Integrand size = 354, antiderivative size = 22 \[ \int \frac {10+22 x+4 x^2+5 x^5+x^6+\left (10+4 x+15 x^4+3 x^5\right ) \log (x)+\left (15 x^3+3 x^4\right ) \log ^2(x)+\left (5 x^2+x^3\right ) \log ^3(x)+\left (10+2 x+\left (10+2 x+15 x^4+3 x^5\right ) \log (x)+\left (30 x^3+6 x^4\right ) \log ^2(x)+\left (15 x^2+3 x^3\right ) \log ^3(x)\right ) \log (5+x)+\left (\left (15 x^3+3 x^4\right ) \log ^2(x)+\left (15 x^2+3 x^3\right ) \log ^3(x)\right ) \log ^2(5+x)+\left (5 x^2+x^3\right ) \log ^3(x) \log ^3(5+x)}{5 x^6+x^7+\left (15 x^5+3 x^6\right ) \log (x)+\left (15 x^4+3 x^5\right ) \log ^2(x)+\left (5 x^3+x^4\right ) \log ^3(x)+\left (\left (15 x^5+3 x^6\right ) \log (x)+\left (30 x^4+6 x^5\right ) \log ^2(x)+\left (15 x^3+3 x^4\right ) \log ^3(x)\right ) \log (5+x)+\left (\left (15 x^4+3 x^5\right ) \log ^2(x)+\left (15 x^3+3 x^4\right ) \log ^3(x)\right ) \log ^2(5+x)+\left (5 x^3+x^4\right ) \log ^3(x) \log ^3(5+x)} \, dx=\log (x)-\frac {1}{\left (x^2+\log (x) (x+x \log (5+x))\right )^2} \]
[Out]
\[ \int \frac {10+22 x+4 x^2+5 x^5+x^6+\left (10+4 x+15 x^4+3 x^5\right ) \log (x)+\left (15 x^3+3 x^4\right ) \log ^2(x)+\left (5 x^2+x^3\right ) \log ^3(x)+\left (10+2 x+\left (10+2 x+15 x^4+3 x^5\right ) \log (x)+\left (30 x^3+6 x^4\right ) \log ^2(x)+\left (15 x^2+3 x^3\right ) \log ^3(x)\right ) \log (5+x)+\left (\left (15 x^3+3 x^4\right ) \log ^2(x)+\left (15 x^2+3 x^3\right ) \log ^3(x)\right ) \log ^2(5+x)+\left (5 x^2+x^3\right ) \log ^3(x) \log ^3(5+x)}{5 x^6+x^7+\left (15 x^5+3 x^6\right ) \log (x)+\left (15 x^4+3 x^5\right ) \log ^2(x)+\left (5 x^3+x^4\right ) \log ^3(x)+\left (\left (15 x^5+3 x^6\right ) \log (x)+\left (30 x^4+6 x^5\right ) \log ^2(x)+\left (15 x^3+3 x^4\right ) \log ^3(x)\right ) \log (5+x)+\left (\left (15 x^4+3 x^5\right ) \log ^2(x)+\left (15 x^3+3 x^4\right ) \log ^3(x)\right ) \log ^2(5+x)+\left (5 x^3+x^4\right ) \log ^3(x) \log ^3(5+x)} \, dx=\int \frac {10+22 x+4 x^2+5 x^5+x^6+\left (10+4 x+15 x^4+3 x^5\right ) \log (x)+\left (15 x^3+3 x^4\right ) \log ^2(x)+\left (5 x^2+x^3\right ) \log ^3(x)+\left (10+2 x+\left (10+2 x+15 x^4+3 x^5\right ) \log (x)+\left (30 x^3+6 x^4\right ) \log ^2(x)+\left (15 x^2+3 x^3\right ) \log ^3(x)\right ) \log (5+x)+\left (\left (15 x^3+3 x^4\right ) \log ^2(x)+\left (15 x^2+3 x^3\right ) \log ^3(x)\right ) \log ^2(5+x)+\left (5 x^2+x^3\right ) \log ^3(x) \log ^3(5+x)}{5 x^6+x^7+\left (15 x^5+3 x^6\right ) \log (x)+\left (15 x^4+3 x^5\right ) \log ^2(x)+\left (5 x^3+x^4\right ) \log ^3(x)+\left (\left (15 x^5+3 x^6\right ) \log (x)+\left (30 x^4+6 x^5\right ) \log ^2(x)+\left (15 x^3+3 x^4\right ) \log ^3(x)\right ) \log (5+x)+\left (\left (15 x^4+3 x^5\right ) \log ^2(x)+\left (15 x^3+3 x^4\right ) \log ^3(x)\right ) \log ^2(5+x)+\left (5 x^3+x^4\right ) \log ^3(x) \log ^3(5+x)} \, dx \]
[In]
[Out]
Rubi steps \begin{align*} \text {integral}& = \int \frac {3 x^3 (5+x) \log ^2(x) (1+\log (5+x))^2+x^2 (5+x) \log ^3(x) (1+\log (5+x))^3+(5+x) \left (2+4 x+x^5+2 \log (5+x)\right )+\log (x) \left (10+4 x+15 x^4+3 x^5+\left (10+2 x+15 x^4+3 x^5\right ) \log (5+x)\right )}{x^3 (5+x) (x+\log (x) (1+\log (5+x)))^3} \, dx \\ & = \int \left (\frac {1}{x}+\frac {2 \left (-5-x+5 \log (x)+x \log (x)+\log ^2(x)\right )}{x^2 (5+x) \log (x) (x+\log (x)+\log (x) \log (5+x))^3}+\frac {2 (1+\log (x))}{x^3 \log (x) (x+\log (x)+\log (x) \log (5+x))^2}\right ) \, dx \\ & = \log (x)+2 \int \frac {-5-x+5 \log (x)+x \log (x)+\log ^2(x)}{x^2 (5+x) \log (x) (x+\log (x)+\log (x) \log (5+x))^3} \, dx+2 \int \frac {1+\log (x)}{x^3 \log (x) (x+\log (x)+\log (x) \log (5+x))^2} \, dx \\ & = \log (x)+2 \int \left (\frac {5+x-5 \log (x)-x \log (x)-\log ^2(x)}{25 x \log (x) (x+\log (x)+\log (x) \log (5+x))^3}+\frac {-5-x+5 \log (x)+x \log (x)+\log ^2(x)}{5 x^2 \log (x) (x+\log (x)+\log (x) \log (5+x))^3}+\frac {-5-x+5 \log (x)+x \log (x)+\log ^2(x)}{25 (5+x) \log (x) (x+\log (x)+\log (x) \log (5+x))^3}\right ) \, dx+2 \int \left (\frac {1}{x^3 (x+\log (x)+\log (x) \log (5+x))^2}+\frac {1}{x^3 \log (x) (x+\log (x)+\log (x) \log (5+x))^2}\right ) \, dx \\ & = \log (x)+\frac {2}{25} \int \frac {5+x-5 \log (x)-x \log (x)-\log ^2(x)}{x \log (x) (x+\log (x)+\log (x) \log (5+x))^3} \, dx+\frac {2}{25} \int \frac {-5-x+5 \log (x)+x \log (x)+\log ^2(x)}{(5+x) \log (x) (x+\log (x)+\log (x) \log (5+x))^3} \, dx+\frac {2}{5} \int \frac {-5-x+5 \log (x)+x \log (x)+\log ^2(x)}{x^2 \log (x) (x+\log (x)+\log (x) \log (5+x))^3} \, dx+2 \int \frac {1}{x^3 (x+\log (x)+\log (x) \log (5+x))^2} \, dx+2 \int \frac {1}{x^3 \log (x) (x+\log (x)+\log (x) \log (5+x))^2} \, dx \\ & = \log (x)+\frac {2}{25} \int \left (-\frac {1}{(x+\log (x)+\log (x) \log (5+x))^3}-\frac {5}{x (x+\log (x)+\log (x) \log (5+x))^3}+\frac {1}{\log (x) (x+\log (x)+\log (x) \log (5+x))^3}+\frac {5}{x \log (x) (x+\log (x)+\log (x) \log (5+x))^3}-\frac {\log (x)}{x (x+\log (x)+\log (x) \log (5+x))^3}\right ) \, dx+\frac {2}{25} \int \left (\frac {5}{(5+x) (x+\log (x)+\log (x) \log (5+x))^3}+\frac {x}{(5+x) (x+\log (x)+\log (x) \log (5+x))^3}-\frac {5}{(5+x) \log (x) (x+\log (x)+\log (x) \log (5+x))^3}-\frac {x}{(5+x) \log (x) (x+\log (x)+\log (x) \log (5+x))^3}+\frac {\log (x)}{(5+x) (x+\log (x)+\log (x) \log (5+x))^3}\right ) \, dx+\frac {2}{5} \int \left (\frac {5}{x^2 (x+\log (x)+\log (x) \log (5+x))^3}+\frac {1}{x (x+\log (x)+\log (x) \log (5+x))^3}-\frac {5}{x^2 \log (x) (x+\log (x)+\log (x) \log (5+x))^3}-\frac {1}{x \log (x) (x+\log (x)+\log (x) \log (5+x))^3}+\frac {\log (x)}{x^2 (x+\log (x)+\log (x) \log (5+x))^3}\right ) \, dx+2 \int \frac {1}{x^3 (x+\log (x)+\log (x) \log (5+x))^2} \, dx+2 \int \frac {1}{x^3 \log (x) (x+\log (x)+\log (x) \log (5+x))^2} \, dx \\ & = \log (x)-\frac {2}{25} \int \frac {1}{(x+\log (x)+\log (x) \log (5+x))^3} \, dx+\frac {2}{25} \int \frac {x}{(5+x) (x+\log (x)+\log (x) \log (5+x))^3} \, dx+\frac {2}{25} \int \frac {1}{\log (x) (x+\log (x)+\log (x) \log (5+x))^3} \, dx-\frac {2}{25} \int \frac {x}{(5+x) \log (x) (x+\log (x)+\log (x) \log (5+x))^3} \, dx-\frac {2}{25} \int \frac {\log (x)}{x (x+\log (x)+\log (x) \log (5+x))^3} \, dx+\frac {2}{25} \int \frac {\log (x)}{(5+x) (x+\log (x)+\log (x) \log (5+x))^3} \, dx+\frac {2}{5} \int \frac {1}{(5+x) (x+\log (x)+\log (x) \log (5+x))^3} \, dx-\frac {2}{5} \int \frac {1}{(5+x) \log (x) (x+\log (x)+\log (x) \log (5+x))^3} \, dx+\frac {2}{5} \int \frac {\log (x)}{x^2 (x+\log (x)+\log (x) \log (5+x))^3} \, dx+2 \int \frac {1}{x^2 (x+\log (x)+\log (x) \log (5+x))^3} \, dx-2 \int \frac {1}{x^2 \log (x) (x+\log (x)+\log (x) \log (5+x))^3} \, dx+2 \int \frac {1}{x^3 (x+\log (x)+\log (x) \log (5+x))^2} \, dx+2 \int \frac {1}{x^3 \log (x) (x+\log (x)+\log (x) \log (5+x))^2} \, dx \\ & = \log (x)-\frac {2}{25} \int \frac {1}{(x+\log (x)+\log (x) \log (5+x))^3} \, dx+\frac {2}{25} \int \frac {1}{\log (x) (x+\log (x)+\log (x) \log (5+x))^3} \, dx-\frac {2}{25} \int \frac {\log (x)}{x (x+\log (x)+\log (x) \log (5+x))^3} \, dx+\frac {2}{25} \int \frac {\log (x)}{(5+x) (x+\log (x)+\log (x) \log (5+x))^3} \, dx+\frac {2}{25} \int \left (\frac {1}{(x+\log (x)+\log (x) \log (5+x))^3}-\frac {5}{(5+x) (x+\log (x)+\log (x) \log (5+x))^3}\right ) \, dx-\frac {2}{25} \int \left (\frac {1}{\log (x) (x+\log (x)+\log (x) \log (5+x))^3}-\frac {5}{(5+x) \log (x) (x+\log (x)+\log (x) \log (5+x))^3}\right ) \, dx+\frac {2}{5} \int \frac {1}{(5+x) (x+\log (x)+\log (x) \log (5+x))^3} \, dx-\frac {2}{5} \int \frac {1}{(5+x) \log (x) (x+\log (x)+\log (x) \log (5+x))^3} \, dx+\frac {2}{5} \int \frac {\log (x)}{x^2 (x+\log (x)+\log (x) \log (5+x))^3} \, dx+2 \int \frac {1}{x^2 (x+\log (x)+\log (x) \log (5+x))^3} \, dx-2 \int \frac {1}{x^2 \log (x) (x+\log (x)+\log (x) \log (5+x))^3} \, dx+2 \int \frac {1}{x^3 (x+\log (x)+\log (x) \log (5+x))^2} \, dx+2 \int \frac {1}{x^3 \log (x) (x+\log (x)+\log (x) \log (5+x))^2} \, dx \\ & = \log (x)-\frac {2}{25} \int \frac {\log (x)}{x (x+\log (x)+\log (x) \log (5+x))^3} \, dx+\frac {2}{25} \int \frac {\log (x)}{(5+x) (x+\log (x)+\log (x) \log (5+x))^3} \, dx+\frac {2}{5} \int \frac {\log (x)}{x^2 (x+\log (x)+\log (x) \log (5+x))^3} \, dx+2 \int \frac {1}{x^2 (x+\log (x)+\log (x) \log (5+x))^3} \, dx-2 \int \frac {1}{x^2 \log (x) (x+\log (x)+\log (x) \log (5+x))^3} \, dx+2 \int \frac {1}{x^3 (x+\log (x)+\log (x) \log (5+x))^2} \, dx+2 \int \frac {1}{x^3 \log (x) (x+\log (x)+\log (x) \log (5+x))^2} \, dx \\ \end{align*}
Time = 0.14 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.95 \[ \int \frac {10+22 x+4 x^2+5 x^5+x^6+\left (10+4 x+15 x^4+3 x^5\right ) \log (x)+\left (15 x^3+3 x^4\right ) \log ^2(x)+\left (5 x^2+x^3\right ) \log ^3(x)+\left (10+2 x+\left (10+2 x+15 x^4+3 x^5\right ) \log (x)+\left (30 x^3+6 x^4\right ) \log ^2(x)+\left (15 x^2+3 x^3\right ) \log ^3(x)\right ) \log (5+x)+\left (\left (15 x^3+3 x^4\right ) \log ^2(x)+\left (15 x^2+3 x^3\right ) \log ^3(x)\right ) \log ^2(5+x)+\left (5 x^2+x^3\right ) \log ^3(x) \log ^3(5+x)}{5 x^6+x^7+\left (15 x^5+3 x^6\right ) \log (x)+\left (15 x^4+3 x^5\right ) \log ^2(x)+\left (5 x^3+x^4\right ) \log ^3(x)+\left (\left (15 x^5+3 x^6\right ) \log (x)+\left (30 x^4+6 x^5\right ) \log ^2(x)+\left (15 x^3+3 x^4\right ) \log ^3(x)\right ) \log (5+x)+\left (\left (15 x^4+3 x^5\right ) \log ^2(x)+\left (15 x^3+3 x^4\right ) \log ^3(x)\right ) \log ^2(5+x)+\left (5 x^3+x^4\right ) \log ^3(x) \log ^3(5+x)} \, dx=\log (x)-\frac {1}{x^2 (x+\log (x)+\log (x) \log (5+x))^2} \]
[In]
[Out]
Time = 6.25 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.00
method | result | size |
default | \(\ln \left (x \right )-\frac {1}{x^{2} \left (\ln \left (x \right ) \ln \left (5+x \right )+\ln \left (x \right )+x \right )^{2}}\) | \(22\) |
risch | \(\ln \left (x \right )-\frac {1}{x^{2} \left (\ln \left (x \right ) \ln \left (5+x \right )+\ln \left (x \right )+x \right )^{2}}\) | \(22\) |
parallelrisch | \(\frac {-20+20 x^{4} \ln \left (x \right )+20 x^{2} \ln \left (x \right )^{3}+40 x^{3} \ln \left (x \right )^{2}+40 \ln \left (x \right )^{3} \ln \left (5+x \right ) x^{2}+40 \ln \left (x \right )^{2} x^{3} \ln \left (5+x \right )+20 x^{2} \ln \left (x \right )^{3} \ln \left (5+x \right )^{2}}{20 x^{2} \left (\ln \left (x \right )^{2} \ln \left (5+x \right )^{2}+2 \ln \left (x \right ) \ln \left (5+x \right ) x +2 \ln \left (x \right )^{2} \ln \left (5+x \right )+x^{2}+2 x \ln \left (x \right )+\ln \left (x \right )^{2}\right )}\) | \(119\) |
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. 119 vs. \(2 (22) = 44\).
Time = 0.26 (sec) , antiderivative size = 119, normalized size of antiderivative = 5.41 \[ \int \frac {10+22 x+4 x^2+5 x^5+x^6+\left (10+4 x+15 x^4+3 x^5\right ) \log (x)+\left (15 x^3+3 x^4\right ) \log ^2(x)+\left (5 x^2+x^3\right ) \log ^3(x)+\left (10+2 x+\left (10+2 x+15 x^4+3 x^5\right ) \log (x)+\left (30 x^3+6 x^4\right ) \log ^2(x)+\left (15 x^2+3 x^3\right ) \log ^3(x)\right ) \log (5+x)+\left (\left (15 x^3+3 x^4\right ) \log ^2(x)+\left (15 x^2+3 x^3\right ) \log ^3(x)\right ) \log ^2(5+x)+\left (5 x^2+x^3\right ) \log ^3(x) \log ^3(5+x)}{5 x^6+x^7+\left (15 x^5+3 x^6\right ) \log (x)+\left (15 x^4+3 x^5\right ) \log ^2(x)+\left (5 x^3+x^4\right ) \log ^3(x)+\left (\left (15 x^5+3 x^6\right ) \log (x)+\left (30 x^4+6 x^5\right ) \log ^2(x)+\left (15 x^3+3 x^4\right ) \log ^3(x)\right ) \log (5+x)+\left (\left (15 x^4+3 x^5\right ) \log ^2(x)+\left (15 x^3+3 x^4\right ) \log ^3(x)\right ) \log ^2(5+x)+\left (5 x^3+x^4\right ) \log ^3(x) \log ^3(5+x)} \, dx=\frac {x^{2} \log \left (x + 5\right )^{2} \log \left (x\right )^{3} + x^{4} \log \left (x\right ) + 2 \, x^{3} \log \left (x\right )^{2} + x^{2} \log \left (x\right )^{3} + 2 \, {\left (x^{3} \log \left (x\right )^{2} + x^{2} \log \left (x\right )^{3}\right )} \log \left (x + 5\right ) - 1}{x^{2} \log \left (x + 5\right )^{2} \log \left (x\right )^{2} + x^{4} + 2 \, x^{3} \log \left (x\right ) + x^{2} \log \left (x\right )^{2} + 2 \, {\left (x^{3} \log \left (x\right ) + x^{2} \log \left (x\right )^{2}\right )} \log \left (x + 5\right )} \]
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. 63 vs. \(2 (20) = 40\).
Time = 0.23 (sec) , antiderivative size = 63, normalized size of antiderivative = 2.86 \[ \int \frac {10+22 x+4 x^2+5 x^5+x^6+\left (10+4 x+15 x^4+3 x^5\right ) \log (x)+\left (15 x^3+3 x^4\right ) \log ^2(x)+\left (5 x^2+x^3\right ) \log ^3(x)+\left (10+2 x+\left (10+2 x+15 x^4+3 x^5\right ) \log (x)+\left (30 x^3+6 x^4\right ) \log ^2(x)+\left (15 x^2+3 x^3\right ) \log ^3(x)\right ) \log (5+x)+\left (\left (15 x^3+3 x^4\right ) \log ^2(x)+\left (15 x^2+3 x^3\right ) \log ^3(x)\right ) \log ^2(5+x)+\left (5 x^2+x^3\right ) \log ^3(x) \log ^3(5+x)}{5 x^6+x^7+\left (15 x^5+3 x^6\right ) \log (x)+\left (15 x^4+3 x^5\right ) \log ^2(x)+\left (5 x^3+x^4\right ) \log ^3(x)+\left (\left (15 x^5+3 x^6\right ) \log (x)+\left (30 x^4+6 x^5\right ) \log ^2(x)+\left (15 x^3+3 x^4\right ) \log ^3(x)\right ) \log (5+x)+\left (\left (15 x^4+3 x^5\right ) \log ^2(x)+\left (15 x^3+3 x^4\right ) \log ^3(x)\right ) \log ^2(5+x)+\left (5 x^3+x^4\right ) \log ^3(x) \log ^3(5+x)} \, dx=\log {\left (x \right )} - \frac {1}{x^{4} + 2 x^{3} \log {\left (x \right )} + x^{2} \log {\left (x \right )}^{2} \log {\left (x + 5 \right )}^{2} + x^{2} \log {\left (x \right )}^{2} + \left (2 x^{3} \log {\left (x \right )} + 2 x^{2} \log {\left (x \right )}^{2}\right ) \log {\left (x + 5 \right )}} \]
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. 61 vs. \(2 (22) = 44\).
Time = 0.29 (sec) , antiderivative size = 61, normalized size of antiderivative = 2.77 \[ \int \frac {10+22 x+4 x^2+5 x^5+x^6+\left (10+4 x+15 x^4+3 x^5\right ) \log (x)+\left (15 x^3+3 x^4\right ) \log ^2(x)+\left (5 x^2+x^3\right ) \log ^3(x)+\left (10+2 x+\left (10+2 x+15 x^4+3 x^5\right ) \log (x)+\left (30 x^3+6 x^4\right ) \log ^2(x)+\left (15 x^2+3 x^3\right ) \log ^3(x)\right ) \log (5+x)+\left (\left (15 x^3+3 x^4\right ) \log ^2(x)+\left (15 x^2+3 x^3\right ) \log ^3(x)\right ) \log ^2(5+x)+\left (5 x^2+x^3\right ) \log ^3(x) \log ^3(5+x)}{5 x^6+x^7+\left (15 x^5+3 x^6\right ) \log (x)+\left (15 x^4+3 x^5\right ) \log ^2(x)+\left (5 x^3+x^4\right ) \log ^3(x)+\left (\left (15 x^5+3 x^6\right ) \log (x)+\left (30 x^4+6 x^5\right ) \log ^2(x)+\left (15 x^3+3 x^4\right ) \log ^3(x)\right ) \log (5+x)+\left (\left (15 x^4+3 x^5\right ) \log ^2(x)+\left (15 x^3+3 x^4\right ) \log ^3(x)\right ) \log ^2(5+x)+\left (5 x^3+x^4\right ) \log ^3(x) \log ^3(5+x)} \, dx=-\frac {1}{x^{2} \log \left (x + 5\right )^{2} \log \left (x\right )^{2} + x^{4} + 2 \, x^{3} \log \left (x\right ) + x^{2} \log \left (x\right )^{2} + 2 \, {\left (x^{3} \log \left (x\right ) + x^{2} \log \left (x\right )^{2}\right )} \log \left (x + 5\right )} + \log \left (x\right ) \]
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. 281 vs. \(2 (22) = 44\).
Time = 0.52 (sec) , antiderivative size = 281, normalized size of antiderivative = 12.77 \[ \int \frac {10+22 x+4 x^2+5 x^5+x^6+\left (10+4 x+15 x^4+3 x^5\right ) \log (x)+\left (15 x^3+3 x^4\right ) \log ^2(x)+\left (5 x^2+x^3\right ) \log ^3(x)+\left (10+2 x+\left (10+2 x+15 x^4+3 x^5\right ) \log (x)+\left (30 x^3+6 x^4\right ) \log ^2(x)+\left (15 x^2+3 x^3\right ) \log ^3(x)\right ) \log (5+x)+\left (\left (15 x^3+3 x^4\right ) \log ^2(x)+\left (15 x^2+3 x^3\right ) \log ^3(x)\right ) \log ^2(5+x)+\left (5 x^2+x^3\right ) \log ^3(x) \log ^3(5+x)}{5 x^6+x^7+\left (15 x^5+3 x^6\right ) \log (x)+\left (15 x^4+3 x^5\right ) \log ^2(x)+\left (5 x^3+x^4\right ) \log ^3(x)+\left (\left (15 x^5+3 x^6\right ) \log (x)+\left (30 x^4+6 x^5\right ) \log ^2(x)+\left (15 x^3+3 x^4\right ) \log ^3(x)\right ) \log (5+x)+\left (\left (15 x^4+3 x^5\right ) \log ^2(x)+\left (15 x^3+3 x^4\right ) \log ^3(x)\right ) \log ^2(5+x)+\left (5 x^3+x^4\right ) \log ^3(x) \log ^3(5+x)} \, dx=-\frac {x \log \left (x\right ) + \log \left (x\right )^{2} - x + 5 \, \log \left (x\right ) - 5}{x^{3} \log \left (x + 5\right )^{2} \log \left (x\right )^{3} + x^{2} \log \left (x + 5\right )^{2} \log \left (x\right )^{4} + 2 \, x^{4} \log \left (x + 5\right ) \log \left (x\right )^{2} - x^{3} \log \left (x + 5\right )^{2} \log \left (x\right )^{2} + 4 \, x^{3} \log \left (x + 5\right ) \log \left (x\right )^{3} + 5 \, x^{2} \log \left (x + 5\right )^{2} \log \left (x\right )^{3} + 2 \, x^{2} \log \left (x + 5\right ) \log \left (x\right )^{4} + x^{5} \log \left (x\right ) - 2 \, x^{4} \log \left (x + 5\right ) \log \left (x\right ) + 3 \, x^{4} \log \left (x\right )^{2} + 8 \, x^{3} \log \left (x + 5\right ) \log \left (x\right )^{2} - 5 \, x^{2} \log \left (x + 5\right )^{2} \log \left (x\right )^{2} + 3 \, x^{3} \log \left (x\right )^{3} + 10 \, x^{2} \log \left (x + 5\right ) \log \left (x\right )^{3} + x^{2} \log \left (x\right )^{4} - x^{5} + 3 \, x^{4} \log \left (x\right ) - 10 \, x^{3} \log \left (x + 5\right ) \log \left (x\right ) + 9 \, x^{3} \log \left (x\right )^{2} - 10 \, x^{2} \log \left (x + 5\right ) \log \left (x\right )^{2} + 5 \, x^{2} \log \left (x\right )^{3} - 5 \, x^{4} - 10 \, x^{3} \log \left (x\right ) - 5 \, x^{2} \log \left (x\right )^{2}} + \log \left (x\right ) \]
[In]
[Out]
Time = 15.76 (sec) , antiderivative size = 82, normalized size of antiderivative = 3.73 \[ \int \frac {10+22 x+4 x^2+5 x^5+x^6+\left (10+4 x+15 x^4+3 x^5\right ) \log (x)+\left (15 x^3+3 x^4\right ) \log ^2(x)+\left (5 x^2+x^3\right ) \log ^3(x)+\left (10+2 x+\left (10+2 x+15 x^4+3 x^5\right ) \log (x)+\left (30 x^3+6 x^4\right ) \log ^2(x)+\left (15 x^2+3 x^3\right ) \log ^3(x)\right ) \log (5+x)+\left (\left (15 x^3+3 x^4\right ) \log ^2(x)+\left (15 x^2+3 x^3\right ) \log ^3(x)\right ) \log ^2(5+x)+\left (5 x^2+x^3\right ) \log ^3(x) \log ^3(5+x)}{5 x^6+x^7+\left (15 x^5+3 x^6\right ) \log (x)+\left (15 x^4+3 x^5\right ) \log ^2(x)+\left (5 x^3+x^4\right ) \log ^3(x)+\left (\left (15 x^5+3 x^6\right ) \log (x)+\left (30 x^4+6 x^5\right ) \log ^2(x)+\left (15 x^3+3 x^4\right ) \log ^3(x)\right ) \log (5+x)+\left (\left (15 x^4+3 x^5\right ) \log ^2(x)+\left (15 x^3+3 x^4\right ) \log ^3(x)\right ) \log ^2(5+x)+\left (5 x^3+x^4\right ) \log ^3(x) \log ^3(5+x)} \, dx=\frac {x^4\,\ln \left (x\right )+2\,x^3\,\ln \left (x+5\right )\,{\ln \left (x\right )}^2+2\,x^3\,{\ln \left (x\right )}^2+x^2\,{\ln \left (x+5\right )}^2\,{\ln \left (x\right )}^3+2\,x^2\,\ln \left (x+5\right )\,{\ln \left (x\right )}^3+x^2\,{\ln \left (x\right )}^3-1}{x^2\,{\left (x+\ln \left (x\right )+\ln \left (x+5\right )\,\ln \left (x\right )\right )}^2} \]
[In]
[Out]