3.66.0 ∫ −x3−2x4+ex(−8x3−2e6x3−2x4)+e2x(18+e12(2−2x)−12x−12x2−2x3+e6(12−10x−4x2))+(x3+x4+ex(6x2+2e6x2+2x3)+e2x(9+e12+6x+x2+e6(6+2x))) log(x3+x4+ex(6x2+2e6x2+2x3)+e2x(9+e12+6x+x2+e6(6+2x)) x2 ) ____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ (x3+x4+ex(6x2+2e6x2+2x3)+e2x(9+e12+6x+x2+e6(6+2x))) log2(x3+x4+ex(6x2+2e6x2+2x3)+e2x(9+e12+6x+x2+e6(6+2x)) x2 ) dx [6539]

Integrand size = 318, antiderivative size = 24 \[ \int \frac {-x^3-2 x^4+e^x \left (-8 x^3-2 e^6 x^3-2 x^4\right )+e^{2 x} \left (18+e^{12} (2-2 x)-12 x-12 x^2-2 x^3+e^6 \left (12-10 x-4 x^2\right )\right )+\left (x^3+x^4+e^x \left (6 x^2+2 e^6 x^2+2 x^3\right )+e^{2 x} \left (9+e^{12}+6 x+x^2+e^6 (6+2 x)\right )\right ) \log \left (\frac {x^3+x^4+e^x \left (6 x^2+2 e^6 x^2+2 x^3\right )+e^{2 x} \left (9+e^{12}+6 x+x^2+e^6 (6+2 x)\right )}{x^2}\right )}{\left (x^3+x^4+e^x \left (6 x^2+2 e^6 x^2+2 x^3\right )+e^{2 x} \left (9+e^{12}+6 x+x^2+e^6 (6+2 x)\right )\right ) \log ^2\left (\frac {x^3+x^4+e^x \left (6 x^2+2 e^6 x^2+2 x^3\right )+e^{2 x} \left (9+e^{12}+6 x+x^2+e^6 (6+2 x)\right )}{x^2}\right )} \, dx=\frac {x}{\log \left (x+\left (x+\frac {e^x \left (3+e^6+x\right )}{x}\right )^2\right )} \]

Rubi [F]

\[ \int \frac {-x^3-2 x^4+e^x \left (-8 x^3-2 e^6 x^3-2 x^4\right )+e^{2 x} \left (18+e^{12} (2-2 x)-12 x-12 x^2-2 x^3+e^6 \left (12-10 x-4 x^2\right )\right )+\left (x^3+x^4+e^x \left (6 x^2+2 e^6 x^2+2 x^3\right )+e^{2 x} \left (9+e^{12}+6 x+x^2+e^6 (6+2 x)\right )\right ) \log \left (\frac {x^3+x^4+e^x \left (6 x^2+2 e^6 x^2+2 x^3\right )+e^{2 x} \left (9+e^{12}+6 x+x^2+e^6 (6+2 x)\right )}{x^2}\right )}{\left (x^3+x^4+e^x \left (6 x^2+2 e^6 x^2+2 x^3\right )+e^{2 x} \left (9+e^{12}+6 x+x^2+e^6 (6+2 x)\right )\right ) \log ^2\left (\frac {x^3+x^4+e^x \left (6 x^2+2 e^6 x^2+2 x^3\right )+e^{2 x} \left (9+e^{12}+6 x+x^2+e^6 (6+2 x)\right )}{x^2}\right )} \, dx=\int \frac {-x^3-2 x^4+e^x \left (-8 x^3-2 e^6 x^3-2 x^4\right )+e^{2 x} \left (18+e^{12} (2-2 x)-12 x-12 x^2-2 x^3+e^6 \left (12-10 x-4 x^2\right )\right )+\left (x^3+x^4+e^x \left (6 x^2+2 e^6 x^2+2 x^3\right )+e^{2 x} \left (9+e^{12}+6 x+x^2+e^6 (6+2 x)\right )\right ) \log \left (\frac {x^3+x^4+e^x \left (6 x^2+2 e^6 x^2+2 x^3\right )+e^{2 x} \left (9+e^{12}+6 x+x^2+e^6 (6+2 x)\right )}{x^2}\right )}{\left (x^3+x^4+e^x \left (6 x^2+2 e^6 x^2+2 x^3\right )+e^{2 x} \left (9+e^{12}+6 x+x^2+e^6 (6+2 x)\right )\right ) \log ^2\left (\frac {x^3+x^4+e^x \left (6 x^2+2 e^6 x^2+2 x^3\right )+e^{2 x} \left (9+e^{12}+6 x+x^2+e^6 (6+2 x)\right )}{x^2}\right )} \, dx \]

Rubi steps \begin{align*} \text {integral}& = \int \frac {-x^3-2 x^4-2 e^x x^3 \left (4+e^6+x\right )-2 e^{2 x} \left (-9+e^{12} (-1+x)+6 x+6 x^2+x^3+e^6 \left (-6+5 x+2 x^2\right )\right )+\left (x^3+x^4+2 e^x x^2 \left (3+e^6+x\right )+e^{2 x} \left (3+e^6+x\right )^2\right ) \log \left (x+x^2+2 e^x \left (3+e^6+x\right )+\frac {e^{2 x} \left (3+e^6+x\right )^2}{x^2}\right )}{\left (x^3+x^4+2 e^x x^2 \left (3+e^6+x\right )+e^{2 x} \left (3+e^6+x\right )^2\right ) \log ^2\left (x+x^2+2 e^x \left (3+e^6+x\right )+\frac {e^{2 x} \left (3+e^6+x\right )^2}{x^2}\right )} \, dx \\ & = \int \left (\frac {x^2 \left (-36 e^x \left (1+\frac {1}{9} e^6 \left (6+e^6\right )\right )-9 \left (1+\frac {e^6}{3}\right ) x+6 e^{6+x} \left (1+\frac {e^6}{3}\right ) x-7 \left (1+\frac {2 e^6}{7}\right ) x^2+10 e^x \left (1+\frac {2 e^6}{5}\right ) x^2+2 e^x x^3+6 \left (1+\frac {e^6}{3}\right ) x^3+2 x^4\right )}{\left (3+e^6+x\right ) \left (9 e^{2 x} \left (1+\frac {1}{9} e^6 \left (6+e^6\right )\right )+6 e^{2 x} \left (1+\frac {e^6}{3}\right ) x+e^{2 x} x^2+6 e^x \left (1+\frac {e^6}{3}\right ) x^2+x^3+2 e^x x^3+x^4\right ) \log ^2\left (x+x^2+2 e^x \left (3+e^6+x\right )+\frac {e^{2 x} \left (3+e^6+x\right )^2}{x^2}\right )}+\frac {6 \left (1+\frac {e^6}{3}\right )-6 \left (1+\frac {e^6}{3}\right ) x-2 x^2+3 \left (1+\frac {e^6}{3}\right ) \log \left (x+x^2+2 e^x \left (3+e^6+x\right )+\frac {e^{2 x} \left (3+e^6+x\right )^2}{x^2}\right )+x \log \left (x+x^2+2 e^x \left (3+e^6+x\right )+\frac {e^{2 x} \left (3+e^6+x\right )^2}{x^2}\right )}{\left (3+e^6+x\right ) \log ^2\left (x+x^2+2 e^x \left (3+e^6+x\right )+\frac {e^{2 x} \left (3+e^6+x\right )^2}{x^2}\right )}\right ) \, dx \\ & = \int \frac {x^2 \left (-36 e^x \left (1+\frac {1}{9} e^6 \left (6+e^6\right )\right )-9 \left (1+\frac {e^6}{3}\right ) x+6 e^{6+x} \left (1+\frac {e^6}{3}\right ) x-7 \left (1+\frac {2 e^6}{7}\right ) x^2+10 e^x \left (1+\frac {2 e^6}{5}\right ) x^2+2 e^x x^3+6 \left (1+\frac {e^6}{3}\right ) x^3+2 x^4\right )}{\left (3+e^6+x\right ) \left (9 e^{2 x} \left (1+\frac {1}{9} e^6 \left (6+e^6\right )\right )+6 e^{2 x} \left (1+\frac {e^6}{3}\right ) x+e^{2 x} x^2+6 e^x \left (1+\frac {e^6}{3}\right ) x^2+x^3+2 e^x x^3+x^4\right ) \log ^2\left (x+x^2+2 e^x \left (3+e^6+x\right )+\frac {e^{2 x} \left (3+e^6+x\right )^2}{x^2}\right )} \, dx+\int \frac {6 \left (1+\frac {e^6}{3}\right )-6 \left (1+\frac {e^6}{3}\right ) x-2 x^2+3 \left (1+\frac {e^6}{3}\right ) \log \left (x+x^2+2 e^x \left (3+e^6+x\right )+\frac {e^{2 x} \left (3+e^6+x\right )^2}{x^2}\right )+x \log \left (x+x^2+2 e^x \left (3+e^6+x\right )+\frac {e^{2 x} \left (3+e^6+x\right )^2}{x^2}\right )}{\left (3+e^6+x\right ) \log ^2\left (x+x^2+2 e^x \left (3+e^6+x\right )+\frac {e^{2 x} \left (3+e^6+x\right )^2}{x^2}\right )} \, dx \\ & = \int \frac {x^2 \left (2 e^{12+x} (-2+x)+e^6 x \left (-3-2 x+2 x^2\right )+e^{6+x} \left (-24+6 x+4 x^2\right )+2 e^x \left (-18+5 x^2+x^3\right )+x \left (-9-7 x+6 x^2+2 x^3\right )\right )}{\left (3+e^6+x\right ) \left (e^{2 (6+x)}+2 e^{6+x} x^2+x^3 (1+x)+2 e^{6+2 x} (3+x)+2 e^x x^2 (3+x)+e^{2 x} (3+x)^2\right ) \log ^2\left (x+x^2+2 e^x \left (3+e^6+x\right )+\frac {e^{2 x} \left (3+e^6+x\right )^2}{x^2}\right )} \, dx+\int \frac {-\frac {2 \left (-3+e^6 (-1+x)+3 x+x^2\right )}{3+e^6+x}+\log \left (x+x^2+2 e^x \left (3+e^6+x\right )+\frac {e^{2 x} \left (3+e^6+x\right )^2}{x^2}\right )}{\log ^2\left (x+x^2+2 e^x \left (3+e^6+x\right )+\frac {e^{2 x} \left (3+e^6+x\right )^2}{x^2}\right )} \, dx \\ & = \int \left (\frac {3 \left (1+\frac {e^6}{3}\right ) \left (36 e^x \left (1+\frac {1}{9} e^6 \left (6+e^6\right )\right )+9 \left (1+\frac {e^6}{3}\right ) x-6 e^{6+x} \left (1+\frac {e^6}{3}\right ) x+7 \left (1+\frac {2 e^6}{7}\right ) x^2-10 e^x \left (1+\frac {2 e^6}{5}\right ) x^2-2 e^x x^3-6 \left (1+\frac {e^6}{3}\right ) x^3-2 x^4\right )}{\left (9 e^{2 x} \left (1+\frac {1}{9} e^6 \left (6+e^6\right )\right )+6 e^{2 x} \left (1+\frac {e^6}{3}\right ) x+e^{2 x} x^2+6 e^x \left (1+\frac {e^6}{3}\right ) x^2+x^3+2 e^x x^3+x^4\right ) \log ^2\left (x+x^2+2 e^x \left (3+e^6+x\right )+\frac {e^{2 x} \left (3+e^6+x\right )^2}{x^2}\right )}+\frac {x \left (-36 e^x \left (1+\frac {1}{9} e^6 \left (6+e^6\right )\right )-9 \left (1+\frac {e^6}{3}\right ) x+6 e^{6+x} \left (1+\frac {e^6}{3}\right ) x-7 \left (1+\frac {2 e^6}{7}\right ) x^2+10 e^x \left (1+\frac {2 e^6}{5}\right ) x^2+2 e^x x^3+6 \left (1+\frac {e^6}{3}\right ) x^3+2 x^4\right )}{\left (9 e^{2 x} \left (1+\frac {1}{9} e^6 \left (6+e^6\right )\right )+6 e^{2 x} \left (1+\frac {e^6}{3}\right ) x+e^{2 x} x^2+6 e^x \left (1+\frac {e^6}{3}\right ) x^2+x^3+2 e^x x^3+x^4\right ) \log ^2\left (x+x^2+2 e^x \left (3+e^6+x\right )+\frac {e^{2 x} \left (3+e^6+x\right )^2}{x^2}\right )}+\frac {\left (3+e^6\right )^2 \left (-36 e^x \left (1+\frac {1}{9} e^6 \left (6+e^6\right )\right )-9 \left (1+\frac {e^6}{3}\right ) x+6 e^{6+x} \left (1+\frac {e^6}{3}\right ) x-7 \left (1+\frac {2 e^6}{7}\right ) x^2+10 e^x \left (1+\frac {2 e^6}{5}\right ) x^2+2 e^x x^3+6 \left (1+\frac {e^6}{3}\right ) x^3+2 x^4\right )}{\left (3+e^6+x\right ) \left (9 e^{2 x} \left (1+\frac {1}{9} e^6 \left (6+e^6\right )\right )+6 e^{2 x} \left (1+\frac {e^6}{3}\right ) x+e^{2 x} x^2+6 e^x \left (1+\frac {e^6}{3}\right ) x^2+x^3+2 e^x x^3+x^4\right ) \log ^2\left (x+x^2+2 e^x \left (3+e^6+x\right )+\frac {e^{2 x} \left (3+e^6+x\right )^2}{x^2}\right )}\right ) \, dx+\int \left (\frac {2 \left (3+e^6-\left (3+e^6\right ) x-x^2\right )}{\left (3+e^6+x\right ) \log ^2\left (x+x^2+2 e^x \left (3+e^6+x\right )+\frac {e^{2 x} \left (3+e^6+x\right )^2}{x^2}\right )}+\frac {1}{\log \left (x+x^2+2 e^x \left (3+e^6+x\right )+\frac {e^{2 x} \left (3+e^6+x\right )^2}{x^2}\right )}\right ) \, dx \\ & = 2 \int \frac {3+e^6-\left (3+e^6\right ) x-x^2}{\left (3+e^6+x\right ) \log ^2\left (x+x^2+2 e^x \left (3+e^6+x\right )+\frac {e^{2 x} \left (3+e^6+x\right )^2}{x^2}\right )} \, dx+\left (3+e^6\right ) \int \frac {36 e^x \left (1+\frac {1}{9} e^6 \left (6+e^6\right )\right )+9 \left (1+\frac {e^6}{3}\right ) x-6 e^{6+x} \left (1+\frac {e^6}{3}\right ) x+7 \left (1+\frac {2 e^6}{7}\right ) x^2-10 e^x \left (1+\frac {2 e^6}{5}\right ) x^2-2 e^x x^3-6 \left (1+\frac {e^6}{3}\right ) x^3-2 x^4}{\left (9 e^{2 x} \left (1+\frac {1}{9} e^6 \left (6+e^6\right )\right )+6 e^{2 x} \left (1+\frac {e^6}{3}\right ) x+e^{2 x} x^2+6 e^x \left (1+\frac {e^6}{3}\right ) x^2+x^3+2 e^x x^3+x^4\right ) \log ^2\left (x+x^2+2 e^x \left (3+e^6+x\right )+\frac {e^{2 x} \left (3+e^6+x\right )^2}{x^2}\right )} \, dx+\left (3+e^6\right )^2 \int \frac {-36 e^x \left (1+\frac {1}{9} e^6 \left (6+e^6\right )\right )-9 \left (1+\frac {e^6}{3}\right ) x+6 e^{6+x} \left (1+\frac {e^6}{3}\right ) x-7 \left (1+\frac {2 e^6}{7}\right ) x^2+10 e^x \left (1+\frac {2 e^6}{5}\right ) x^2+2 e^x x^3+6 \left (1+\frac {e^6}{3}\right ) x^3+2 x^4}{\left (3+e^6+x\right ) \left (9 e^{2 x} \left (1+\frac {1}{9} e^6 \left (6+e^6\right )\right )+6 e^{2 x} \left (1+\frac {e^6}{3}\right ) x+e^{2 x} x^2+6 e^x \left (1+\frac {e^6}{3}\right ) x^2+x^3+2 e^x x^3+x^4\right ) \log ^2\left (x+x^2+2 e^x \left (3+e^6+x\right )+\frac {e^{2 x} \left (3+e^6+x\right )^2}{x^2}\right )} \, dx+\int \frac {x \left (-36 e^x \left (1+\frac {1}{9} e^6 \left (6+e^6\right )\right )-9 \left (1+\frac {e^6}{3}\right ) x+6 e^{6+x} \left (1+\frac {e^6}{3}\right ) x-7 \left (1+\frac {2 e^6}{7}\right ) x^2+10 e^x \left (1+\frac {2 e^6}{5}\right ) x^2+2 e^x x^3+6 \left (1+\frac {e^6}{3}\right ) x^3+2 x^4\right )}{\left (9 e^{2 x} \left (1+\frac {1}{9} e^6 \left (6+e^6\right )\right )+6 e^{2 x} \left (1+\frac {e^6}{3}\right ) x+e^{2 x} x^2+6 e^x \left (1+\frac {e^6}{3}\right ) x^2+x^3+2 e^x x^3+x^4\right ) \log ^2\left (x+x^2+2 e^x \left (3+e^6+x\right )+\frac {e^{2 x} \left (3+e^6+x\right )^2}{x^2}\right )} \, dx+\int \frac {1}{\log \left (x+x^2+2 e^x \left (3+e^6+x\right )+\frac {e^{2 x} \left (3+e^6+x\right )^2}{x^2}\right )} \, dx \\ & = 2 \int \left (-\frac {x}{\log ^2\left (x+x^2+2 e^x \left (3+e^6+x\right )+\frac {e^{2 x} \left (3+e^6+x\right )^2}{x^2}\right )}+\frac {3+e^6}{\left (3+e^6+x\right ) \log ^2\left (x+x^2+2 e^x \left (3+e^6+x\right )+\frac {e^{2 x} \left (3+e^6+x\right )^2}{x^2}\right )}\right ) \, dx+\left (3+e^6\right ) \int \frac {-2 e^{12+x} (-2+x)+e^{6+x} \left (24-6 x-4 x^2\right )+e^6 x \left (3+2 x-2 x^2\right )+x \left (9+7 x-6 x^2-2 x^3\right )-2 e^x \left (-18+5 x^2+x^3\right )}{\left (e^{2 (6+x)}+2 e^{6+x} x^2+x^3 (1+x)+2 e^{6+2 x} (3+x)+2 e^x x^2 (3+x)+e^{2 x} (3+x)^2\right ) \log ^2\left (x+x^2+2 e^x \left (3+e^6+x\right )+\frac {e^{2 x} \left (3+e^6+x\right )^2}{x^2}\right )} \, dx+\left (3+e^6\right )^2 \int \frac {2 e^{12+x} (-2+x)+e^6 x \left (-3-2 x+2 x^2\right )+e^{6+x} \left (-24+6 x+4 x^2\right )+2 e^x \left (-18+5 x^2+x^3\right )+x \left (-9-7 x+6 x^2+2 x^3\right )}{\left (3+e^6+x\right ) \left (e^{2 (6+x)}+2 e^{6+x} x^2+x^3 (1+x)+2 e^{6+2 x} (3+x)+2 e^x x^2 (3+x)+e^{2 x} (3+x)^2\right ) \log ^2\left (x+x^2+2 e^x \left (3+e^6+x\right )+\frac {e^{2 x} \left (3+e^6+x\right )^2}{x^2}\right )} \, dx+\int \frac {x \left (2 e^{12+x} (-2+x)+e^6 x \left (-3-2 x+2 x^2\right )+e^{6+x} \left (-24+6 x+4 x^2\right )+2 e^x \left (-18+5 x^2+x^3\right )+x \left (-9-7 x+6 x^2+2 x^3\right )\right )}{\left (e^{2 (6+x)}+2 e^{6+x} x^2+x^3 (1+x)+2 e^{6+2 x} (3+x)+2 e^x x^2 (3+x)+e^{2 x} (3+x)^2\right ) \log ^2\left (x+x^2+2 e^x \left (3+e^6+x\right )+\frac {e^{2 x} \left (3+e^6+x\right )^2}{x^2}\right )} \, dx+\int \frac {1}{\log \left (x+x^2+2 e^x \left (3+e^6+x\right )+\frac {e^{2 x} \left (3+e^6+x\right )^2}{x^2}\right )} \, dx \\ & = \text {Too large to display} \\ \end{align*}

Mathematica [A] (veriﬁed)

Time = 0.21 (sec) , antiderivative size = 38, normalized size of antiderivative = 1.58 \[ \int \frac {-x^3-2 x^4+e^x \left (-8 x^3-2 e^6 x^3-2 x^4\right )+e^{2 x} \left (18+e^{12} (2-2 x)-12 x-12 x^2-2 x^3+e^6 \left (12-10 x-4 x^2\right )\right )+\left (x^3+x^4+e^x \left (6 x^2+2 e^6 x^2+2 x^3\right )+e^{2 x} \left (9+e^{12}+6 x+x^2+e^6 (6+2 x)\right )\right ) \log \left (\frac {x^3+x^4+e^x \left (6 x^2+2 e^6 x^2+2 x^3\right )+e^{2 x} \left (9+e^{12}+6 x+x^2+e^6 (6+2 x)\right )}{x^2}\right )}{\left (x^3+x^4+e^x \left (6 x^2+2 e^6 x^2+2 x^3\right )+e^{2 x} \left (9+e^{12}+6 x+x^2+e^6 (6+2 x)\right )\right ) \log ^2\left (\frac {x^3+x^4+e^x \left (6 x^2+2 e^6 x^2+2 x^3\right )+e^{2 x} \left (9+e^{12}+6 x+x^2+e^6 (6+2 x)\right )}{x^2}\right )} \, dx=\frac {x}{\log \left (x+x^2+2 e^x \left (3+e^6+x\right )+\frac {e^{2 x} \left (3+e^6+x\right )^2}{x^2}\right )} \]

Maple [B] (veriﬁed)

Leaf count of result is larger than twice the leaf count of optimal. \(62\) vs. \(2(22)=44\).

Time = 7.45 (sec) , antiderivative size = 63, normalized size of antiderivative = 2.62


method	result	size

parallelrisch	\(\frac {x}{\ln \left (\frac {\left ({\mathrm e}^{12}+\left (2 x +6\right ) {\mathrm e}^{6}+x^{2}+6 x +9\right ) {\mathrm e}^{2 x}+\left (2 x^{2} {\mathrm e}^{6}+2 x^{3}+6 x^{2}\right ) {\mathrm e}^{x}+x^{4}+x^{3}}{x^{2}}\right )}\)	\(63\)
risch	\(-\frac {2 i x}{\pi \,\operatorname {csgn}\left (i \left (2 x^{2} {\mathrm e}^{6+x}+2 \,{\mathrm e}^{x} x^{3}+x^{4}+6 \,{\mathrm e}^{x} x^{2}+2 x \,{\mathrm e}^{2 x +6}+{\mathrm e}^{2 x} x^{2}+x^{3}+{\mathrm e}^{2 x +12}+6 \,{\mathrm e}^{2 x +6}+6 x \,{\mathrm e}^{2 x}+9 \,{\mathrm e}^{2 x}\right )\right ) {\operatorname {csgn}\left (\frac {i \left (2 x^{2} {\mathrm e}^{6+x}+2 \,{\mathrm e}^{x} x^{3}+x^{4}+6 \,{\mathrm e}^{x} x^{2}+2 x \,{\mathrm e}^{2 x +6}+{\mathrm e}^{2 x} x^{2}+x^{3}+{\mathrm e}^{2 x +12}+6 \,{\mathrm e}^{2 x +6}+6 x \,{\mathrm e}^{2 x}+9 \,{\mathrm e}^{2 x}\right )}{x^{2}}\right )}^{2}-\pi \,\operatorname {csgn}\left (i \left (2 x^{2} {\mathrm e}^{6+x}+2 \,{\mathrm e}^{x} x^{3}+x^{4}+6 \,{\mathrm e}^{x} x^{2}+2 x \,{\mathrm e}^{2 x +6}+{\mathrm e}^{2 x} x^{2}+x^{3}+{\mathrm e}^{2 x +12}+6 \,{\mathrm e}^{2 x +6}+6 x \,{\mathrm e}^{2 x}+9 \,{\mathrm e}^{2 x}\right )\right ) \operatorname {csgn}\left (\frac {i \left (2 x^{2} {\mathrm e}^{6+x}+2 \,{\mathrm e}^{x} x^{3}+x^{4}+6 \,{\mathrm e}^{x} x^{2}+2 x \,{\mathrm e}^{2 x +6}+{\mathrm e}^{2 x} x^{2}+x^{3}+{\mathrm e}^{2 x +12}+6 \,{\mathrm e}^{2 x +6}+6 x \,{\mathrm e}^{2 x}+9 \,{\mathrm e}^{2 x}\right )}{x^{2}}\right ) \operatorname {csgn}\left (\frac {i}{x^{2}}\right )-\pi {\operatorname {csgn}\left (\frac {i \left (2 x^{2} {\mathrm e}^{6+x}+2 \,{\mathrm e}^{x} x^{3}+x^{4}+6 \,{\mathrm e}^{x} x^{2}+2 x \,{\mathrm e}^{2 x +6}+{\mathrm e}^{2 x} x^{2}+x^{3}+{\mathrm e}^{2 x +12}+6 \,{\mathrm e}^{2 x +6}+6 x \,{\mathrm e}^{2 x}+9 \,{\mathrm e}^{2 x}\right )}{x^{2}}\right )}^{3}+\pi {\operatorname {csgn}\left (\frac {i \left (2 x^{2} {\mathrm e}^{6+x}+2 \,{\mathrm e}^{x} x^{3}+x^{4}+6 \,{\mathrm e}^{x} x^{2}+2 x \,{\mathrm e}^{2 x +6}+{\mathrm e}^{2 x} x^{2}+x^{3}+{\mathrm e}^{2 x +12}+6 \,{\mathrm e}^{2 x +6}+6 x \,{\mathrm e}^{2 x}+9 \,{\mathrm e}^{2 x}\right )}{x^{2}}\right )}^{2} \operatorname {csgn}\left (\frac {i}{x^{2}}\right )+\pi \operatorname {csgn}\left (i x \right )^{2} \operatorname {csgn}\left (i x^{2}\right )-2 \pi \,\operatorname {csgn}\left (i x \right ) \operatorname {csgn}\left (i x^{2}\right )^{2}+\pi \operatorname {csgn}\left (i x^{2}\right )^{3}+4 i \ln \left (x \right )-2 i \ln \left (2 x^{2} {\mathrm e}^{6+x}+2 \,{\mathrm e}^{x} x^{3}+x^{4}+6 \,{\mathrm e}^{x} x^{2}+2 x \,{\mathrm e}^{2 x +6}+{\mathrm e}^{2 x} x^{2}+x^{3}+{\mathrm e}^{2 x +12}+6 \,{\mathrm e}^{2 x +6}+6 x \,{\mathrm e}^{2 x}+9 \,{\mathrm e}^{2 x}\right )}\)	\(645\)

Fricas [B] (veriﬁcation not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 57 vs. \(2 (22) = 44\).

Time = 0.29 (sec) , antiderivative size = 57, normalized size of antiderivative = 2.38 \[ \int \frac {-x^3-2 x^4+e^x \left (-8 x^3-2 e^6 x^3-2 x^4\right )+e^{2 x} \left (18+e^{12} (2-2 x)-12 x-12 x^2-2 x^3+e^6 \left (12-10 x-4 x^2\right )\right )+\left (x^3+x^4+e^x \left (6 x^2+2 e^6 x^2+2 x^3\right )+e^{2 x} \left (9+e^{12}+6 x+x^2+e^6 (6+2 x)\right )\right ) \log \left (\frac {x^3+x^4+e^x \left (6 x^2+2 e^6 x^2+2 x^3\right )+e^{2 x} \left (9+e^{12}+6 x+x^2+e^6 (6+2 x)\right )}{x^2}\right )}{\left (x^3+x^4+e^x \left (6 x^2+2 e^6 x^2+2 x^3\right )+e^{2 x} \left (9+e^{12}+6 x+x^2+e^6 (6+2 x)\right )\right ) \log ^2\left (\frac {x^3+x^4+e^x \left (6 x^2+2 e^6 x^2+2 x^3\right )+e^{2 x} \left (9+e^{12}+6 x+x^2+e^6 (6+2 x)\right )}{x^2}\right )} \, dx=\frac {x}{\log \left (\frac {x^{4} + x^{3} + {\left (x^{2} + 2 \, {\left (x + 3\right )} e^{6} + 6 \, x + e^{12} + 9\right )} e^{\left (2 \, x\right )} + 2 \, {\left (x^{3} + x^{2} e^{6} + 3 \, x^{2}\right )} e^{x}}{x^{2}}\right )} \]

Sympy [B] (veriﬁcation not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 60 vs. \(2 (19) = 38\).

Time = 0.68 (sec) , antiderivative size = 60, normalized size of antiderivative = 2.50 \[ \int \frac {-x^3-2 x^4+e^x \left (-8 x^3-2 e^6 x^3-2 x^4\right )+e^{2 x} \left (18+e^{12} (2-2 x)-12 x-12 x^2-2 x^3+e^6 \left (12-10 x-4 x^2\right )\right )+\left (x^3+x^4+e^x \left (6 x^2+2 e^6 x^2+2 x^3\right )+e^{2 x} \left (9+e^{12}+6 x+x^2+e^6 (6+2 x)\right )\right ) \log \left (\frac {x^3+x^4+e^x \left (6 x^2+2 e^6 x^2+2 x^3\right )+e^{2 x} \left (9+e^{12}+6 x+x^2+e^6 (6+2 x)\right )}{x^2}\right )}{\left (x^3+x^4+e^x \left (6 x^2+2 e^6 x^2+2 x^3\right )+e^{2 x} \left (9+e^{12}+6 x+x^2+e^6 (6+2 x)\right )\right ) \log ^2\left (\frac {x^3+x^4+e^x \left (6 x^2+2 e^6 x^2+2 x^3\right )+e^{2 x} \left (9+e^{12}+6 x+x^2+e^6 (6+2 x)\right )}{x^2}\right )} \, dx=\frac {x}{\log {\left (\frac {x^{4} + x^{3} + \left (2 x^{3} + 6 x^{2} + 2 x^{2} e^{6}\right ) e^{x} + \left (x^{2} + 6 x + \left (2 x + 6\right ) e^{6} + 9 + e^{12}\right ) e^{2 x}}{x^{2}} \right )}} \]

Maxima [B] (veriﬁcation not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 56 vs. \(2 (22) = 44\).

Time = 4.00 (sec) , antiderivative size = 56, normalized size of antiderivative = 2.33 \[ \int \frac {-x^3-2 x^4+e^x \left (-8 x^3-2 e^6 x^3-2 x^4\right )+e^{2 x} \left (18+e^{12} (2-2 x)-12 x-12 x^2-2 x^3+e^6 \left (12-10 x-4 x^2\right )\right )+\left (x^3+x^4+e^x \left (6 x^2+2 e^6 x^2+2 x^3\right )+e^{2 x} \left (9+e^{12}+6 x+x^2+e^6 (6+2 x)\right )\right ) \log \left (\frac {x^3+x^4+e^x \left (6 x^2+2 e^6 x^2+2 x^3\right )+e^{2 x} \left (9+e^{12}+6 x+x^2+e^6 (6+2 x)\right )}{x^2}\right )}{\left (x^3+x^4+e^x \left (6 x^2+2 e^6 x^2+2 x^3\right )+e^{2 x} \left (9+e^{12}+6 x+x^2+e^6 (6+2 x)\right )\right ) \log ^2\left (\frac {x^3+x^4+e^x \left (6 x^2+2 e^6 x^2+2 x^3\right )+e^{2 x} \left (9+e^{12}+6 x+x^2+e^6 (6+2 x)\right )}{x^2}\right )} \, dx=\frac {x}{\log \left (x^{4} + x^{3} + {\left (x^{2} + 2 \, x {\left (e^{6} + 3\right )} + e^{12} + 6 \, e^{6} + 9\right )} e^{\left (2 \, x\right )} + 2 \, {\left (x^{3} + x^{2} {\left (e^{6} + 3\right )}\right )} e^{x}\right ) - 2 \, \log \left (x\right )} \]

Giac [B] (veriﬁcation not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 86 vs. \(2 (22) = 44\).

Time = 5.91 (sec) , antiderivative size = 86, normalized size of antiderivative = 3.58 \[ \int \frac {-x^3-2 x^4+e^x \left (-8 x^3-2 e^6 x^3-2 x^4\right )+e^{2 x} \left (18+e^{12} (2-2 x)-12 x-12 x^2-2 x^3+e^6 \left (12-10 x-4 x^2\right )\right )+\left (x^3+x^4+e^x \left (6 x^2+2 e^6 x^2+2 x^3\right )+e^{2 x} \left (9+e^{12}+6 x+x^2+e^6 (6+2 x)\right )\right ) \log \left (\frac {x^3+x^4+e^x \left (6 x^2+2 e^6 x^2+2 x^3\right )+e^{2 x} \left (9+e^{12}+6 x+x^2+e^6 (6+2 x)\right )}{x^2}\right )}{\left (x^3+x^4+e^x \left (6 x^2+2 e^6 x^2+2 x^3\right )+e^{2 x} \left (9+e^{12}+6 x+x^2+e^6 (6+2 x)\right )\right ) \log ^2\left (\frac {x^3+x^4+e^x \left (6 x^2+2 e^6 x^2+2 x^3\right )+e^{2 x} \left (9+e^{12}+6 x+x^2+e^6 (6+2 x)\right )}{x^2}\right )} \, dx=\frac {x}{\log \left (x^{4} + 2 \, x^{3} e^{x} + x^{3} + x^{2} e^{\left (2 \, x\right )} + 2 \, x^{2} e^{\left (x + 6\right )} + 6 \, x^{2} e^{x} + 6 \, x e^{\left (2 \, x\right )} + 2 \, x e^{\left (2 \, x + 6\right )} + 9 \, e^{\left (2 \, x\right )} + e^{\left (2 \, x + 12\right )} + 6 \, e^{\left (2 \, x + 6\right )}\right ) - \log \left (x^{2}\right )} \]

Mupad [F(-1)]

Timed out. \[ \int \frac {-x^3-2 x^4+e^x \left (-8 x^3-2 e^6 x^3-2 x^4\right )+e^{2 x} \left (18+e^{12} (2-2 x)-12 x-12 x^2-2 x^3+e^6 \left (12-10 x-4 x^2\right )\right )+\left (x^3+x^4+e^x \left (6 x^2+2 e^6 x^2+2 x^3\right )+e^{2 x} \left (9+e^{12}+6 x+x^2+e^6 (6+2 x)\right )\right ) \log \left (\frac {x^3+x^4+e^x \left (6 x^2+2 e^6 x^2+2 x^3\right )+e^{2 x} \left (9+e^{12}+6 x+x^2+e^6 (6+2 x)\right )}{x^2}\right )}{\left (x^3+x^4+e^x \left (6 x^2+2 e^6 x^2+2 x^3\right )+e^{2 x} \left (9+e^{12}+6 x+x^2+e^6 (6+2 x)\right )\right ) \log ^2\left (\frac {x^3+x^4+e^x \left (6 x^2+2 e^6 x^2+2 x^3\right )+e^{2 x} \left (9+e^{12}+6 x+x^2+e^6 (6+2 x)\right )}{x^2}\right )} \, dx=-\int \frac {{\mathrm {e}}^{2\,x}\,\left (12\,x+{\mathrm {e}}^6\,\left (4\,x^2+10\,x-12\right )+12\,x^2+2\,x^3+{\mathrm {e}}^{12}\,\left (2\,x-2\right )-18\right )-\ln \left (\frac {{\mathrm {e}}^{2\,x}\,\left (6\,x+{\mathrm {e}}^{12}+x^2+{\mathrm {e}}^6\,\left (2\,x+6\right )+9\right )+{\mathrm {e}}^x\,\left (2\,x^2\,{\mathrm {e}}^6+6\,x^2+2\,x^3\right )+x^3+x^4}{x^2}\right )\,\left ({\mathrm {e}}^{2\,x}\,\left (6\,x+{\mathrm {e}}^{12}+x^2+{\mathrm {e}}^6\,\left (2\,x+6\right )+9\right )+{\mathrm {e}}^x\,\left (2\,x^2\,{\mathrm {e}}^6+6\,x^2+2\,x^3\right )+x^3+x^4\right )+{\mathrm {e}}^x\,\left (2\,x^3\,{\mathrm {e}}^6+8\,x^3+2\,x^4\right )+x^3+2\,x^4}{{\ln \left (\frac {{\mathrm {e}}^{2\,x}\,\left (6\,x+{\mathrm {e}}^{12}+x^2+{\mathrm {e}}^6\,\left (2\,x+6\right )+9\right )+{\mathrm {e}}^x\,\left (2\,x^2\,{\mathrm {e}}^6+6\,x^2+2\,x^3\right )+x^3+x^4}{x^2}\right )}^2\,\left ({\mathrm {e}}^{2\,x}\,\left (6\,x+{\mathrm {e}}^{12}+x^2+{\mathrm {e}}^6\,\left (2\,x+6\right )+9\right )+{\mathrm {e}}^x\,\left (2\,x^2\,{\mathrm {e}}^6+6\,x^2+2\,x^3\right )+x^3+x^4\right )} \,d x \]

Optimal result