Integrand size = 237, antiderivative size = 27 \[ \int \frac {e^x \left (-x-x^2\right )+4 e^{5 x} x \log ^3(1+x)+e^{5 x} \left (4 x+4 x^2\right ) \log ^4(1+x)+\left (e^x \left (-x-x^2\right )+e^{5 x} (1+x) \log ^4(1+x)\right ) \log \left (\frac {1}{3} \left (2 x-2 e^{4 x} \log ^4(1+x)\right )\right )+\left (e^x \left (-x^2-x^3\right )+e^{5 x} \left (x+x^2\right ) \log ^4(1+x)\right ) \log \left (\frac {1}{3} \left (2 x-2 e^{4 x} \log ^4(1+x)\right )\right ) \log \left (x \log \left (\frac {1}{3} \left (2 x-2 e^{4 x} \log ^4(1+x)\right )\right )\right )}{\left (-x^2-x^3+e^{4 x} \left (x+x^2\right ) \log ^4(1+x)\right ) \log \left (\frac {1}{3} \left (2 x-2 e^{4 x} \log ^4(1+x)\right )\right )} \, dx=e^x \log \left (x \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )\right ) \]
[Out]
Time = 23.45 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.00, number of steps used = 41, number of rules used = 6, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.025, Rules used = {6873, 6874, 6820, 2209, 2225, 2635} \[ \int \frac {e^x \left (-x-x^2\right )+4 e^{5 x} x \log ^3(1+x)+e^{5 x} \left (4 x+4 x^2\right ) \log ^4(1+x)+\left (e^x \left (-x-x^2\right )+e^{5 x} (1+x) \log ^4(1+x)\right ) \log \left (\frac {1}{3} \left (2 x-2 e^{4 x} \log ^4(1+x)\right )\right )+\left (e^x \left (-x^2-x^3\right )+e^{5 x} \left (x+x^2\right ) \log ^4(1+x)\right ) \log \left (\frac {1}{3} \left (2 x-2 e^{4 x} \log ^4(1+x)\right )\right ) \log \left (x \log \left (\frac {1}{3} \left (2 x-2 e^{4 x} \log ^4(1+x)\right )\right )\right )}{\left (-x^2-x^3+e^{4 x} \left (x+x^2\right ) \log ^4(1+x)\right ) \log \left (\frac {1}{3} \left (2 x-2 e^{4 x} \log ^4(1+x)\right )\right )} \, dx=e^x \log \left (x \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(x+1)\right )\right )\right ) \]
[In]
[Out]
Rule 2209
Rule 2225
Rule 2635
Rule 6820
Rule 6873
Rule 6874
Rubi steps \begin{align*} \text {integral}& = \int \frac {-e^x \left (-x-x^2\right )-4 e^{5 x} x \log ^3(1+x)-e^{5 x} \left (4 x+4 x^2\right ) \log ^4(1+x)-\left (e^x \left (-x-x^2\right )+e^{5 x} (1+x) \log ^4(1+x)\right ) \log \left (\frac {1}{3} \left (2 x-2 e^{4 x} \log ^4(1+x)\right )\right )-\left (e^x \left (-x^2-x^3\right )+e^{5 x} \left (x+x^2\right ) \log ^4(1+x)\right ) \log \left (\frac {1}{3} \left (2 x-2 e^{4 x} \log ^4(1+x)\right )\right ) \log \left (x \log \left (\frac {1}{3} \left (2 x-2 e^{4 x} \log ^4(1+x)\right )\right )\right )}{x (1+x) \left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx \\ & = \int \left (\frac {e^x \left (4 x-\log (1+x)+3 x \log (1+x)+4 x^2 \log (1+x)\right )}{(1+x) \log (1+x) \left (-x+e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )}+\frac {e^x \left (4 x+4 x \log (1+x)+4 x^2 \log (1+x)+\log (1+x) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )+x \log (1+x) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )+x \log (1+x) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right ) \log \left (x \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )\right )+x^2 \log (1+x) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right ) \log \left (x \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )\right )\right )}{x (1+x) \log (1+x) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )}\right ) \, dx \\ & = \int \frac {e^x \left (4 x-\log (1+x)+3 x \log (1+x)+4 x^2 \log (1+x)\right )}{(1+x) \log (1+x) \left (-x+e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx+\int \frac {e^x \left (4 x+4 x \log (1+x)+4 x^2 \log (1+x)+\log (1+x) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )+x \log (1+x) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )+x \log (1+x) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right ) \log \left (x \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )\right )+x^2 \log (1+x) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right ) \log \left (x \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )\right )\right )}{x (1+x) \log (1+x) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx \\ & = \int \left (\frac {e^x}{(1+x) \left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )}-\frac {3 e^x x}{(1+x) \left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )}-\frac {4 e^x x^2}{(1+x) \left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )}-\frac {4 e^x x}{(1+x) \log (1+x) \left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )}\right ) \, dx+\int \frac {e^x \left (4 x+(1+x) \log (1+x) \left (4 x+\log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right ) \left (1+x \log \left (x \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )\right )\right )\right )\right )}{x (1+x) \log (1+x) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx \\ & = -\left (3 \int \frac {e^x x}{(1+x) \left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx\right )-4 \int \frac {e^x x^2}{(1+x) \left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx-4 \int \frac {e^x x}{(1+x) \log (1+x) \left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx+\int \frac {e^x}{(1+x) \left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx+\int \left (\frac {e^x \left (4 x+4 x \log (1+x)+4 x^2 \log (1+x)+\log (1+x) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )+x \log (1+x) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )\right )}{x (1+x) \log (1+x) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )}+e^x \log \left (x \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )\right )\right ) \, dx \\ & = -\left (3 \int \left (\frac {e^x}{\left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )}-\frac {e^x}{(1+x) \left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )}\right ) \, dx\right )-4 \int \left (-\frac {e^x}{\left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )}+\frac {e^x x}{\left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )}+\frac {e^x}{(1+x) \left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )}\right ) \, dx-4 \int \left (-\frac {e^x}{(1+x) \log (1+x) \left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )}-\frac {e^x}{\log (1+x) \left (-x+e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )}\right ) \, dx+\int \frac {e^x}{(1+x) \left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx+\int \frac {e^x \left (4 x+4 x \log (1+x)+4 x^2 \log (1+x)+\log (1+x) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )+x \log (1+x) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )\right )}{x (1+x) \log (1+x) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx+\int e^x \log \left (x \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )\right ) \, dx \\ & = e^x \log \left (x \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )\right )-3 \int \frac {e^x}{\left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx+3 \int \frac {e^x}{(1+x) \left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx+4 \int \frac {e^x}{\left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx-4 \int \frac {e^x x}{\left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx-4 \int \frac {e^x}{(1+x) \left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx+4 \int \frac {e^x}{(1+x) \log (1+x) \left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx+4 \int \frac {e^x}{\log (1+x) \left (-x+e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx-\int e^x \left (\frac {1}{x}+\frac {1-\frac {4 e^{4 x} \log ^3(1+x)}{1+x}-4 e^{4 x} \log ^4(1+x)}{\left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )}\right ) \, dx+\int \frac {e^x}{(1+x) \left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx+\int \frac {e^x \left (4 x+(1+x) \log (1+x) \left (4 x+\log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )\right )\right )}{x (1+x) \log (1+x) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx \\ & = e^x \log \left (x \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )\right )-3 \int \frac {e^x}{\left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx+3 \int \frac {e^x}{(1+x) \left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx+4 \int \frac {e^x}{\left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx-4 \int \frac {e^x x}{\left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx-4 \int \frac {e^x}{(1+x) \left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx+4 \int \frac {e^x}{(1+x) \log (1+x) \left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx+4 \int \frac {e^x}{\log (1+x) \left (-x+e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx+\int \left (\frac {e^x}{x}+\frac {4 e^x (1+\log (1+x)+x \log (1+x))}{(1+x) \log (1+x) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )}\right ) \, dx-\int \left (\frac {e^x}{x}-\frac {e^x \left (-1-x+4 e^{4 x} \log ^3(1+x)+4 e^{4 x} \log ^4(1+x)+4 e^{4 x} x \log ^4(1+x)\right )}{(1+x) \left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )}\right ) \, dx+\int \frac {e^x}{(1+x) \left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx \\ & = e^x \log \left (x \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )\right )-3 \int \frac {e^x}{\left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx+3 \int \frac {e^x}{(1+x) \left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx+4 \int \frac {e^x (1+\log (1+x)+x \log (1+x))}{(1+x) \log (1+x) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx+4 \int \frac {e^x}{\left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx-4 \int \frac {e^x x}{\left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx-4 \int \frac {e^x}{(1+x) \left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx+4 \int \frac {e^x}{(1+x) \log (1+x) \left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx+4 \int \frac {e^x}{\log (1+x) \left (-x+e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx+\int \frac {e^x}{(1+x) \left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx+\int \frac {e^x \left (-1-x+4 e^{4 x} \log ^3(1+x)+4 e^{4 x} \log ^4(1+x)+4 e^{4 x} x \log ^4(1+x)\right )}{(1+x) \left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx \\ & = e^x \log \left (x \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )\right )-3 \int \frac {e^x}{\left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx+3 \int \frac {e^x}{(1+x) \left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx+4 \int \left (\frac {e^x}{(1+x) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )}+\frac {e^x x}{(1+x) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )}+\frac {e^x}{(1+x) \log (1+x) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )}\right ) \, dx+4 \int \frac {e^x}{\left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx-4 \int \frac {e^x x}{\left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx-4 \int \frac {e^x}{(1+x) \left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx+4 \int \frac {e^x}{(1+x) \log (1+x) \left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx+4 \int \frac {e^x}{\log (1+x) \left (-x+e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx+\int \left (-\frac {4 e^x (1+\log (1+x)+x \log (1+x))}{(1+x) \log (1+x) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )}+\frac {e^x \left (4 x-\log (1+x)+3 x \log (1+x)+4 x^2 \log (1+x)\right )}{(1+x) \log (1+x) \left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )}\right ) \, dx+\int \frac {e^x}{(1+x) \left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx \\ & = e^x \log \left (x \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )\right )-3 \int \frac {e^x}{\left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx+3 \int \frac {e^x}{(1+x) \left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx+4 \int \frac {e^x}{(1+x) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx+4 \int \frac {e^x x}{(1+x) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx+4 \int \frac {e^x}{(1+x) \log (1+x) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx-4 \int \frac {e^x (1+\log (1+x)+x \log (1+x))}{(1+x) \log (1+x) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx+4 \int \frac {e^x}{\left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx-4 \int \frac {e^x x}{\left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx-4 \int \frac {e^x}{(1+x) \left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx+4 \int \frac {e^x}{(1+x) \log (1+x) \left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx+4 \int \frac {e^x}{\log (1+x) \left (-x+e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx+\int \frac {e^x}{(1+x) \left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx+\int \frac {e^x \left (4 x-\log (1+x)+3 x \log (1+x)+4 x^2 \log (1+x)\right )}{(1+x) \log (1+x) \left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx \\ & = e^x \log \left (x \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )\right )-3 \int \frac {e^x}{\left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx+3 \int \frac {e^x}{(1+x) \left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx+4 \int \left (\frac {e^x}{\log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )}-\frac {e^x}{(1+x) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )}\right ) \, dx-4 \int \left (\frac {e^x}{(1+x) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )}+\frac {e^x x}{(1+x) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )}+\frac {e^x}{(1+x) \log (1+x) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )}\right ) \, dx+4 \int \frac {e^x}{(1+x) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx+4 \int \frac {e^x}{(1+x) \log (1+x) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx+4 \int \frac {e^x}{\left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx-4 \int \frac {e^x x}{\left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx-4 \int \frac {e^x}{(1+x) \left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx+4 \int \frac {e^x}{(1+x) \log (1+x) \left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx+4 \int \frac {e^x}{\log (1+x) \left (-x+e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx+\int \frac {e^x}{(1+x) \left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx+\int \frac {e^x \left (4 x+\left (-1+3 x+4 x^2\right ) \log (1+x)\right )}{(1+x) \log (1+x) \left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx \\ & = e^x \log \left (x \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )\right )-3 \int \frac {e^x}{\left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx+3 \int \frac {e^x}{(1+x) \left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx+4 \int \frac {e^x}{\log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx-4 \int \frac {e^x}{(1+x) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx-4 \int \frac {e^x x}{(1+x) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx+4 \int \frac {e^x}{\left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx-4 \int \frac {e^x x}{\left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx-4 \int \frac {e^x}{(1+x) \left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx+4 \int \frac {e^x}{(1+x) \log (1+x) \left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx+4 \int \frac {e^x}{\log (1+x) \left (-x+e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx+\int \left (-\frac {e^x}{(1+x) \left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )}+\frac {3 e^x x}{(1+x) \left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )}+\frac {4 e^x x^2}{(1+x) \left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )}+\frac {4 e^x x}{(1+x) \log (1+x) \left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )}\right ) \, dx+\int \frac {e^x}{(1+x) \left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx \\ & = e^x \log \left (x \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )\right )-3 \int \frac {e^x}{\left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx+3 \int \frac {e^x}{(1+x) \left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx+3 \int \frac {e^x x}{(1+x) \left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx-4 \int \left (\frac {e^x}{\log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )}-\frac {e^x}{(1+x) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )}\right ) \, dx+4 \int \frac {e^x}{\log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx-4 \int \frac {e^x}{(1+x) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx+4 \int \frac {e^x}{\left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx-4 \int \frac {e^x x}{\left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx-4 \int \frac {e^x}{(1+x) \left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx+4 \int \frac {e^x x^2}{(1+x) \left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx+4 \int \frac {e^x}{(1+x) \log (1+x) \left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx+4 \int \frac {e^x x}{(1+x) \log (1+x) \left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx+4 \int \frac {e^x}{\log (1+x) \left (-x+e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx \\ & = e^x \log \left (x \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )\right )+3 \int \left (\frac {e^x}{\left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )}-\frac {e^x}{(1+x) \left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )}\right ) \, dx-3 \int \frac {e^x}{\left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx+3 \int \frac {e^x}{(1+x) \left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx+4 \int \left (-\frac {e^x}{\left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )}+\frac {e^x x}{\left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )}+\frac {e^x}{(1+x) \left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )}\right ) \, dx+4 \int \left (-\frac {e^x}{(1+x) \log (1+x) \left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )}-\frac {e^x}{\log (1+x) \left (-x+e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )}\right ) \, dx+4 \int \frac {e^x}{\left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx-4 \int \frac {e^x x}{\left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx-4 \int \frac {e^x}{(1+x) \left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx+4 \int \frac {e^x}{(1+x) \log (1+x) \left (x-e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx+4 \int \frac {e^x}{\log (1+x) \left (-x+e^{4 x} \log ^4(1+x)\right ) \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )} \, dx \\ & = e^x \log \left (x \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )\right ) \\ \end{align*}
Time = 0.25 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.00 \[ \int \frac {e^x \left (-x-x^2\right )+4 e^{5 x} x \log ^3(1+x)+e^{5 x} \left (4 x+4 x^2\right ) \log ^4(1+x)+\left (e^x \left (-x-x^2\right )+e^{5 x} (1+x) \log ^4(1+x)\right ) \log \left (\frac {1}{3} \left (2 x-2 e^{4 x} \log ^4(1+x)\right )\right )+\left (e^x \left (-x^2-x^3\right )+e^{5 x} \left (x+x^2\right ) \log ^4(1+x)\right ) \log \left (\frac {1}{3} \left (2 x-2 e^{4 x} \log ^4(1+x)\right )\right ) \log \left (x \log \left (\frac {1}{3} \left (2 x-2 e^{4 x} \log ^4(1+x)\right )\right )\right )}{\left (-x^2-x^3+e^{4 x} \left (x+x^2\right ) \log ^4(1+x)\right ) \log \left (\frac {1}{3} \left (2 x-2 e^{4 x} \log ^4(1+x)\right )\right )} \, dx=e^x \log \left (x \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )\right ) \]
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Result contains higher order function than in optimal. Order 9 vs. order 3.
Time = 1.24 (sec) , antiderivative size = 198, normalized size of antiderivative = 7.33
\[{\mathrm e}^{x} \ln \left (\ln \left (-\frac {2 \,{\mathrm e}^{4 x} \ln \left (1+x \right )^{4}}{3}+\frac {2 x}{3}\right )\right )+{\mathrm e}^{x} \ln \left (x \right )-\frac {i \pi \,\operatorname {csgn}\left (i x \right ) \operatorname {csgn}\left (i \ln \left (-\frac {2 \,{\mathrm e}^{4 x} \ln \left (1+x \right )^{4}}{3}+\frac {2 x}{3}\right )\right ) \operatorname {csgn}\left (i x \ln \left (-\frac {2 \,{\mathrm e}^{4 x} \ln \left (1+x \right )^{4}}{3}+\frac {2 x}{3}\right )\right ) {\mathrm e}^{x}}{2}+\frac {i \pi \,\operatorname {csgn}\left (i x \right ) {\operatorname {csgn}\left (i x \ln \left (-\frac {2 \,{\mathrm e}^{4 x} \ln \left (1+x \right )^{4}}{3}+\frac {2 x}{3}\right )\right )}^{2} {\mathrm e}^{x}}{2}+\frac {i \pi \,\operatorname {csgn}\left (i \ln \left (-\frac {2 \,{\mathrm e}^{4 x} \ln \left (1+x \right )^{4}}{3}+\frac {2 x}{3}\right )\right ) {\operatorname {csgn}\left (i x \ln \left (-\frac {2 \,{\mathrm e}^{4 x} \ln \left (1+x \right )^{4}}{3}+\frac {2 x}{3}\right )\right )}^{2} {\mathrm e}^{x}}{2}-\frac {i \pi {\operatorname {csgn}\left (i x \ln \left (-\frac {2 \,{\mathrm e}^{4 x} \ln \left (1+x \right )^{4}}{3}+\frac {2 x}{3}\right )\right )}^{3} {\mathrm e}^{x}}{2}\]
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Time = 0.26 (sec) , antiderivative size = 23, normalized size of antiderivative = 0.85 \[ \int \frac {e^x \left (-x-x^2\right )+4 e^{5 x} x \log ^3(1+x)+e^{5 x} \left (4 x+4 x^2\right ) \log ^4(1+x)+\left (e^x \left (-x-x^2\right )+e^{5 x} (1+x) \log ^4(1+x)\right ) \log \left (\frac {1}{3} \left (2 x-2 e^{4 x} \log ^4(1+x)\right )\right )+\left (e^x \left (-x^2-x^3\right )+e^{5 x} \left (x+x^2\right ) \log ^4(1+x)\right ) \log \left (\frac {1}{3} \left (2 x-2 e^{4 x} \log ^4(1+x)\right )\right ) \log \left (x \log \left (\frac {1}{3} \left (2 x-2 e^{4 x} \log ^4(1+x)\right )\right )\right )}{\left (-x^2-x^3+e^{4 x} \left (x+x^2\right ) \log ^4(1+x)\right ) \log \left (\frac {1}{3} \left (2 x-2 e^{4 x} \log ^4(1+x)\right )\right )} \, dx=e^{x} \log \left (x \log \left (-\frac {2}{3} \, e^{\left (4 \, x\right )} \log \left (x + 1\right )^{4} + \frac {2}{3} \, x\right )\right ) \]
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Timed out. \[ \int \frac {e^x \left (-x-x^2\right )+4 e^{5 x} x \log ^3(1+x)+e^{5 x} \left (4 x+4 x^2\right ) \log ^4(1+x)+\left (e^x \left (-x-x^2\right )+e^{5 x} (1+x) \log ^4(1+x)\right ) \log \left (\frac {1}{3} \left (2 x-2 e^{4 x} \log ^4(1+x)\right )\right )+\left (e^x \left (-x^2-x^3\right )+e^{5 x} \left (x+x^2\right ) \log ^4(1+x)\right ) \log \left (\frac {1}{3} \left (2 x-2 e^{4 x} \log ^4(1+x)\right )\right ) \log \left (x \log \left (\frac {1}{3} \left (2 x-2 e^{4 x} \log ^4(1+x)\right )\right )\right )}{\left (-x^2-x^3+e^{4 x} \left (x+x^2\right ) \log ^4(1+x)\right ) \log \left (\frac {1}{3} \left (2 x-2 e^{4 x} \log ^4(1+x)\right )\right )} \, dx=\text {Timed out} \]
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\[ \int \frac {e^x \left (-x-x^2\right )+4 e^{5 x} x \log ^3(1+x)+e^{5 x} \left (4 x+4 x^2\right ) \log ^4(1+x)+\left (e^x \left (-x-x^2\right )+e^{5 x} (1+x) \log ^4(1+x)\right ) \log \left (\frac {1}{3} \left (2 x-2 e^{4 x} \log ^4(1+x)\right )\right )+\left (e^x \left (-x^2-x^3\right )+e^{5 x} \left (x+x^2\right ) \log ^4(1+x)\right ) \log \left (\frac {1}{3} \left (2 x-2 e^{4 x} \log ^4(1+x)\right )\right ) \log \left (x \log \left (\frac {1}{3} \left (2 x-2 e^{4 x} \log ^4(1+x)\right )\right )\right )}{\left (-x^2-x^3+e^{4 x} \left (x+x^2\right ) \log ^4(1+x)\right ) \log \left (\frac {1}{3} \left (2 x-2 e^{4 x} \log ^4(1+x)\right )\right )} \, dx=\int { \frac {4 \, {\left (x^{2} + x\right )} e^{\left (5 \, x\right )} \log \left (x + 1\right )^{4} + 4 \, x e^{\left (5 \, x\right )} \log \left (x + 1\right )^{3} + {\left ({\left (x^{2} + x\right )} e^{\left (5 \, x\right )} \log \left (x + 1\right )^{4} - {\left (x^{3} + x^{2}\right )} e^{x}\right )} \log \left (-\frac {2}{3} \, e^{\left (4 \, x\right )} \log \left (x + 1\right )^{4} + \frac {2}{3} \, x\right ) \log \left (x \log \left (-\frac {2}{3} \, e^{\left (4 \, x\right )} \log \left (x + 1\right )^{4} + \frac {2}{3} \, x\right )\right ) - {\left (x^{2} + x\right )} e^{x} + {\left ({\left (x + 1\right )} e^{\left (5 \, x\right )} \log \left (x + 1\right )^{4} - {\left (x^{2} + x\right )} e^{x}\right )} \log \left (-\frac {2}{3} \, e^{\left (4 \, x\right )} \log \left (x + 1\right )^{4} + \frac {2}{3} \, x\right )}{{\left ({\left (x^{2} + x\right )} e^{\left (4 \, x\right )} \log \left (x + 1\right )^{4} - x^{3} - x^{2}\right )} \log \left (-\frac {2}{3} \, e^{\left (4 \, x\right )} \log \left (x + 1\right )^{4} + \frac {2}{3} \, x\right )} \,d x } \]
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\[ \int \frac {e^x \left (-x-x^2\right )+4 e^{5 x} x \log ^3(1+x)+e^{5 x} \left (4 x+4 x^2\right ) \log ^4(1+x)+\left (e^x \left (-x-x^2\right )+e^{5 x} (1+x) \log ^4(1+x)\right ) \log \left (\frac {1}{3} \left (2 x-2 e^{4 x} \log ^4(1+x)\right )\right )+\left (e^x \left (-x^2-x^3\right )+e^{5 x} \left (x+x^2\right ) \log ^4(1+x)\right ) \log \left (\frac {1}{3} \left (2 x-2 e^{4 x} \log ^4(1+x)\right )\right ) \log \left (x \log \left (\frac {1}{3} \left (2 x-2 e^{4 x} \log ^4(1+x)\right )\right )\right )}{\left (-x^2-x^3+e^{4 x} \left (x+x^2\right ) \log ^4(1+x)\right ) \log \left (\frac {1}{3} \left (2 x-2 e^{4 x} \log ^4(1+x)\right )\right )} \, dx=\int { \frac {4 \, {\left (x^{2} + x\right )} e^{\left (5 \, x\right )} \log \left (x + 1\right )^{4} + 4 \, x e^{\left (5 \, x\right )} \log \left (x + 1\right )^{3} + {\left ({\left (x^{2} + x\right )} e^{\left (5 \, x\right )} \log \left (x + 1\right )^{4} - {\left (x^{3} + x^{2}\right )} e^{x}\right )} \log \left (-\frac {2}{3} \, e^{\left (4 \, x\right )} \log \left (x + 1\right )^{4} + \frac {2}{3} \, x\right ) \log \left (x \log \left (-\frac {2}{3} \, e^{\left (4 \, x\right )} \log \left (x + 1\right )^{4} + \frac {2}{3} \, x\right )\right ) - {\left (x^{2} + x\right )} e^{x} + {\left ({\left (x + 1\right )} e^{\left (5 \, x\right )} \log \left (x + 1\right )^{4} - {\left (x^{2} + x\right )} e^{x}\right )} \log \left (-\frac {2}{3} \, e^{\left (4 \, x\right )} \log \left (x + 1\right )^{4} + \frac {2}{3} \, x\right )}{{\left ({\left (x^{2} + x\right )} e^{\left (4 \, x\right )} \log \left (x + 1\right )^{4} - x^{3} - x^{2}\right )} \log \left (-\frac {2}{3} \, e^{\left (4 \, x\right )} \log \left (x + 1\right )^{4} + \frac {2}{3} \, x\right )} \,d x } \]
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Time = 14.91 (sec) , antiderivative size = 23, normalized size of antiderivative = 0.85 \[ \int \frac {e^x \left (-x-x^2\right )+4 e^{5 x} x \log ^3(1+x)+e^{5 x} \left (4 x+4 x^2\right ) \log ^4(1+x)+\left (e^x \left (-x-x^2\right )+e^{5 x} (1+x) \log ^4(1+x)\right ) \log \left (\frac {1}{3} \left (2 x-2 e^{4 x} \log ^4(1+x)\right )\right )+\left (e^x \left (-x^2-x^3\right )+e^{5 x} \left (x+x^2\right ) \log ^4(1+x)\right ) \log \left (\frac {1}{3} \left (2 x-2 e^{4 x} \log ^4(1+x)\right )\right ) \log \left (x \log \left (\frac {1}{3} \left (2 x-2 e^{4 x} \log ^4(1+x)\right )\right )\right )}{\left (-x^2-x^3+e^{4 x} \left (x+x^2\right ) \log ^4(1+x)\right ) \log \left (\frac {1}{3} \left (2 x-2 e^{4 x} \log ^4(1+x)\right )\right )} \, dx=\ln \left (x\,\ln \left (\frac {2\,x}{3}-\frac {2\,{\ln \left (x+1\right )}^4\,{\mathrm {e}}^{4\,x}}{3}\right )\right )\,{\mathrm {e}}^x \]
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