Optimal. Leaf size=27 \[ e^x \log \left (x \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )\right ) \]
[Out]
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Rubi [A]
time = 41.83, antiderivative size = 27, normalized size of antiderivative = 1.00, number of steps
used = 41, number of rules used = 6, integrand size = 237, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.025, Rules used = {6873, 6874,
6820, 2209, 2225, 2635} \begin {gather*} e^x \log \left (x \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(x+1)\right )\right )\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 2209
Rule 2225
Rule 2635
Rule 6820
Rule 6873
Rule 6874
Rubi steps
\begin {gather*} \begin {aligned} \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\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.19, size = 27, normalized size = 1.00 \begin {gather*} e^x \log \left (x \log \left (\frac {2}{3} \left (x-e^{4 x} \log ^4(1+x)\right )\right )\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
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Maple [C] Result contains higher order function than in optimal. Order 9 vs. order
3.
time = 0.80, size = 198, normalized size = 7.33
method | result | size |
risch | \({\mathrm e}^{x} \ln \left (\ln \left (-\frac {2 \,{\mathrm e}^{4 x} \ln \left (x +1\right )^{4}}{3}+\frac {2 x}{3}\right )\right )+{\mathrm e}^{x} \ln \left (x \right )-\frac {i \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i \ln \left (-\frac {2 \,{\mathrm e}^{4 x} \ln \left (x +1\right )^{4}}{3}+\frac {2 x}{3}\right )\right ) \mathrm {csgn}\left (i x \ln \left (-\frac {2 \,{\mathrm e}^{4 x} \ln \left (x +1\right )^{4}}{3}+\frac {2 x}{3}\right )\right ) {\mathrm e}^{x}}{2}+\frac {i \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x \ln \left (-\frac {2 \,{\mathrm e}^{4 x} \ln \left (x +1\right )^{4}}{3}+\frac {2 x}{3}\right )\right )^{2} {\mathrm e}^{x}}{2}+\frac {i \pi \,\mathrm {csgn}\left (i \ln \left (-\frac {2 \,{\mathrm e}^{4 x} \ln \left (x +1\right )^{4}}{3}+\frac {2 x}{3}\right )\right ) \mathrm {csgn}\left (i x \ln \left (-\frac {2 \,{\mathrm e}^{4 x} \ln \left (x +1\right )^{4}}{3}+\frac {2 x}{3}\right )\right )^{2} {\mathrm e}^{x}}{2}-\frac {i \pi \mathrm {csgn}\left (i x \ln \left (-\frac {2 \,{\mathrm e}^{4 x} \ln \left (x +1\right )^{4}}{3}+\frac {2 x}{3}\right )\right )^{3} {\mathrm e}^{x}}{2}\) | \(198\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.34, size = 23, normalized size = 0.85 \begin {gather*} 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 ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] Timed out
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 4.27, size = 23, normalized size = 0.85 \begin {gather*} \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 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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