left (- x - 2\right ) \log {\left (\frac {x}{8 x^{2} - 10} \right )}}{6 x + 12}} \log {\left (3 \right )} \]
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\[ \int \frac {e^{\frac {6 x+(-2-x) \log \left (\frac {x}{-10+8 x^2}\right )}{12+6 x}} \left (20-40 x+21 x^2+64 x^3+4 x^4\right ) \log (3)}{-120 x-120 x^2+66 x^3+96 x^4+24 x^5} \, dx=\int { \frac {{\left (4 \, x^{4} + 64 \, x^{3} + 21 \, x^{2} - 40 \, x + 20\right )} e^{\left (-\frac {{\left (x + 2\right )} \log \left (\frac {x}{2 \, {\left (4 \, x^{2} - 5\right )}}\right ) - 6 \, x}{6 \, {\left (x + 2\right )}}\right )} \log \left (3\right )}{6 \, {\left (4 \, x^{5} + 16 \, x^{4} + 11 \, x^{3} - 20 \, x^{2} - 20 \, x\right )}} \,d x } \]
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Time = 0.30 (sec) , antiderivative size = 53, normalized size of antiderivative = 1.66 \[ \int \frac {e^{\frac {6 x+(-2-x) \log \left (\frac {x}{-10+8 x^2}\right )}{12+6 x}} \left (20-40 x+21 x^2+64 x^3+4 x^4\right ) \log (3)}{-120 x-120 x^2+66 x^3+96 x^4+24 x^5} \, dx=e^{\left (-\frac {x \log \left (\frac {x}{2 \, {\left (4 \, x^{2} - 5\right )}}\right )}{6 \, {\left (x + 2\right )}} + \frac {x}{x + 2} - \frac {\log \left (\frac {x}{2 \, {\left (4 \, x^{2} - 5\right )}}\right )}{3 \, {\left (x + 2\right )}}\right )} \log \left (3\right ) \]
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Timed out. \[ \int \frac {e^{\frac {6 x+(-2-x) \log \left (\frac {x}{-10+8 x^2}\right )}{12+6 x}} \left (20-40 x+21 x^2+64 x^3+4 x^4\right ) \log (3)}{-120 x-120 x^2+66 x^3+96 x^4+24 x^5} \, dx=\int \frac {{\mathrm {e}}^{\frac {6\,x-\ln \left (\frac {x}{8\,x^2-10}\right )\,\left (x+2\right )}{6\,x+12}}\,\ln \left (3\right )\,\left (4\,x^4+64\,x^3+21\,x^2-40\,x+20\right )}{24\,x^5+96\,x^4+66\,x^3-120\,x^2-120\,x} \,d x \]
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