Integrand size = 222, antiderivative size = 31 \[ \int \frac {-16-27 x-2 x^2+\left (3 x+x^2\right ) \log \left (e^{4 x} x^4\right )+\left (5 x-2 x^2+\left (-4 x-x^2\right ) \log \left (e^{4 x} x^4\right )+\left (-5+2 x+(4+x) \log \left (e^{4 x} x^4\right )\right ) \log \left (-5+2 x+(4+x) \log \left (e^{4 x} x^4\right )\right )\right ) \log \left (x-\log \left (-5+2 x+(4+x) \log \left (e^{4 x} x^4\right )\right )\right )}{\left (5 x-2 x^2+\left (-4 x-x^2\right ) \log \left (e^{4 x} x^4\right )+\left (-5+2 x+(4+x) \log \left (e^{4 x} x^4\right )\right ) \log \left (-5+2 x+(4+x) \log \left (e^{4 x} x^4\right )\right )\right ) \log ^2\left (x-\log \left (-5+2 x+(4+x) \log \left (e^{4 x} x^4\right )\right )\right )} \, dx=-5+\frac {x}{\log \left (x-\log \left (-5+2 x+(4+x) \log \left (e^{4 x} x^4\right )\right )\right )} \]
Time = 0.09 (sec) , antiderivative size = 29, normalized size of antiderivative = 0.94 \[ \int \frac {-16-27 x-2 x^2+\left (3 x+x^2\right ) \log \left (e^{4 x} x^4\right )+\left (5 x-2 x^2+\left (-4 x-x^2\right ) \log \left (e^{4 x} x^4\right )+\left (-5+2 x+(4+x) \log \left (e^{4 x} x^4\right )\right ) \log \left (-5+2 x+(4+x) \log \left (e^{4 x} x^4\right )\right )\right ) \log \left (x-\log \left (-5+2 x+(4+x) \log \left (e^{4 x} x^4\right )\right )\right )}{\left (5 x-2 x^2+\left (-4 x-x^2\right ) \log \left (e^{4 x} x^4\right )+\left (-5+2 x+(4+x) \log \left (e^{4 x} x^4\right )\right ) \log \left (-5+2 x+(4+x) \log \left (e^{4 x} x^4\right )\right )\right ) \log ^2\left (x-\log \left (-5+2 x+(4+x) \log \left (e^{4 x} x^4\right )\right )\right )} \, dx=\frac {x}{\log \left (x-\log \left (-5+2 x+(4+x) \log \left (e^{4 x} x^4\right )\right )\right )} \]
Integrate[(-16 - 27*x - 2*x^2 + (3*x + x^2)*Log[E^(4*x)*x^4] + (5*x - 2*x^ 2 + (-4*x - x^2)*Log[E^(4*x)*x^4] + (-5 + 2*x + (4 + x)*Log[E^(4*x)*x^4])* Log[-5 + 2*x + (4 + x)*Log[E^(4*x)*x^4]])*Log[x - Log[-5 + 2*x + (4 + x)*L og[E^(4*x)*x^4]]])/((5*x - 2*x^2 + (-4*x - x^2)*Log[E^(4*x)*x^4] + (-5 + 2 *x + (4 + x)*Log[E^(4*x)*x^4])*Log[-5 + 2*x + (4 + x)*Log[E^(4*x)*x^4]])*L og[x - Log[-5 + 2*x + (4 + x)*Log[E^(4*x)*x^4]]]^2),x]
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
\(\displaystyle \int \frac {-2 x^2+\left (x^2+3 x\right ) \log \left (e^{4 x} x^4\right )+\left (\left ((x+4) \log \left (e^{4 x} x^4\right )+2 x-5\right ) \log \left ((x+4) \log \left (e^{4 x} x^4\right )+2 x-5\right )-2 x^2+\left (-x^2-4 x\right ) \log \left (e^{4 x} x^4\right )+5 x\right ) \log \left (x-\log \left ((x+4) \log \left (e^{4 x} x^4\right )+2 x-5\right )\right )-27 x-16}{\left (\left ((x+4) \log \left (e^{4 x} x^4\right )+2 x-5\right ) \log \left ((x+4) \log \left (e^{4 x} x^4\right )+2 x-5\right )-2 x^2+\left (-x^2-4 x\right ) \log \left (e^{4 x} x^4\right )+5 x\right ) \log ^2\left (x-\log \left ((x+4) \log \left (e^{4 x} x^4\right )+2 x-5\right )\right )} \, dx\) |
\(\Big \downarrow \) 7292 |
\(\displaystyle \int \frac {-2 x^2+\left (x^2+3 x\right ) \log \left (e^{4 x} x^4\right )+\left (\left ((x+4) \log \left (e^{4 x} x^4\right )+2 x-5\right ) \log \left ((x+4) \log \left (e^{4 x} x^4\right )+2 x-5\right )-2 x^2+\left (-x^2-4 x\right ) \log \left (e^{4 x} x^4\right )+5 x\right ) \log \left (x-\log \left ((x+4) \log \left (e^{4 x} x^4\right )+2 x-5\right )\right )-27 x-16}{\left (x \left (-\log \left (e^{4 x} x^4\right )\right )-4 \log \left (e^{4 x} x^4\right )-2 x+5\right ) \left (x-\log \left ((x+4) \log \left (e^{4 x} x^4\right )+2 x-5\right )\right ) \log ^2\left (x-\log \left ((x+4) \log \left (e^{4 x} x^4\right )+2 x-5\right )\right )}dx\) |
\(\Big \downarrow \) 7293 |
\(\displaystyle \int \left (\frac {1}{\log \left (x-\log \left ((x+4) \log \left (e^{4 x} x^4\right )+2 x-5\right )\right )}+\frac {-3 x \log \left (e^{4 x} x^4\right )+2 x^2+x^2 \left (-\log \left (e^{4 x} x^4\right )\right )+27 x+16}{\left (x \log \left (e^{4 x} x^4\right )+4 \log \left (e^{4 x} x^4\right )+2 x-5\right ) \left (x-\log \left ((x+4) \log \left (e^{4 x} x^4\right )+2 x-5\right )\right ) \log ^2\left (x-\log \left ((x+4) \log \left (e^{4 x} x^4\right )+2 x-5\right )\right )}\right )dx\) |
\(\Big \downarrow \) 2009 |
\(\displaystyle 16 \int \frac {1}{\left (\log \left (e^{4 x} x^4\right ) x+2 x+4 \log \left (e^{4 x} x^4\right )-5\right ) \left (x-\log \left (2 x+(x+4) \log \left (e^{4 x} x^4\right )-5\right )\right ) \log ^2\left (x-\log \left (2 x+(x+4) \log \left (e^{4 x} x^4\right )-5\right )\right )}dx+27 \int \frac {x}{\left (\log \left (e^{4 x} x^4\right ) x+2 x+4 \log \left (e^{4 x} x^4\right )-5\right ) \left (x-\log \left (2 x+(x+4) \log \left (e^{4 x} x^4\right )-5\right )\right ) \log ^2\left (x-\log \left (2 x+(x+4) \log \left (e^{4 x} x^4\right )-5\right )\right )}dx-3 \int \frac {x \log \left (e^{4 x} x^4\right )}{\left (\log \left (e^{4 x} x^4\right ) x+2 x+4 \log \left (e^{4 x} x^4\right )-5\right ) \left (x-\log \left (2 x+(x+4) \log \left (e^{4 x} x^4\right )-5\right )\right ) \log ^2\left (x-\log \left (2 x+(x+4) \log \left (e^{4 x} x^4\right )-5\right )\right )}dx+\int \frac {1}{\log \left (x-\log \left (2 x+(x+4) \log \left (e^{4 x} x^4\right )-5\right )\right )}dx+2 \int \frac {x^2}{\left (\log \left (e^{4 x} x^4\right ) x+2 x+4 \log \left (e^{4 x} x^4\right )-5\right ) \left (x-\log \left (2 x+(x+4) \log \left (e^{4 x} x^4\right )-5\right )\right ) \log ^2\left (x-\log \left (2 x+(x+4) \log \left (e^{4 x} x^4\right )-5\right )\right )}dx-\int \frac {x^2 \log \left (e^{4 x} x^4\right )}{\left (\log \left (e^{4 x} x^4\right ) x+2 x+4 \log \left (e^{4 x} x^4\right )-5\right ) \left (x-\log \left (2 x+(x+4) \log \left (e^{4 x} x^4\right )-5\right )\right ) \log ^2\left (x-\log \left (2 x+(x+4) \log \left (e^{4 x} x^4\right )-5\right )\right )}dx\) |
Int[(-16 - 27*x - 2*x^2 + (3*x + x^2)*Log[E^(4*x)*x^4] + (5*x - 2*x^2 + (- 4*x - x^2)*Log[E^(4*x)*x^4] + (-5 + 2*x + (4 + x)*Log[E^(4*x)*x^4])*Log[-5 + 2*x + (4 + x)*Log[E^(4*x)*x^4]])*Log[x - Log[-5 + 2*x + (4 + x)*Log[E^( 4*x)*x^4]]])/((5*x - 2*x^2 + (-4*x - x^2)*Log[E^(4*x)*x^4] + (-5 + 2*x + ( 4 + x)*Log[E^(4*x)*x^4])*Log[-5 + 2*x + (4 + x)*Log[E^(4*x)*x^4]])*Log[x - Log[-5 + 2*x + (4 + x)*Log[E^(4*x)*x^4]]]^2),x]
3.25.84.3.1 Defintions of rubi rules used
Result contains higher order function than in optimal. Order 9 vs. order 3.
Time = 29.17 (sec) , antiderivative size = 329, normalized size of antiderivative = 10.61
\[\frac {x}{\ln \left (-\ln \left (\left (4+x \right ) \left (4 \ln \left (x \right )+4 \ln \left ({\mathrm e}^{x}\right )-\frac {i \pi \,\operatorname {csgn}\left (i {\mathrm e}^{2 x}\right ) {\left (-\operatorname {csgn}\left (i {\mathrm e}^{2 x}\right )+\operatorname {csgn}\left (i {\mathrm e}^{x}\right )\right )}^{2}}{2}-\frac {i \pi \,\operatorname {csgn}\left (i {\mathrm e}^{3 x}\right ) \left (-\operatorname {csgn}\left (i {\mathrm e}^{3 x}\right )+\operatorname {csgn}\left (i {\mathrm e}^{2 x}\right )\right ) \left (-\operatorname {csgn}\left (i {\mathrm e}^{3 x}\right )+\operatorname {csgn}\left (i {\mathrm e}^{x}\right )\right )}{2}-\frac {i \pi \,\operatorname {csgn}\left (i {\mathrm e}^{4 x}\right ) \left (-\operatorname {csgn}\left (i {\mathrm e}^{4 x}\right )+\operatorname {csgn}\left (i {\mathrm e}^{3 x}\right )\right ) \left (-\operatorname {csgn}\left (i {\mathrm e}^{4 x}\right )+\operatorname {csgn}\left (i {\mathrm e}^{x}\right )\right )}{2}-\frac {i \pi \,\operatorname {csgn}\left (i x^{2}\right ) {\left (-\operatorname {csgn}\left (i x^{2}\right )+\operatorname {csgn}\left (i x \right )\right )}^{2}}{2}-\frac {i \pi \,\operatorname {csgn}\left (i x^{3}\right ) \left (-\operatorname {csgn}\left (i x^{3}\right )+\operatorname {csgn}\left (i x^{2}\right )\right ) \left (-\operatorname {csgn}\left (i x^{3}\right )+\operatorname {csgn}\left (i x \right )\right )}{2}-\frac {i \pi \,\operatorname {csgn}\left (i x^{4}\right ) \left (-\operatorname {csgn}\left (i x^{4}\right )+\operatorname {csgn}\left (i x^{3}\right )\right ) \left (-\operatorname {csgn}\left (i x^{4}\right )+\operatorname {csgn}\left (i x \right )\right )}{2}-\frac {i \pi \,\operatorname {csgn}\left (i x^{4} {\mathrm e}^{4 x}\right ) \left (-\operatorname {csgn}\left (i x^{4} {\mathrm e}^{4 x}\right )+\operatorname {csgn}\left (i x^{4}\right )\right ) \left (-\operatorname {csgn}\left (i x^{4} {\mathrm e}^{4 x}\right )+\operatorname {csgn}\left (i {\mathrm e}^{4 x}\right )\right )}{2}\right )+2 x -5\right )+x \right )}\]
int(((((4+x)*ln(x^4*exp(x)^4)+2*x-5)*ln((4+x)*ln(x^4*exp(x)^4)+2*x-5)+(-x^ 2-4*x)*ln(x^4*exp(x)^4)-2*x^2+5*x)*ln(-ln((4+x)*ln(x^4*exp(x)^4)+2*x-5)+x) +(x^2+3*x)*ln(x^4*exp(x)^4)-2*x^2-27*x-16)/(((4+x)*ln(x^4*exp(x)^4)+2*x-5) *ln((4+x)*ln(x^4*exp(x)^4)+2*x-5)+(-x^2-4*x)*ln(x^4*exp(x)^4)-2*x^2+5*x)/l n(-ln((4+x)*ln(x^4*exp(x)^4)+2*x-5)+x)^2,x)
x/ln(-ln((4+x)*(4*ln(x)+4*ln(exp(x))-1/2*I*Pi*csgn(I*exp(2*x))*(-csgn(I*ex p(2*x))+csgn(I*exp(x)))^2-1/2*I*Pi*csgn(I*exp(3*x))*(-csgn(I*exp(3*x))+csg n(I*exp(2*x)))*(-csgn(I*exp(3*x))+csgn(I*exp(x)))-1/2*I*Pi*csgn(I*exp(4*x) )*(-csgn(I*exp(4*x))+csgn(I*exp(3*x)))*(-csgn(I*exp(4*x))+csgn(I*exp(x)))- 1/2*I*Pi*csgn(I*x^2)*(-csgn(I*x^2)+csgn(I*x))^2-1/2*I*Pi*csgn(I*x^3)*(-csg n(I*x^3)+csgn(I*x^2))*(-csgn(I*x^3)+csgn(I*x))-1/2*I*Pi*csgn(I*x^4)*(-csgn (I*x^4)+csgn(I*x^3))*(-csgn(I*x^4)+csgn(I*x))-1/2*I*Pi*csgn(I*x^4*exp(4*x) )*(-csgn(I*x^4*exp(4*x))+csgn(I*x^4))*(-csgn(I*x^4*exp(4*x))+csgn(I*exp(4* x))))+2*x-5)+x)
Time = 0.26 (sec) , antiderivative size = 28, normalized size of antiderivative = 0.90 \[ \int \frac {-16-27 x-2 x^2+\left (3 x+x^2\right ) \log \left (e^{4 x} x^4\right )+\left (5 x-2 x^2+\left (-4 x-x^2\right ) \log \left (e^{4 x} x^4\right )+\left (-5+2 x+(4+x) \log \left (e^{4 x} x^4\right )\right ) \log \left (-5+2 x+(4+x) \log \left (e^{4 x} x^4\right )\right )\right ) \log \left (x-\log \left (-5+2 x+(4+x) \log \left (e^{4 x} x^4\right )\right )\right )}{\left (5 x-2 x^2+\left (-4 x-x^2\right ) \log \left (e^{4 x} x^4\right )+\left (-5+2 x+(4+x) \log \left (e^{4 x} x^4\right )\right ) \log \left (-5+2 x+(4+x) \log \left (e^{4 x} x^4\right )\right )\right ) \log ^2\left (x-\log \left (-5+2 x+(4+x) \log \left (e^{4 x} x^4\right )\right )\right )} \, dx=\frac {x}{\log \left (x - \log \left ({\left (x + 4\right )} \log \left (x^{4} e^{\left (4 \, x\right )}\right ) + 2 \, x - 5\right )\right )} \]
integrate(((((4+x)*log(x^4*exp(x)^4)+2*x-5)*log((4+x)*log(x^4*exp(x)^4)+2* x-5)+(-x^2-4*x)*log(x^4*exp(x)^4)-2*x^2+5*x)*log(-log((4+x)*log(x^4*exp(x) ^4)+2*x-5)+x)+(x^2+3*x)*log(x^4*exp(x)^4)-2*x^2-27*x-16)/(((4+x)*log(x^4*e xp(x)^4)+2*x-5)*log((4+x)*log(x^4*exp(x)^4)+2*x-5)+(-x^2-4*x)*log(x^4*exp( x)^4)-2*x^2+5*x)/log(-log((4+x)*log(x^4*exp(x)^4)+2*x-5)+x)^2,x, algorithm =\
Time = 117.05 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.77 \[ \int \frac {-16-27 x-2 x^2+\left (3 x+x^2\right ) \log \left (e^{4 x} x^4\right )+\left (5 x-2 x^2+\left (-4 x-x^2\right ) \log \left (e^{4 x} x^4\right )+\left (-5+2 x+(4+x) \log \left (e^{4 x} x^4\right )\right ) \log \left (-5+2 x+(4+x) \log \left (e^{4 x} x^4\right )\right )\right ) \log \left (x-\log \left (-5+2 x+(4+x) \log \left (e^{4 x} x^4\right )\right )\right )}{\left (5 x-2 x^2+\left (-4 x-x^2\right ) \log \left (e^{4 x} x^4\right )+\left (-5+2 x+(4+x) \log \left (e^{4 x} x^4\right )\right ) \log \left (-5+2 x+(4+x) \log \left (e^{4 x} x^4\right )\right )\right ) \log ^2\left (x-\log \left (-5+2 x+(4+x) \log \left (e^{4 x} x^4\right )\right )\right )} \, dx=\frac {x}{\log {\left (x - \log {\left (2 x + \left (x + 4\right ) \log {\left (x^{4} e^{4 x} \right )} - 5 \right )} \right )}} \]
integrate(((((4+x)*ln(x**4*exp(x)**4)+2*x-5)*ln((4+x)*ln(x**4*exp(x)**4)+2 *x-5)+(-x**2-4*x)*ln(x**4*exp(x)**4)-2*x**2+5*x)*ln(-ln((4+x)*ln(x**4*exp( x)**4)+2*x-5)+x)+(x**2+3*x)*ln(x**4*exp(x)**4)-2*x**2-27*x-16)/(((4+x)*ln( x**4*exp(x)**4)+2*x-5)*ln((4+x)*ln(x**4*exp(x)**4)+2*x-5)+(-x**2-4*x)*ln(x **4*exp(x)**4)-2*x**2+5*x)/ln(-ln((4+x)*ln(x**4*exp(x)**4)+2*x-5)+x)**2,x)
Time = 0.52 (sec) , antiderivative size = 27, normalized size of antiderivative = 0.87 \[ \int \frac {-16-27 x-2 x^2+\left (3 x+x^2\right ) \log \left (e^{4 x} x^4\right )+\left (5 x-2 x^2+\left (-4 x-x^2\right ) \log \left (e^{4 x} x^4\right )+\left (-5+2 x+(4+x) \log \left (e^{4 x} x^4\right )\right ) \log \left (-5+2 x+(4+x) \log \left (e^{4 x} x^4\right )\right )\right ) \log \left (x-\log \left (-5+2 x+(4+x) \log \left (e^{4 x} x^4\right )\right )\right )}{\left (5 x-2 x^2+\left (-4 x-x^2\right ) \log \left (e^{4 x} x^4\right )+\left (-5+2 x+(4+x) \log \left (e^{4 x} x^4\right )\right ) \log \left (-5+2 x+(4+x) \log \left (e^{4 x} x^4\right )\right )\right ) \log ^2\left (x-\log \left (-5+2 x+(4+x) \log \left (e^{4 x} x^4\right )\right )\right )} \, dx=\frac {x}{\log \left (x - \log \left (4 \, x^{2} + 4 \, {\left (x + 4\right )} \log \left (x\right ) + 18 \, x - 5\right )\right )} \]
integrate(((((4+x)*log(x^4*exp(x)^4)+2*x-5)*log((4+x)*log(x^4*exp(x)^4)+2* x-5)+(-x^2-4*x)*log(x^4*exp(x)^4)-2*x^2+5*x)*log(-log((4+x)*log(x^4*exp(x) ^4)+2*x-5)+x)+(x^2+3*x)*log(x^4*exp(x)^4)-2*x^2-27*x-16)/(((4+x)*log(x^4*e xp(x)^4)+2*x-5)*log((4+x)*log(x^4*exp(x)^4)+2*x-5)+(-x^2-4*x)*log(x^4*exp( x)^4)-2*x^2+5*x)/log(-log((4+x)*log(x^4*exp(x)^4)+2*x-5)+x)^2,x, algorithm =\
Time = 1.94 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.03 \[ \int \frac {-16-27 x-2 x^2+\left (3 x+x^2\right ) \log \left (e^{4 x} x^4\right )+\left (5 x-2 x^2+\left (-4 x-x^2\right ) \log \left (e^{4 x} x^4\right )+\left (-5+2 x+(4+x) \log \left (e^{4 x} x^4\right )\right ) \log \left (-5+2 x+(4+x) \log \left (e^{4 x} x^4\right )\right )\right ) \log \left (x-\log \left (-5+2 x+(4+x) \log \left (e^{4 x} x^4\right )\right )\right )}{\left (5 x-2 x^2+\left (-4 x-x^2\right ) \log \left (e^{4 x} x^4\right )+\left (-5+2 x+(4+x) \log \left (e^{4 x} x^4\right )\right ) \log \left (-5+2 x+(4+x) \log \left (e^{4 x} x^4\right )\right )\right ) \log ^2\left (x-\log \left (-5+2 x+(4+x) \log \left (e^{4 x} x^4\right )\right )\right )} \, dx=\frac {x}{\log \left (x - \log \left (4 \, x^{2} + x \log \left (x^{4}\right ) + 18 \, x + 4 \, \log \left (x^{4}\right ) - 5\right )\right )} \]
integrate(((((4+x)*log(x^4*exp(x)^4)+2*x-5)*log((4+x)*log(x^4*exp(x)^4)+2* x-5)+(-x^2-4*x)*log(x^4*exp(x)^4)-2*x^2+5*x)*log(-log((4+x)*log(x^4*exp(x) ^4)+2*x-5)+x)+(x^2+3*x)*log(x^4*exp(x)^4)-2*x^2-27*x-16)/(((4+x)*log(x^4*e xp(x)^4)+2*x-5)*log((4+x)*log(x^4*exp(x)^4)+2*x-5)+(-x^2-4*x)*log(x^4*exp( x)^4)-2*x^2+5*x)/log(-log((4+x)*log(x^4*exp(x)^4)+2*x-5)+x)^2,x, algorithm =\
Timed out. \[ \int \frac {-16-27 x-2 x^2+\left (3 x+x^2\right ) \log \left (e^{4 x} x^4\right )+\left (5 x-2 x^2+\left (-4 x-x^2\right ) \log \left (e^{4 x} x^4\right )+\left (-5+2 x+(4+x) \log \left (e^{4 x} x^4\right )\right ) \log \left (-5+2 x+(4+x) \log \left (e^{4 x} x^4\right )\right )\right ) \log \left (x-\log \left (-5+2 x+(4+x) \log \left (e^{4 x} x^4\right )\right )\right )}{\left (5 x-2 x^2+\left (-4 x-x^2\right ) \log \left (e^{4 x} x^4\right )+\left (-5+2 x+(4+x) \log \left (e^{4 x} x^4\right )\right ) \log \left (-5+2 x+(4+x) \log \left (e^{4 x} x^4\right )\right )\right ) \log ^2\left (x-\log \left (-5+2 x+(4+x) \log \left (e^{4 x} x^4\right )\right )\right )} \, dx=\int -\frac {27\,x-\ln \left (x^4\,{\mathrm {e}}^{4\,x}\right )\,\left (x^2+3\,x\right )+2\,x^2-\ln \left (x-\ln \left (2\,x+\ln \left (x^4\,{\mathrm {e}}^{4\,x}\right )\,\left (x+4\right )-5\right )\right )\,\left (5\,x-\ln \left (x^4\,{\mathrm {e}}^{4\,x}\right )\,\left (x^2+4\,x\right )+\ln \left (2\,x+\ln \left (x^4\,{\mathrm {e}}^{4\,x}\right )\,\left (x+4\right )-5\right )\,\left (2\,x+\ln \left (x^4\,{\mathrm {e}}^{4\,x}\right )\,\left (x+4\right )-5\right )-2\,x^2\right )+16}{{\ln \left (x-\ln \left (2\,x+\ln \left (x^4\,{\mathrm {e}}^{4\,x}\right )\,\left (x+4\right )-5\right )\right )}^2\,\left (5\,x-\ln \left (x^4\,{\mathrm {e}}^{4\,x}\right )\,\left (x^2+4\,x\right )+\ln \left (2\,x+\ln \left (x^4\,{\mathrm {e}}^{4\,x}\right )\,\left (x+4\right )-5\right )\,\left (2\,x+\ln \left (x^4\,{\mathrm {e}}^{4\,x}\right )\,\left (x+4\right )-5\right )-2\,x^2\right )} \,d x \]
int(-(27*x - log(x^4*exp(4*x))*(3*x + x^2) + 2*x^2 - log(x - log(2*x + log (x^4*exp(4*x))*(x + 4) - 5))*(5*x - log(x^4*exp(4*x))*(4*x + x^2) + log(2* x + log(x^4*exp(4*x))*(x + 4) - 5)*(2*x + log(x^4*exp(4*x))*(x + 4) - 5) - 2*x^2) + 16)/(log(x - log(2*x + log(x^4*exp(4*x))*(x + 4) - 5))^2*(5*x - log(x^4*exp(4*x))*(4*x + x^2) + log(2*x + log(x^4*exp(4*x))*(x + 4) - 5)*( 2*x + log(x^4*exp(4*x))*(x + 4) - 5) - 2*x^2)),x)
int(-(27*x - log(x^4*exp(4*x))*(3*x + x^2) + 2*x^2 - log(x - log(2*x + log (x^4*exp(4*x))*(x + 4) - 5))*(5*x - log(x^4*exp(4*x))*(4*x + x^2) + log(2* x + log(x^4*exp(4*x))*(x + 4) - 5)*(2*x + log(x^4*exp(4*x))*(x + 4) - 5) - 2*x^2) + 16)/(log(x - log(2*x + log(x^4*exp(4*x))*(x + 4) - 5))^2*(5*x - log(x^4*exp(4*x))*(4*x + x^2) + log(2*x + log(x^4*exp(4*x))*(x + 4) - 5)*( 2*x + log(x^4*exp(4*x))*(x + 4) - 5) - 2*x^2)), x)