Integrand size = 145, antiderivative size = 25 \[ \int \frac {e^x \left (-8+e^{20} (-32+6 x)\right ) \log \left (\log \left (-\frac {e^{20} x^4}{-1+e^{20} (-4+x)}\right )\right )+e^x \left (1-x+e^{20} \left (4-5 x+x^2\right )\right ) \log \left (-\frac {e^{20} x^4}{-1+e^{20} (-4+x)}\right ) \log ^2\left (\log \left (-\frac {e^{20} x^4}{-1+e^{20} (-4+x)}\right )\right )}{\left (-x^2+e^{20} \left (-4 x^2+x^3\right )\right ) \log \left (-\frac {e^{20} x^4}{-1+e^{20} (-4+x)}\right )} \, dx=\frac {e^x \log ^2\left (\log \left (\frac {x^4}{4+\frac {1}{e^{20}}-x}\right )\right )}{x} \] Output:
ln(ln(x^4/(4-x+exp(-10)^2)))^2*exp(x)/x
\[ \int \frac {e^x \left (-8+e^{20} (-32+6 x)\right ) \log \left (\log \left (-\frac {e^{20} x^4}{-1+e^{20} (-4+x)}\right )\right )+e^x \left (1-x+e^{20} \left (4-5 x+x^2\right )\right ) \log \left (-\frac {e^{20} x^4}{-1+e^{20} (-4+x)}\right ) \log ^2\left (\log \left (-\frac {e^{20} x^4}{-1+e^{20} (-4+x)}\right )\right )}{\left (-x^2+e^{20} \left (-4 x^2+x^3\right )\right ) \log \left (-\frac {e^{20} x^4}{-1+e^{20} (-4+x)}\right )} \, dx=\int \frac {e^x \left (-8+e^{20} (-32+6 x)\right ) \log \left (\log \left (-\frac {e^{20} x^4}{-1+e^{20} (-4+x)}\right )\right )+e^x \left (1-x+e^{20} \left (4-5 x+x^2\right )\right ) \log \left (-\frac {e^{20} x^4}{-1+e^{20} (-4+x)}\right ) \log ^2\left (\log \left (-\frac {e^{20} x^4}{-1+e^{20} (-4+x)}\right )\right )}{\left (-x^2+e^{20} \left (-4 x^2+x^3\right )\right ) \log \left (-\frac {e^{20} x^4}{-1+e^{20} (-4+x)}\right )} \, dx \] Input:
Integrate[(E^x*(-8 + E^20*(-32 + 6*x))*Log[Log[-((E^20*x^4)/(-1 + E^20*(-4 + x)))]] + E^x*(1 - x + E^20*(4 - 5*x + x^2))*Log[-((E^20*x^4)/(-1 + E^20 *(-4 + x)))]*Log[Log[-((E^20*x^4)/(-1 + E^20*(-4 + x)))]]^2)/((-x^2 + E^20 *(-4*x^2 + x^3))*Log[-((E^20*x^4)/(-1 + E^20*(-4 + x)))]),x]
Output:
Integrate[(E^x*(-8 + E^20*(-32 + 6*x))*Log[Log[-((E^20*x^4)/(-1 + E^20*(-4 + x)))]] + E^x*(1 - x + E^20*(4 - 5*x + x^2))*Log[-((E^20*x^4)/(-1 + E^20 *(-4 + x)))]*Log[Log[-((E^20*x^4)/(-1 + E^20*(-4 + x)))]]^2)/((-x^2 + E^20 *(-4*x^2 + x^3))*Log[-((E^20*x^4)/(-1 + E^20*(-4 + x)))]), 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.
| \(\displaystyle \int \frac {e^x \left (e^{20} (6 x-32)-8\right ) \log \left (\log \left (-\frac {e^{20} x^4}{e^{20} (x-4)-1}\right )\right )+e^x \left (e^{20} \left (x^2-5 x+4\right )-x+1\right ) \log \left (-\frac {e^{20} x^4}{e^{20} (x-4)-1}\right ) \log ^2\left (\log \left (-\frac {e^{20} x^4}{e^{20} (x-4)-1}\right )\right )}{\left (e^{20} \left (x^3-4 x^2\right )-x^2\right ) \log \left (-\frac {e^{20} x^4}{e^{20} (x-4)-1}\right )} \, dx\) |
| \(\Big \downarrow \) 2026 |
| \(\displaystyle \int \frac {e^x \left (e^{20} (6 x-32)-8\right ) \log \left (\log \left (-\frac {e^{20} x^4}{e^{20} (x-4)-1}\right )\right )+e^x \left (e^{20} \left (x^2-5 x+4\right )-x+1\right ) \log \left (-\frac {e^{20} x^4}{e^{20} (x-4)-1}\right ) \log ^2\left (\log \left (-\frac {e^{20} x^4}{e^{20} (x-4)-1}\right )\right )}{x^2 \left (e^{20} x-4 e^{20}-1\right ) \log \left (-\frac {e^{20} x^4}{e^{20} (x-4)-1}\right )}dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {-e^x \left (e^{20} (6 x-32)-8\right ) \log \left (\log \left (-\frac {e^{20} x^4}{e^{20} (x-4)-1}\right )\right )-e^x \left (e^{20} \left (x^2-5 x+4\right )-x+1\right ) \log \left (-\frac {e^{20} x^4}{e^{20} (x-4)-1}\right ) \log ^2\left (\log \left (-\frac {e^{20} x^4}{e^{20} (x-4)-1}\right )\right )}{x^2 \left (-e^{20} x+4 e^{20}+1\right ) \log \left (-\frac {e^{20} x^4}{e^{20} x-4 e^{20}-1}\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {e^{x+20} \left (\left (1+5 e^{20}\right ) x \log \left (-\frac {e^{20} x^4}{e^{20} (x-4)-1}\right ) \log \left (\log \left (-\frac {e^{20} x^4}{e^{20} (x-4)-1}\right )\right )-\left (1+4 e^{20}\right ) \log \left (-\frac {e^{20} x^4}{e^{20} (x-4)-1}\right ) \log \left (\log \left (-\frac {e^{20} x^4}{e^{20} (x-4)-1}\right )\right )-e^{20} x^2 \log \left (-\frac {e^{20} x^4}{e^{20} (x-4)-1}\right ) \log \left (\log \left (-\frac {e^{20} x^4}{e^{20} (x-4)-1}\right )\right )-6 e^{20} x+8 \left (1+4 e^{20}\right )\right ) \log \left (\log \left (-\frac {e^{20} x^4}{e^{20} x-4 e^{20}-1}\right )\right )}{\left (1+4 e^{20}\right )^2 x \log \left (-\frac {e^{20} x^4}{e^{20} x-4 e^{20}-1}\right )}+\frac {e^{x+40} \left (\left (1+5 e^{20}\right ) x \log \left (-\frac {e^{20} x^4}{e^{20} (x-4)-1}\right ) \log \left (\log \left (-\frac {e^{20} x^4}{e^{20} (x-4)-1}\right )\right )-\left (1+4 e^{20}\right ) \log \left (-\frac {e^{20} x^4}{e^{20} (x-4)-1}\right ) \log \left (\log \left (-\frac {e^{20} x^4}{e^{20} (x-4)-1}\right )\right )-e^{20} x^2 \log \left (-\frac {e^{20} x^4}{e^{20} (x-4)-1}\right ) \log \left (\log \left (-\frac {e^{20} x^4}{e^{20} (x-4)-1}\right )\right )-6 e^{20} x+8 \left (1+4 e^{20}\right )\right ) \log \left (\log \left (-\frac {e^{20} x^4}{e^{20} x-4 e^{20}-1}\right )\right )}{\left (1+4 e^{20}\right )^2 \left (-e^{20} x+4 e^{20}+1\right ) \log \left (-\frac {e^{20} x^4}{e^{20} x-4 e^{20}-1}\right )}+\frac {e^x \left (\left (1+5 e^{20}\right ) x \log \left (-\frac {e^{20} x^4}{e^{20} (x-4)-1}\right ) \log \left (\log \left (-\frac {e^{20} x^4}{e^{20} (x-4)-1}\right )\right )-\left (1+4 e^{20}\right ) \log \left (-\frac {e^{20} x^4}{e^{20} (x-4)-1}\right ) \log \left (\log \left (-\frac {e^{20} x^4}{e^{20} (x-4)-1}\right )\right )-e^{20} x^2 \log \left (-\frac {e^{20} x^4}{e^{20} (x-4)-1}\right ) \log \left (\log \left (-\frac {e^{20} x^4}{e^{20} (x-4)-1}\right )\right )-6 e^{20} x+8 \left (1+4 e^{20}\right )\right ) \log \left (\log \left (-\frac {e^{20} x^4}{e^{20} x-4 e^{20}-1}\right )\right )}{\left (1+4 e^{20}\right ) x^2 \log \left (-\frac {e^{20} x^4}{e^{20} x-4 e^{20}-1}\right )}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle \frac {\left (1+5 e^{20}\right ) \int \frac {e^x \log ^2\left (\log \left (-\frac {e^{20} x^4}{e^{20} x-4 e^{20}-1}\right )\right )}{x}dx}{1+4 e^{20}}-\frac {\int \frac {e^{x+20} \log ^2\left (\log \left (-\frac {e^{20} x^4}{e^{20} x-4 e^{20}-1}\right )\right )}{x}dx}{1+4 e^{20}}+\frac {\left (1+5 e^{20}\right ) \int \frac {e^{x+20} \log ^2\left (\log \left (-\frac {e^{20} x^4}{e^{20} x-4 e^{20}-1}\right )\right )}{-e^{20} x+4 e^{20}+1}dx}{1+4 e^{20}}+\int \frac {e^{x+20} \log ^2\left (\log \left (-\frac {e^{20} x^4}{e^{20} x-4 e^{20}-1}\right )\right )}{e^{20} x-4 e^{20}-1}dx+\frac {\int \frac {e^{x+40} \log ^2\left (\log \left (-\frac {e^{20} x^4}{e^{20} x-4 e^{20}-1}\right )\right )}{e^{20} x-4 e^{20}-1}dx}{1+4 e^{20}}+\frac {2 \int \frac {e^{x+20} \log \left (\log \left (-\frac {e^{20} x^4}{e^{20} x-4 e^{20}-1}\right )\right )}{x \log \left (-\frac {e^{20} x^4}{e^{20} x-4 e^{20}-1}\right )}dx}{1+4 e^{20}}+\frac {2 \int \frac {e^{x+40} \log \left (\log \left (-\frac {e^{20} x^4}{e^{20} x-4 e^{20}-1}\right )\right )}{\left (-e^{20} x+4 e^{20}+1\right ) \log \left (-\frac {e^{20} x^4}{e^{20} x-4 e^{20}-1}\right )}dx}{1+4 e^{20}}-\int \frac {e^x \log ^2\left (\log \left (-\frac {e^{20} x^4}{e^{20} x-4 e^{20}-1}\right )\right )}{x^2}dx+8 \int \frac {e^x \log \left (\log \left (-\frac {e^{20} x^4}{e^{20} x-4 e^{20}-1}\right )\right )}{x^2 \log \left (-\frac {e^{20} x^4}{e^{20} x-4 e^{20}-1}\right )}dx\) |
Input:
Int[(E^x*(-8 + E^20*(-32 + 6*x))*Log[Log[-((E^20*x^4)/(-1 + E^20*(-4 + x)) )]] + E^x*(1 - x + E^20*(4 - 5*x + x^2))*Log[-((E^20*x^4)/(-1 + E^20*(-4 + x)))]*Log[Log[-((E^20*x^4)/(-1 + E^20*(-4 + x)))]]^2)/((-x^2 + E^20*(-4*x ^2 + x^3))*Log[-((E^20*x^4)/(-1 + E^20*(-4 + x)))]),x]
Output:
$Aborted
Time = 20.64 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.44
| method | result | size |
| parallelrisch | \(\frac {{\ln \left (\ln \left (-\frac {x^{4} {\mathrm e}^{20}}{x \,{\mathrm e}^{20}-4 \,{\mathrm e}^{20}-1}\right )\right )}^{2} {\mathrm e}^{x}}{x}\) | \(36\) |
| risch | \(\frac {{\mathrm e}^{x} {\ln \left (20+i \pi +4 \ln \left (x \right )-\ln \left (\left (x -4\right ) {\mathrm e}^{20}-1\right )-\frac {i \pi \,\operatorname {csgn}\left (i x^{2}\right ) {\left (-\operatorname {csgn}\left (i x^{2}\right )+\operatorname {csgn}\left (i x \right )\right )}^{2}}{2}-\frac {i \pi \,\operatorname {csgn}\left (i x^{3}\right ) \left (-\operatorname {csgn}\left (i x^{3}\right )+\operatorname {csgn}\left (i x^{2}\right )\right ) \left (-\operatorname {csgn}\left (i x^{3}\right )+\operatorname {csgn}\left (i x \right )\right )}{2}-\frac {i \pi \,\operatorname {csgn}\left (i x^{4}\right ) \left (-\operatorname {csgn}\left (i x^{4}\right )+\operatorname {csgn}\left (i x^{3}\right )\right ) \left (-\operatorname {csgn}\left (i x^{4}\right )+\operatorname {csgn}\left (i x \right )\right )}{2}-\frac {i \pi \,\operatorname {csgn}\left (\frac {i x^{4}}{\left (x -4\right ) {\mathrm e}^{20}-1}\right ) \left (-\operatorname {csgn}\left (\frac {i x^{4}}{\left (x -4\right ) {\mathrm e}^{20}-1}\right )+\operatorname {csgn}\left (i x^{4}\right )\right ) \left (-\operatorname {csgn}\left (\frac {i x^{4}}{\left (x -4\right ) {\mathrm e}^{20}-1}\right )+\operatorname {csgn}\left (\frac {i}{\left (x -4\right ) {\mathrm e}^{20}-1}\right )\right )}{2}+i \pi \operatorname {csgn}\left (\frac {i x^{4}}{\left (x -4\right ) {\mathrm e}^{20}-1}\right )^{2} \left (\operatorname {csgn}\left (\frac {i x^{4}}{\left (x -4\right ) {\mathrm e}^{20}-1}\right )-1\right )\right )}^{2}}{x}\) | \(269\) |
Input:
int((((x^2-5*x+4)*exp(10)^2-x+1)*exp(x)*ln(-x^4*exp(10)^2/((x-4)*exp(10)^2 -1))*ln(ln(-x^4*exp(10)^2/((x-4)*exp(10)^2-1)))^2+((6*x-32)*exp(10)^2-8)*e xp(x)*ln(ln(-x^4*exp(10)^2/((x-4)*exp(10)^2-1))))/((x^3-4*x^2)*exp(10)^2-x ^2)/ln(-x^4*exp(10)^2/((x-4)*exp(10)^2-1)),x,method=_RETURNVERBOSE)
Output:
ln(ln(-x^4*exp(10)^2/(x*exp(10)^2-4*exp(10)^2-1)))^2*exp(x)/x
Time = 0.10 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.08 \[ \int \frac {e^x \left (-8+e^{20} (-32+6 x)\right ) \log \left (\log \left (-\frac {e^{20} x^4}{-1+e^{20} (-4+x)}\right )\right )+e^x \left (1-x+e^{20} \left (4-5 x+x^2\right )\right ) \log \left (-\frac {e^{20} x^4}{-1+e^{20} (-4+x)}\right ) \log ^2\left (\log \left (-\frac {e^{20} x^4}{-1+e^{20} (-4+x)}\right )\right )}{\left (-x^2+e^{20} \left (-4 x^2+x^3\right )\right ) \log \left (-\frac {e^{20} x^4}{-1+e^{20} (-4+x)}\right )} \, dx=\frac {e^{x} \log \left (\log \left (-\frac {x^{4} e^{20}}{{\left (x - 4\right )} e^{20} - 1}\right )\right )^{2}}{x} \] Input:
integrate((((x^2-5*x+4)*exp(10)^2-x+1)*exp(x)*log(-x^4*exp(10)^2/((-4+x)*e xp(10)^2-1))*log(log(-x^4*exp(10)^2/((-4+x)*exp(10)^2-1)))^2+((6*x-32)*exp (10)^2-8)*exp(x)*log(log(-x^4*exp(10)^2/((-4+x)*exp(10)^2-1))))/((x^3-4*x^ 2)*exp(10)^2-x^2)/log(-x^4*exp(10)^2/((-4+x)*exp(10)^2-1)),x, algorithm="f ricas")
Output:
e^x*log(log(-x^4*e^20/((x - 4)*e^20 - 1)))^2/x
Time = 0.57 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.04 \[ \int \frac {e^x \left (-8+e^{20} (-32+6 x)\right ) \log \left (\log \left (-\frac {e^{20} x^4}{-1+e^{20} (-4+x)}\right )\right )+e^x \left (1-x+e^{20} \left (4-5 x+x^2\right )\right ) \log \left (-\frac {e^{20} x^4}{-1+e^{20} (-4+x)}\right ) \log ^2\left (\log \left (-\frac {e^{20} x^4}{-1+e^{20} (-4+x)}\right )\right )}{\left (-x^2+e^{20} \left (-4 x^2+x^3\right )\right ) \log \left (-\frac {e^{20} x^4}{-1+e^{20} (-4+x)}\right )} \, dx=\frac {e^{x} \log {\left (\log {\left (- \frac {x^{4} e^{20}}{\left (x - 4\right ) e^{20} - 1} \right )} \right )}^{2}}{x} \] Input:
integrate((((x**2-5*x+4)*exp(10)**2-x+1)*exp(x)*ln(-x**4*exp(10)**2/((-4+x )*exp(10)**2-1))*ln(ln(-x**4*exp(10)**2/((-4+x)*exp(10)**2-1)))**2+((6*x-3 2)*exp(10)**2-8)*exp(x)*ln(ln(-x**4*exp(10)**2/((-4+x)*exp(10)**2-1))))/(( x**3-4*x**2)*exp(10)**2-x**2)/ln(-x**4*exp(10)**2/((-4+x)*exp(10)**2-1)),x )
Output:
exp(x)*log(log(-x**4*exp(20)/((x - 4)*exp(20) - 1)))**2/x
Time = 0.11 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.16 \[ \int \frac {e^x \left (-8+e^{20} (-32+6 x)\right ) \log \left (\log \left (-\frac {e^{20} x^4}{-1+e^{20} (-4+x)}\right )\right )+e^x \left (1-x+e^{20} \left (4-5 x+x^2\right )\right ) \log \left (-\frac {e^{20} x^4}{-1+e^{20} (-4+x)}\right ) \log ^2\left (\log \left (-\frac {e^{20} x^4}{-1+e^{20} (-4+x)}\right )\right )}{\left (-x^2+e^{20} \left (-4 x^2+x^3\right )\right ) \log \left (-\frac {e^{20} x^4}{-1+e^{20} (-4+x)}\right )} \, dx=\frac {e^{x} \log \left (-\log \left (-x e^{20} + 4 \, e^{20} + 1\right ) + 4 \, \log \left (x\right ) + 20\right )^{2}}{x} \] Input:
integrate((((x^2-5*x+4)*exp(10)^2-x+1)*exp(x)*log(-x^4*exp(10)^2/((-4+x)*e xp(10)^2-1))*log(log(-x^4*exp(10)^2/((-4+x)*exp(10)^2-1)))^2+((6*x-32)*exp (10)^2-8)*exp(x)*log(log(-x^4*exp(10)^2/((-4+x)*exp(10)^2-1))))/((x^3-4*x^ 2)*exp(10)^2-x^2)/log(-x^4*exp(10)^2/((-4+x)*exp(10)^2-1)),x, algorithm="m axima")
Output:
e^x*log(-log(-x*e^20 + 4*e^20 + 1) + 4*log(x) + 20)^2/x
\[ \int \frac {e^x \left (-8+e^{20} (-32+6 x)\right ) \log \left (\log \left (-\frac {e^{20} x^4}{-1+e^{20} (-4+x)}\right )\right )+e^x \left (1-x+e^{20} \left (4-5 x+x^2\right )\right ) \log \left (-\frac {e^{20} x^4}{-1+e^{20} (-4+x)}\right ) \log ^2\left (\log \left (-\frac {e^{20} x^4}{-1+e^{20} (-4+x)}\right )\right )}{\left (-x^2+e^{20} \left (-4 x^2+x^3\right )\right ) \log \left (-\frac {e^{20} x^4}{-1+e^{20} (-4+x)}\right )} \, dx=\int { -\frac {{\left ({\left (x^{2} - 5 \, x + 4\right )} e^{20} - x + 1\right )} e^{x} \log \left (-\frac {x^{4} e^{20}}{{\left (x - 4\right )} e^{20} - 1}\right ) \log \left (\log \left (-\frac {x^{4} e^{20}}{{\left (x - 4\right )} e^{20} - 1}\right )\right )^{2} + 2 \, {\left ({\left (3 \, x - 16\right )} e^{20} - 4\right )} e^{x} \log \left (\log \left (-\frac {x^{4} e^{20}}{{\left (x - 4\right )} e^{20} - 1}\right )\right )}{{\left (x^{2} - {\left (x^{3} - 4 \, x^{2}\right )} e^{20}\right )} \log \left (-\frac {x^{4} e^{20}}{{\left (x - 4\right )} e^{20} - 1}\right )} \,d x } \] Input:
integrate((((x^2-5*x+4)*exp(10)^2-x+1)*exp(x)*log(-x^4*exp(10)^2/((-4+x)*e xp(10)^2-1))*log(log(-x^4*exp(10)^2/((-4+x)*exp(10)^2-1)))^2+((6*x-32)*exp (10)^2-8)*exp(x)*log(log(-x^4*exp(10)^2/((-4+x)*exp(10)^2-1))))/((x^3-4*x^ 2)*exp(10)^2-x^2)/log(-x^4*exp(10)^2/((-4+x)*exp(10)^2-1)),x, algorithm="g iac")
Output:
integrate(-(((x^2 - 5*x + 4)*e^20 - x + 1)*e^x*log(-x^4*e^20/((x - 4)*e^20 - 1))*log(log(-x^4*e^20/((x - 4)*e^20 - 1)))^2 + 2*((3*x - 16)*e^20 - 4)* e^x*log(log(-x^4*e^20/((x - 4)*e^20 - 1))))/((x^2 - (x^3 - 4*x^2)*e^20)*lo g(-x^4*e^20/((x - 4)*e^20 - 1))), x)
Timed out. \[ \int \frac {e^x \left (-8+e^{20} (-32+6 x)\right ) \log \left (\log \left (-\frac {e^{20} x^4}{-1+e^{20} (-4+x)}\right )\right )+e^x \left (1-x+e^{20} \left (4-5 x+x^2\right )\right ) \log \left (-\frac {e^{20} x^4}{-1+e^{20} (-4+x)}\right ) \log ^2\left (\log \left (-\frac {e^{20} x^4}{-1+e^{20} (-4+x)}\right )\right )}{\left (-x^2+e^{20} \left (-4 x^2+x^3\right )\right ) \log \left (-\frac {e^{20} x^4}{-1+e^{20} (-4+x)}\right )} \, dx=\int -\frac {\ln \left (-\frac {x^4\,{\mathrm {e}}^{20}}{{\mathrm {e}}^{20}\,\left (x-4\right )-1}\right )\,{\mathrm {e}}^x\,\left ({\mathrm {e}}^{20}\,\left (x^2-5\,x+4\right )-x+1\right )\,{\ln \left (\ln \left (-\frac {x^4\,{\mathrm {e}}^{20}}{{\mathrm {e}}^{20}\,\left (x-4\right )-1}\right )\right )}^2+{\mathrm {e}}^x\,\left ({\mathrm {e}}^{20}\,\left (6\,x-32\right )-8\right )\,\ln \left (\ln \left (-\frac {x^4\,{\mathrm {e}}^{20}}{{\mathrm {e}}^{20}\,\left (x-4\right )-1}\right )\right )}{\ln \left (-\frac {x^4\,{\mathrm {e}}^{20}}{{\mathrm {e}}^{20}\,\left (x-4\right )-1}\right )\,\left ({\mathrm {e}}^{20}\,\left (4\,x^2-x^3\right )+x^2\right )} \,d x \] Input:
int(-(exp(x)*log(log(-(x^4*exp(20))/(exp(20)*(x - 4) - 1)))*(exp(20)*(6*x - 32) - 8) + log(-(x^4*exp(20))/(exp(20)*(x - 4) - 1))*exp(x)*log(log(-(x^ 4*exp(20))/(exp(20)*(x - 4) - 1)))^2*(exp(20)*(x^2 - 5*x + 4) - x + 1))/(l og(-(x^4*exp(20))/(exp(20)*(x - 4) - 1))*(exp(20)*(4*x^2 - x^3) + x^2)),x)
Output:
int(-(exp(x)*log(log(-(x^4*exp(20))/(exp(20)*(x - 4) - 1)))*(exp(20)*(6*x - 32) - 8) + log(-(x^4*exp(20))/(exp(20)*(x - 4) - 1))*exp(x)*log(log(-(x^ 4*exp(20))/(exp(20)*(x - 4) - 1)))^2*(exp(20)*(x^2 - 5*x + 4) - x + 1))/(l og(-(x^4*exp(20))/(exp(20)*(x - 4) - 1))*(exp(20)*(4*x^2 - x^3) + x^2)), x )
Time = 0.17 (sec) , antiderivative size = 33, normalized size of antiderivative = 1.32 \[ \int \frac {e^x \left (-8+e^{20} (-32+6 x)\right ) \log \left (\log \left (-\frac {e^{20} x^4}{-1+e^{20} (-4+x)}\right )\right )+e^x \left (1-x+e^{20} \left (4-5 x+x^2\right )\right ) \log \left (-\frac {e^{20} x^4}{-1+e^{20} (-4+x)}\right ) \log ^2\left (\log \left (-\frac {e^{20} x^4}{-1+e^{20} (-4+x)}\right )\right )}{\left (-x^2+e^{20} \left (-4 x^2+x^3\right )\right ) \log \left (-\frac {e^{20} x^4}{-1+e^{20} (-4+x)}\right )} \, dx=\frac {e^{x} {\mathrm {log}\left (\mathrm {log}\left (-\frac {e^{20} x^{4}}{e^{20} x -4 e^{20}-1}\right )\right )}^{2}}{x} \] Input:
int((((x^2-5*x+4)*exp(10)^2-x+1)*exp(x)*log(-x^4*exp(10)^2/((-4+x)*exp(10) ^2-1))*log(log(-x^4*exp(10)^2/((-4+x)*exp(10)^2-1)))^2+((6*x-32)*exp(10)^2 -8)*exp(x)*log(log(-x^4*exp(10)^2/((-4+x)*exp(10)^2-1))))/((x^3-4*x^2)*exp (10)^2-x^2)/log(-x^4*exp(10)^2/((-4+x)*exp(10)^2-1)),x)
Output:
(e**x*log(log(( - e**20*x**4)/(e**20*x - 4*e**20 - 1)))**2)/x