Integrand size = 100, antiderivative size = 30 \[ \int \frac {-42+10 x+36 x^2-9 x^4-2 x^5+\left (45+27 x-29 x^2-17 x^3+x^4+x^5\right ) \log \left (\frac {e^{2 x}}{3+x}\right )}{-3 x-x^2+\left (27-9 x-21 x^2+x^3+5 x^4+x^5\right ) \log \left (\frac {e^{2 x}}{3+x}\right )} \, dx=-4+x-\log \left (x-\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )\right ) \]
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\[ \int \frac {-42+10 x+36 x^2-9 x^4-2 x^5+\left (45+27 x-29 x^2-17 x^3+x^4+x^5\right ) \log \left (\frac {e^{2 x}}{3+x}\right )}{-3 x-x^2+\left (27-9 x-21 x^2+x^3+5 x^4+x^5\right ) \log \left (\frac {e^{2 x}}{3+x}\right )} \, dx=\int \frac {-42+10 x+36 x^2-9 x^4-2 x^5+\left (45+27 x-29 x^2-17 x^3+x^4+x^5\right ) \log \left (\frac {e^{2 x}}{3+x}\right )}{-3 x-x^2+\left (27-9 x-21 x^2+x^3+5 x^4+x^5\right ) \log \left (\frac {e^{2 x}}{3+x}\right )} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {-5-3 x+x^2}{-3+x+x^2}+\frac {126-87 x-154 x^2+46 x^3+64 x^4-3 x^5-11 x^6-2 x^7}{(3+x) \left (-3+x+x^2\right ) \left (-x+9 \log \left (\frac {e^{2 x}}{3+x}\right )-6 x \log \left (\frac {e^{2 x}}{3+x}\right )-5 x^2 \log \left (\frac {e^{2 x}}{3+x}\right )+2 x^3 \log \left (\frac {e^{2 x}}{3+x}\right )+x^4 \log \left (\frac {e^{2 x}}{3+x}\right )\right )}\right ) \, dx \\ & = \int \frac {-5-3 x+x^2}{-3+x+x^2} \, dx+\int \frac {126-87 x-154 x^2+46 x^3+64 x^4-3 x^5-11 x^6-2 x^7}{(3+x) \left (-3+x+x^2\right ) \left (-x+9 \log \left (\frac {e^{2 x}}{3+x}\right )-6 x \log \left (\frac {e^{2 x}}{3+x}\right )-5 x^2 \log \left (\frac {e^{2 x}}{3+x}\right )+2 x^3 \log \left (\frac {e^{2 x}}{3+x}\right )+x^4 \log \left (\frac {e^{2 x}}{3+x}\right )\right )} \, dx \\ & = \int \left (1-\frac {2 (1+2 x)}{-3+x+x^2}\right ) \, dx+\int \frac {126-87 x-154 x^2+46 x^3+64 x^4-3 x^5-11 x^6-2 x^7}{(3+x) \left (3-x-x^2\right ) \left (x-\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )\right )} \, dx \\ & = x-2 \int \frac {1+2 x}{-3+x+x^2} \, dx+\int \left (-\frac {21}{-x+9 \log \left (\frac {e^{2 x}}{3+x}\right )-6 x \log \left (\frac {e^{2 x}}{3+x}\right )-5 x^2 \log \left (\frac {e^{2 x}}{3+x}\right )+2 x^3 \log \left (\frac {e^{2 x}}{3+x}\right )+x^4 \log \left (\frac {e^{2 x}}{3+x}\right )}+\frac {10 x}{-x+9 \log \left (\frac {e^{2 x}}{3+x}\right )-6 x \log \left (\frac {e^{2 x}}{3+x}\right )-5 x^2 \log \left (\frac {e^{2 x}}{3+x}\right )+2 x^3 \log \left (\frac {e^{2 x}}{3+x}\right )+x^4 \log \left (\frac {e^{2 x}}{3+x}\right )}+\frac {9 x^2}{-x+9 \log \left (\frac {e^{2 x}}{3+x}\right )-6 x \log \left (\frac {e^{2 x}}{3+x}\right )-5 x^2 \log \left (\frac {e^{2 x}}{3+x}\right )+2 x^3 \log \left (\frac {e^{2 x}}{3+x}\right )+x^4 \log \left (\frac {e^{2 x}}{3+x}\right )}-\frac {3 x^3}{-x+9 \log \left (\frac {e^{2 x}}{3+x}\right )-6 x \log \left (\frac {e^{2 x}}{3+x}\right )-5 x^2 \log \left (\frac {e^{2 x}}{3+x}\right )+2 x^3 \log \left (\frac {e^{2 x}}{3+x}\right )+x^4 \log \left (\frac {e^{2 x}}{3+x}\right )}-\frac {2 x^4}{-x+9 \log \left (\frac {e^{2 x}}{3+x}\right )-6 x \log \left (\frac {e^{2 x}}{3+x}\right )-5 x^2 \log \left (\frac {e^{2 x}}{3+x}\right )+2 x^3 \log \left (\frac {e^{2 x}}{3+x}\right )+x^4 \log \left (\frac {e^{2 x}}{3+x}\right )}+\frac {9}{(3+x) \left (-x+9 \log \left (\frac {e^{2 x}}{3+x}\right )-6 x \log \left (\frac {e^{2 x}}{3+x}\right )-5 x^2 \log \left (\frac {e^{2 x}}{3+x}\right )+2 x^3 \log \left (\frac {e^{2 x}}{3+x}\right )+x^4 \log \left (\frac {e^{2 x}}{3+x}\right )\right )}+\frac {2 (-6+x)}{\left (-3+x+x^2\right ) \left (-x+9 \log \left (\frac {e^{2 x}}{3+x}\right )-6 x \log \left (\frac {e^{2 x}}{3+x}\right )-5 x^2 \log \left (\frac {e^{2 x}}{3+x}\right )+2 x^3 \log \left (\frac {e^{2 x}}{3+x}\right )+x^4 \log \left (\frac {e^{2 x}}{3+x}\right )\right )}\right ) \, dx \\ & = x-2 \log \left (3-x-x^2\right )-2 \int \frac {x^4}{-x+9 \log \left (\frac {e^{2 x}}{3+x}\right )-6 x \log \left (\frac {e^{2 x}}{3+x}\right )-5 x^2 \log \left (\frac {e^{2 x}}{3+x}\right )+2 x^3 \log \left (\frac {e^{2 x}}{3+x}\right )+x^4 \log \left (\frac {e^{2 x}}{3+x}\right )} \, dx+2 \int \frac {-6+x}{\left (-3+x+x^2\right ) \left (-x+9 \log \left (\frac {e^{2 x}}{3+x}\right )-6 x \log \left (\frac {e^{2 x}}{3+x}\right )-5 x^2 \log \left (\frac {e^{2 x}}{3+x}\right )+2 x^3 \log \left (\frac {e^{2 x}}{3+x}\right )+x^4 \log \left (\frac {e^{2 x}}{3+x}\right )\right )} \, dx-3 \int \frac {x^3}{-x+9 \log \left (\frac {e^{2 x}}{3+x}\right )-6 x \log \left (\frac {e^{2 x}}{3+x}\right )-5 x^2 \log \left (\frac {e^{2 x}}{3+x}\right )+2 x^3 \log \left (\frac {e^{2 x}}{3+x}\right )+x^4 \log \left (\frac {e^{2 x}}{3+x}\right )} \, dx+9 \int \frac {x^2}{-x+9 \log \left (\frac {e^{2 x}}{3+x}\right )-6 x \log \left (\frac {e^{2 x}}{3+x}\right )-5 x^2 \log \left (\frac {e^{2 x}}{3+x}\right )+2 x^3 \log \left (\frac {e^{2 x}}{3+x}\right )+x^4 \log \left (\frac {e^{2 x}}{3+x}\right )} \, dx+9 \int \frac {1}{(3+x) \left (-x+9 \log \left (\frac {e^{2 x}}{3+x}\right )-6 x \log \left (\frac {e^{2 x}}{3+x}\right )-5 x^2 \log \left (\frac {e^{2 x}}{3+x}\right )+2 x^3 \log \left (\frac {e^{2 x}}{3+x}\right )+x^4 \log \left (\frac {e^{2 x}}{3+x}\right )\right )} \, dx+10 \int \frac {x}{-x+9 \log \left (\frac {e^{2 x}}{3+x}\right )-6 x \log \left (\frac {e^{2 x}}{3+x}\right )-5 x^2 \log \left (\frac {e^{2 x}}{3+x}\right )+2 x^3 \log \left (\frac {e^{2 x}}{3+x}\right )+x^4 \log \left (\frac {e^{2 x}}{3+x}\right )} \, dx-21 \int \frac {1}{-x+9 \log \left (\frac {e^{2 x}}{3+x}\right )-6 x \log \left (\frac {e^{2 x}}{3+x}\right )-5 x^2 \log \left (\frac {e^{2 x}}{3+x}\right )+2 x^3 \log \left (\frac {e^{2 x}}{3+x}\right )+x^4 \log \left (\frac {e^{2 x}}{3+x}\right )} \, dx \\ & = x-2 \log \left (3-x-x^2\right )+2 \int \frac {-6+x}{\left (3-x-x^2\right ) \left (x-\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )\right )} \, dx-2 \int \frac {x^4}{-x+\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )} \, dx-3 \int \frac {x^3}{-x+\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )} \, dx+9 \int \frac {1}{(-3-x) \left (x-\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )\right )} \, dx+9 \int \frac {x^2}{-x+\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )} \, dx+10 \int \frac {x}{-x+\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )} \, dx-21 \int \frac {1}{-x+\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )} \, dx \\ & = x-2 \log \left (3-x-x^2\right )-2 \int \frac {x^4}{-x+\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )} \, dx+2 \int \left (-\frac {6}{\left (-3+x+x^2\right ) \left (-x+9 \log \left (\frac {e^{2 x}}{3+x}\right )-6 x \log \left (\frac {e^{2 x}}{3+x}\right )-5 x^2 \log \left (\frac {e^{2 x}}{3+x}\right )+2 x^3 \log \left (\frac {e^{2 x}}{3+x}\right )+x^4 \log \left (\frac {e^{2 x}}{3+x}\right )\right )}+\frac {x}{\left (-3+x+x^2\right ) \left (-x+9 \log \left (\frac {e^{2 x}}{3+x}\right )-6 x \log \left (\frac {e^{2 x}}{3+x}\right )-5 x^2 \log \left (\frac {e^{2 x}}{3+x}\right )+2 x^3 \log \left (\frac {e^{2 x}}{3+x}\right )+x^4 \log \left (\frac {e^{2 x}}{3+x}\right )\right )}\right ) \, dx-3 \int \frac {x^3}{-x+\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )} \, dx+9 \int \frac {1}{(-3-x) \left (x-\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )\right )} \, dx+9 \int \frac {x^2}{-x+\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )} \, dx+10 \int \frac {x}{-x+\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )} \, dx-21 \int \frac {1}{-x+\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )} \, dx \\ & = x-2 \log \left (3-x-x^2\right )+2 \int \frac {x}{\left (-3+x+x^2\right ) \left (-x+9 \log \left (\frac {e^{2 x}}{3+x}\right )-6 x \log \left (\frac {e^{2 x}}{3+x}\right )-5 x^2 \log \left (\frac {e^{2 x}}{3+x}\right )+2 x^3 \log \left (\frac {e^{2 x}}{3+x}\right )+x^4 \log \left (\frac {e^{2 x}}{3+x}\right )\right )} \, dx-2 \int \frac {x^4}{-x+\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )} \, dx-3 \int \frac {x^3}{-x+\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )} \, dx+9 \int \frac {1}{(-3-x) \left (x-\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )\right )} \, dx+9 \int \frac {x^2}{-x+\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )} \, dx+10 \int \frac {x}{-x+\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )} \, dx-12 \int \frac {1}{\left (-3+x+x^2\right ) \left (-x+9 \log \left (\frac {e^{2 x}}{3+x}\right )-6 x \log \left (\frac {e^{2 x}}{3+x}\right )-5 x^2 \log \left (\frac {e^{2 x}}{3+x}\right )+2 x^3 \log \left (\frac {e^{2 x}}{3+x}\right )+x^4 \log \left (\frac {e^{2 x}}{3+x}\right )\right )} \, dx-21 \int \frac {1}{-x+\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )} \, dx \\ & = x-2 \log \left (3-x-x^2\right )+2 \int \frac {x}{\left (3-x-x^2\right ) \left (x-\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )\right )} \, dx-2 \int \frac {x^4}{-x+\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )} \, dx-3 \int \frac {x^3}{-x+\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )} \, dx+9 \int \frac {1}{(-3-x) \left (x-\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )\right )} \, dx+9 \int \frac {x^2}{-x+\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )} \, dx+10 \int \frac {x}{-x+\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )} \, dx-12 \int \frac {1}{\left (3-x-x^2\right ) \left (x-\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )\right )} \, dx-21 \int \frac {1}{-x+\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )} \, dx \\ & = x-2 \log \left (3-x-x^2\right )-2 \int \frac {x^4}{-x+\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )} \, dx+2 \int \left (\frac {1+\frac {1}{\sqrt {13}}}{\left (-1-\sqrt {13}-2 x\right ) \left (x-\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )\right )}+\frac {1-\frac {1}{\sqrt {13}}}{\left (-1+\sqrt {13}-2 x\right ) \left (x-\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )\right )}\right ) \, dx-3 \int \frac {x^3}{-x+\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )} \, dx+9 \int \frac {1}{(-3-x) \left (x-\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )\right )} \, dx+9 \int \frac {x^2}{-x+\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )} \, dx+10 \int \frac {x}{-x+\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )} \, dx-12 \int \left (\frac {2}{\sqrt {13} \left (-1+\sqrt {13}-2 x\right ) \left (x-\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )\right )}+\frac {2}{\sqrt {13} \left (1+\sqrt {13}+2 x\right ) \left (x-\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )\right )}\right ) \, dx-21 \int \frac {1}{-x+\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )} \, dx \\ & = x-2 \log \left (3-x-x^2\right )-2 \int \frac {x^4}{-x+\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )} \, dx-3 \int \frac {x^3}{-x+\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )} \, dx+9 \int \frac {1}{(-3-x) \left (x-\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )\right )} \, dx+9 \int \frac {x^2}{-x+\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )} \, dx+10 \int \frac {x}{-x+\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )} \, dx-21 \int \frac {1}{-x+\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )} \, dx-\frac {24 \int \frac {1}{\left (-1+\sqrt {13}-2 x\right ) \left (x-\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )\right )} \, dx}{\sqrt {13}}-\frac {24 \int \frac {1}{\left (1+\sqrt {13}+2 x\right ) \left (x-\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )\right )} \, dx}{\sqrt {13}}+\frac {1}{13} \left (2 \left (13-\sqrt {13}\right )\right ) \int \frac {1}{\left (-1+\sqrt {13}-2 x\right ) \left (x-\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )\right )} \, dx+\frac {1}{13} \left (2 \left (13+\sqrt {13}\right )\right ) \int \frac {1}{\left (-1-\sqrt {13}-2 x\right ) \left (x-\left (-3+x+x^2\right )^2 \log \left (\frac {e^{2 x}}{3+x}\right )\right )} \, dx \\ \end{align*}
Leaf count is larger than twice the leaf count of optimal. \(217\) vs. \(2(30)=60\).
Time = 0.07 (sec) , antiderivative size = 217, normalized size of antiderivative = 7.23 \[ \int \frac {-42+10 x+36 x^2-9 x^4-2 x^5+\left (45+27 x-29 x^2-17 x^3+x^4+x^5\right ) \log \left (\frac {e^{2 x}}{3+x}\right )}{-3 x-x^2+\left (27-9 x-21 x^2+x^3+5 x^4+x^5\right ) \log \left (\frac {e^{2 x}}{3+x}\right )} \, dx=x-\log \left (17 x-12 x^2-10 x^3+4 x^4+2 x^5+9 \log \left (\frac {1}{3+x}\right )-6 x \log \left (\frac {1}{3+x}\right )-5 x^2 \log \left (\frac {1}{3+x}\right )+2 x^3 \log \left (\frac {1}{3+x}\right )+x^4 \log \left (\frac {1}{3+x}\right )+9 \left (-2 x-\log \left (\frac {1}{3+x}\right )+\log \left (\frac {e^{2 x}}{3+x}\right )\right )-6 x \left (-2 x-\log \left (\frac {1}{3+x}\right )+\log \left (\frac {e^{2 x}}{3+x}\right )\right )-5 x^2 \left (-2 x-\log \left (\frac {1}{3+x}\right )+\log \left (\frac {e^{2 x}}{3+x}\right )\right )+2 x^3 \left (-2 x-\log \left (\frac {1}{3+x}\right )+\log \left (\frac {e^{2 x}}{3+x}\right )\right )+x^4 \left (-2 x-\log \left (\frac {1}{3+x}\right )+\log \left (\frac {e^{2 x}}{3+x}\right )\right )\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. \(84\) vs. \(2(29)=58\).
Time = 0.86 (sec) , antiderivative size = 85, normalized size of antiderivative = 2.83
method | result | size |
parallelrisch | \(-6-\ln \left (\ln \left (\frac {{\mathrm e}^{2 x}}{3+x}\right ) x^{4}+2 \ln \left (\frac {{\mathrm e}^{2 x}}{3+x}\right ) x^{3}-5 \ln \left (\frac {{\mathrm e}^{2 x}}{3+x}\right ) x^{2}-6 x \ln \left (\frac {{\mathrm e}^{2 x}}{3+x}\right )+9 \ln \left (\frac {{\mathrm e}^{2 x}}{3+x}\right )-x \right )+x\) | \(85\) |
default | \(3+x -\ln \left (\ln \left (3+x \right ) \left (3+x \right )^{4}-2 \left (3+x \right )^{5}-\left (3+x \right )^{4} \left (\ln \left (\frac {{\mathrm e}^{2 x}}{3+x}\right )-2 x +\ln \left (3+x \right )\right )-10 \left (3+x \right )^{3} \ln \left (3+x \right )+26 \left (3+x \right )^{4}+10 \left (3+x \right )^{3} \left (\ln \left (\frac {{\mathrm e}^{2 x}}{3+x}\right )-2 x +\ln \left (3+x \right )\right )+31 \left (3+x \right )^{2} \ln \left (3+x \right )-122 \left (3+x \right )^{3}-31 \left (3+x \right )^{2} \left (\ln \left (\frac {{\mathrm e}^{2 x}}{3+x}\right )-2 x +\ln \left (3+x \right )\right )-30 \left (3+x \right ) \ln \left (3+x \right )+246 \left (3+x \right )^{2}+30 \left (3+x \right ) \left (\ln \left (\frac {{\mathrm e}^{2 x}}{3+x}\right )-2 x +\ln \left (3+x \right )\right )-540-179 x -9 \ln \left (\frac {{\mathrm e}^{2 x}}{3+x}\right )\right )\) | \(196\) |
risch | \(x -2 \ln \left (x^{2}+x -3\right )-\ln \left (\ln \left ({\mathrm e}^{2 x}\right )-\frac {i \left (-18 i \ln \left (3+x \right )+9 \pi \operatorname {csgn}\left (\frac {i {\mathrm e}^{2 x}}{3+x}\right )^{3}-2 i x -2 \pi \,x^{3} \operatorname {csgn}\left (i {\mathrm e}^{2 x}\right ) \operatorname {csgn}\left (\frac {i {\mathrm e}^{2 x}}{3+x}\right )^{2}+5 \pi \,x^{2} \operatorname {csgn}\left (i {\mathrm e}^{2 x}\right ) \operatorname {csgn}\left (\frac {i {\mathrm e}^{2 x}}{3+x}\right )^{2}+6 \pi x \,\operatorname {csgn}\left (i {\mathrm e}^{2 x}\right ) \operatorname {csgn}\left (\frac {i {\mathrm e}^{2 x}}{3+x}\right )^{2}-\pi \,x^{4} \operatorname {csgn}\left (\frac {i}{3+x}\right ) \operatorname {csgn}\left (\frac {i {\mathrm e}^{2 x}}{3+x}\right )^{2}+5 \pi \,x^{2} \operatorname {csgn}\left (\frac {i}{3+x}\right ) \operatorname {csgn}\left (\frac {i {\mathrm e}^{2 x}}{3+x}\right )^{2}+6 \pi x \,\operatorname {csgn}\left (\frac {i}{3+x}\right ) \operatorname {csgn}\left (\frac {i {\mathrm e}^{2 x}}{3+x}\right )^{2}-\pi \,x^{4} \operatorname {csgn}\left (i {\mathrm e}^{2 x}\right ) \operatorname {csgn}\left (\frac {i {\mathrm e}^{2 x}}{3+x}\right )^{2}-2 \pi \,x^{3} \operatorname {csgn}\left (\frac {i}{3+x}\right ) \operatorname {csgn}\left (\frac {i {\mathrm e}^{2 x}}{3+x}\right )^{2}+9 \pi \,\operatorname {csgn}\left (\frac {i}{3+x}\right ) \operatorname {csgn}\left (i {\mathrm e}^{2 x}\right ) \operatorname {csgn}\left (\frac {i {\mathrm e}^{2 x}}{3+x}\right )+\pi \,x^{4} \operatorname {csgn}\left (\frac {i}{3+x}\right ) \operatorname {csgn}\left (i {\mathrm e}^{2 x}\right ) \operatorname {csgn}\left (\frac {i {\mathrm e}^{2 x}}{3+x}\right )+2 \pi \,x^{3} \operatorname {csgn}\left (\frac {i}{3+x}\right ) \operatorname {csgn}\left (i {\mathrm e}^{2 x}\right ) \operatorname {csgn}\left (\frac {i {\mathrm e}^{2 x}}{3+x}\right )-5 \pi \,x^{2} \operatorname {csgn}\left (\frac {i}{3+x}\right ) \operatorname {csgn}\left (i {\mathrm e}^{2 x}\right ) \operatorname {csgn}\left (\frac {i {\mathrm e}^{2 x}}{3+x}\right )-6 \pi x \,\operatorname {csgn}\left (\frac {i}{3+x}\right ) \operatorname {csgn}\left (i {\mathrm e}^{2 x}\right ) \operatorname {csgn}\left (\frac {i {\mathrm e}^{2 x}}{3+x}\right )-2 i x^{4} \ln \left (3+x \right )+10 i x^{2} \ln \left (3+x \right )+12 i x \ln \left (3+x \right )-4 i x^{3} \ln \left (3+x \right )-9 \pi \,\operatorname {csgn}\left (\frac {i}{3+x}\right ) \operatorname {csgn}\left (\frac {i {\mathrm e}^{2 x}}{3+x}\right )^{2}-9 \pi \,\operatorname {csgn}\left (i {\mathrm e}^{2 x}\right ) \operatorname {csgn}\left (\frac {i {\mathrm e}^{2 x}}{3+x}\right )^{2}-5 \pi \,x^{2} \operatorname {csgn}\left (\frac {i {\mathrm e}^{2 x}}{3+x}\right )^{3}-6 \pi x \operatorname {csgn}\left (\frac {i {\mathrm e}^{2 x}}{3+x}\right )^{3}+\pi \,x^{4} \operatorname {csgn}\left (\frac {i {\mathrm e}^{2 x}}{3+x}\right )^{3}+2 \pi \,x^{3} \operatorname {csgn}\left (\frac {i {\mathrm e}^{2 x}}{3+x}\right )^{3}\right )}{2 \left (x^{4}+2 x^{3}-5 x^{2}-6 x +9\right )}\right )\) | \(652\) |
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Leaf count of result is larger than twice the leaf count of optimal. 69 vs. \(2 (29) = 58\).
Time = 0.26 (sec) , antiderivative size = 69, normalized size of antiderivative = 2.30 \[ \int \frac {-42+10 x+36 x^2-9 x^4-2 x^5+\left (45+27 x-29 x^2-17 x^3+x^4+x^5\right ) \log \left (\frac {e^{2 x}}{3+x}\right )}{-3 x-x^2+\left (27-9 x-21 x^2+x^3+5 x^4+x^5\right ) \log \left (\frac {e^{2 x}}{3+x}\right )} \, dx=x - 2 \, \log \left (x^{2} + x - 3\right ) - \log \left (\frac {{\left (x^{4} + 2 \, x^{3} - 5 \, x^{2} - 6 \, x + 9\right )} \log \left (\frac {e^{\left (2 \, x\right )}}{x + 3}\right ) - x}{x^{4} + 2 \, x^{3} - 5 \, x^{2} - 6 \, x + 9}\right ) \]
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Time = 0.55 (sec) , antiderivative size = 42, normalized size of antiderivative = 1.40 \[ \int \frac {-42+10 x+36 x^2-9 x^4-2 x^5+\left (45+27 x-29 x^2-17 x^3+x^4+x^5\right ) \log \left (\frac {e^{2 x}}{3+x}\right )}{-3 x-x^2+\left (27-9 x-21 x^2+x^3+5 x^4+x^5\right ) \log \left (\frac {e^{2 x}}{3+x}\right )} \, dx=x - \log {\left (- \frac {x}{x^{4} + 2 x^{3} - 5 x^{2} - 6 x + 9} + \log {\left (\frac {e^{2 x}}{x + 3} \right )} \right )} - 2 \log {\left (x^{2} + x - 3 \right )} \]
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Leaf count of result is larger than twice the leaf count of optimal. 84 vs. \(2 (29) = 58\).
Time = 0.26 (sec) , antiderivative size = 84, normalized size of antiderivative = 2.80 \[ \int \frac {-42+10 x+36 x^2-9 x^4-2 x^5+\left (45+27 x-29 x^2-17 x^3+x^4+x^5\right ) \log \left (\frac {e^{2 x}}{3+x}\right )}{-3 x-x^2+\left (27-9 x-21 x^2+x^3+5 x^4+x^5\right ) \log \left (\frac {e^{2 x}}{3+x}\right )} \, dx=x - 2 \, \log \left (x^{2} + x - 3\right ) - \log \left (-\frac {2 \, x^{5} + 4 \, x^{4} - 10 \, x^{3} - 12 \, x^{2} - {\left (x^{4} + 2 \, x^{3} - 5 \, x^{2} - 6 \, x + 9\right )} \log \left (x + 3\right ) + 17 \, x}{x^{4} + 2 \, x^{3} - 5 \, x^{2} - 6 \, x + 9}\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. 68 vs. \(2 (29) = 58\).
Time = 0.26 (sec) , antiderivative size = 68, normalized size of antiderivative = 2.27 \[ \int \frac {-42+10 x+36 x^2-9 x^4-2 x^5+\left (45+27 x-29 x^2-17 x^3+x^4+x^5\right ) \log \left (\frac {e^{2 x}}{3+x}\right )}{-3 x-x^2+\left (27-9 x-21 x^2+x^3+5 x^4+x^5\right ) \log \left (\frac {e^{2 x}}{3+x}\right )} \, dx=x - \log \left (-2 \, x^{5} + x^{4} \log \left (x + 3\right ) - 4 \, x^{4} + 2 \, x^{3} \log \left (x + 3\right ) + 10 \, x^{3} - 5 \, x^{2} \log \left (x + 3\right ) + 12 \, x^{2} - 6 \, x \log \left (x + 3\right ) - 17 \, x + 9 \, \log \left (x + 3\right )\right ) \]
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Timed out. \[ \int \frac {-42+10 x+36 x^2-9 x^4-2 x^5+\left (45+27 x-29 x^2-17 x^3+x^4+x^5\right ) \log \left (\frac {e^{2 x}}{3+x}\right )}{-3 x-x^2+\left (27-9 x-21 x^2+x^3+5 x^4+x^5\right ) \log \left (\frac {e^{2 x}}{3+x}\right )} \, dx=-\int \frac {10\,x+36\,x^2-9\,x^4-2\,x^5+\ln \left (\frac {{\mathrm {e}}^{2\,x}}{x+3}\right )\,\left (x^5+x^4-17\,x^3-29\,x^2+27\,x+45\right )-42}{3\,x+x^2-\ln \left (\frac {{\mathrm {e}}^{2\,x}}{x+3}\right )\,\left (x^5+5\,x^4+x^3-21\,x^2-9\,x+27\right )} \,d x \]
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