Integrand size = 118, antiderivative size = 27 \[ \int \frac {-8+4 x-26 x^2+28 x^3-6 x^4+\left (4-4 x-3 x^2+4 x^3-x^4\right ) \log \left (\frac {e^{\frac {x}{-2+x}} \left (1-2 x^2+x^4\right )}{x}\right )}{\left (-4 x^2+4 x^3+3 x^4-4 x^5+x^6\right ) \log ^3\left (\frac {e^{\frac {x}{-2+x}} \left (1-2 x^2+x^4\right )}{x}\right )} \, dx=\frac {1}{x \log ^2\left (\frac {e^{\frac {x}{-2+x}} \left (-1+x^2\right )^2}{x}\right )} \] Output:
1/x/ln(exp(x/(-2+x))/x*(x^2-1)^2)^2
Time = 0.05 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.00 \[ \int \frac {-8+4 x-26 x^2+28 x^3-6 x^4+\left (4-4 x-3 x^2+4 x^3-x^4\right ) \log \left (\frac {e^{\frac {x}{-2+x}} \left (1-2 x^2+x^4\right )}{x}\right )}{\left (-4 x^2+4 x^3+3 x^4-4 x^5+x^6\right ) \log ^3\left (\frac {e^{\frac {x}{-2+x}} \left (1-2 x^2+x^4\right )}{x}\right )} \, dx=\frac {1}{x \log ^2\left (\frac {e^{\frac {x}{-2+x}} \left (-1+x^2\right )^2}{x}\right )} \] Input:
Integrate[(-8 + 4*x - 26*x^2 + 28*x^3 - 6*x^4 + (4 - 4*x - 3*x^2 + 4*x^3 - x^4)*Log[(E^(x/(-2 + x))*(1 - 2*x^2 + x^4))/x])/((-4*x^2 + 4*x^3 + 3*x^4 - 4*x^5 + x^6)*Log[(E^(x/(-2 + x))*(1 - 2*x^2 + x^4))/x]^3),x]
Output:
1/(x*Log[(E^(x/(-2 + x))*(-1 + x^2)^2)/x]^2)
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.
| \(\displaystyle \int \frac {-6 x^4+28 x^3-26 x^2+\left (-x^4+4 x^3-3 x^2-4 x+4\right ) \log \left (\frac {e^{\frac {x}{x-2}} \left (x^4-2 x^2+1\right )}{x}\right )+4 x-8}{\left (x^6-4 x^5+3 x^4+4 x^3-4 x^2\right ) \log ^3\left (\frac {e^{\frac {x}{x-2}} \left (x^4-2 x^2+1\right )}{x}\right )} \, dx\) |
| \(\Big \downarrow \) 2026 |
| \(\displaystyle \int \frac {-6 x^4+28 x^3-26 x^2+\left (-x^4+4 x^3-3 x^2-4 x+4\right ) \log \left (\frac {e^{\frac {x}{x-2}} \left (x^4-2 x^2+1\right )}{x}\right )+4 x-8}{x^2 \left (x^4-4 x^3+3 x^2+4 x-4\right ) \log ^3\left (\frac {e^{\frac {x}{x-2}} \left (x^4-2 x^2+1\right )}{x}\right )}dx\) |
| \(\Big \downarrow \) 2463 |
| \(\displaystyle \int \left (-\frac {-6 x^4+28 x^3-26 x^2+\left (-x^4+4 x^3-3 x^2-4 x+4\right ) \log \left (\frac {e^{\frac {x}{x-2}} \left (x^4-2 x^2+1\right )}{x}\right )+4 x-8}{18 x^2 (x+1) \log ^3\left (\frac {e^{\frac {x}{x-2}} \left (x^4-2 x^2+1\right )}{x}\right )}-\frac {4 \left (-6 x^4+28 x^3-26 x^2+\left (-x^4+4 x^3-3 x^2-4 x+4\right ) \log \left (\frac {e^{\frac {x}{x-2}} \left (x^4-2 x^2+1\right )}{x}\right )+4 x-8\right )}{9 (x-2) x^2 \log ^3\left (\frac {e^{\frac {x}{x-2}} \left (x^4-2 x^2+1\right )}{x}\right )}+\frac {-6 x^4+28 x^3-26 x^2+\left (-x^4+4 x^3-3 x^2-4 x+4\right ) \log \left (\frac {e^{\frac {x}{x-2}} \left (x^4-2 x^2+1\right )}{x}\right )+4 x-8}{2 (x-1) x^2 \log ^3\left (\frac {e^{\frac {x}{x-2}} \left (x^4-2 x^2+1\right )}{x}\right )}+\frac {-6 x^4+28 x^3-26 x^2+\left (-x^4+4 x^3-3 x^2-4 x+4\right ) \log \left (\frac {e^{\frac {x}{x-2}} \left (x^4-2 x^2+1\right )}{x}\right )+4 x-8}{3 (x-2)^2 x^2 \log ^3\left (\frac {e^{\frac {x}{x-2}} \left (x^4-2 x^2+1\right )}{x}\right )}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle 2 \int \frac {1}{(x-2)^2 \log ^3\left (\frac {e^{\frac {x}{x-2}} \left (x^2-1\right )^2}{x}\right )}dx-\int \frac {1}{(x-2) \log ^3\left (\frac {e^{\frac {x}{x-2}} \left (x^2-1\right )^2}{x}\right )}dx-4 \int \frac {1}{(x-1) \log ^3\left (\frac {e^{\frac {x}{x-2}} \left (x^2-1\right )^2}{x}\right )}dx+2 \int \frac {1}{x^2 \log ^3\left (\frac {e^{\frac {x}{x-2}} \left (x^2-1\right )^2}{x}\right )}dx+\int \frac {1}{x \log ^3\left (\frac {e^{\frac {x}{x-2}} \left (x^2-1\right )^2}{x}\right )}dx+4 \int \frac {1}{(x+1) \log ^3\left (\frac {e^{\frac {x}{x-2}} \left (x^2-1\right )^2}{x}\right )}dx-\int \frac {1}{x^2 \log ^2\left (\frac {e^{\frac {x}{x-2}} \left (x^2-1\right )^2}{x}\right )}dx\) |
Input:
Int[(-8 + 4*x - 26*x^2 + 28*x^3 - 6*x^4 + (4 - 4*x - 3*x^2 + 4*x^3 - x^4)* Log[(E^(x/(-2 + x))*(1 - 2*x^2 + x^4))/x])/((-4*x^2 + 4*x^3 + 3*x^4 - 4*x^ 5 + x^6)*Log[(E^(x/(-2 + x))*(1 - 2*x^2 + x^4))/x]^3),x]
Output:
$Aborted
Time = 12.89 (sec) , antiderivative size = 41, normalized size of antiderivative = 1.52
| method | result | size |
| parallelrisch | \(-\frac {384-192 x}{192 x {\ln \left (\frac {\left (x^{4}-2 x^{2}+1\right ) {\mathrm e}^{\frac {x}{-2+x}}}{x}\right )}^{2} \left (-2+x \right )}\) | \(41\) |
| default | \(\frac {\left (-2+x \right )^{2}}{x {\left (x \ln \left (x \right )-2 \ln \left (1+x \right ) x -2 \ln \left (-1+x \right ) x -\left (\ln \left (\frac {\left (-1+x \right )^{2} \left (1+x \right )^{2} {\mathrm e}^{\frac {x}{-2+x}}}{x}\right )-2 \ln \left (-1+x \right )-2 \ln \left (1+x \right )-\frac {x}{-2+x}+\ln \left (x \right )\right ) x -x +2 \ln \left (\frac {\left (-1+x \right )^{2} \left (1+x \right )^{2} {\mathrm e}^{\frac {x}{-2+x}}}{x}\right )-\frac {2 x}{-2+x}\right )}^{2}}\) | \(116\) |
| risch | \(-\frac {4}{x {\left (\pi \,\operatorname {csgn}\left (\frac {i}{x}\right ) \operatorname {csgn}\left (i {\mathrm e}^{\frac {x}{-2+x}} \left (x^{2}-1\right )^{2}\right ) \operatorname {csgn}\left (\frac {i \left (x^{2}-1\right )^{2} {\mathrm e}^{\frac {x}{-2+x}}}{x}\right )-\pi \,\operatorname {csgn}\left (\frac {i}{x}\right ) {\operatorname {csgn}\left (\frac {i \left (x^{2}-1\right )^{2} {\mathrm e}^{\frac {x}{-2+x}}}{x}\right )}^{2}+\pi {\operatorname {csgn}\left (i \left (x^{2}-1\right )\right )}^{2} \operatorname {csgn}\left (i \left (x^{2}-1\right )^{2}\right )-2 \pi \,\operatorname {csgn}\left (i \left (x^{2}-1\right )\right ) {\operatorname {csgn}\left (i \left (x^{2}-1\right )^{2}\right )}^{2}+\pi {\operatorname {csgn}\left (i \left (x^{2}-1\right )^{2}\right )}^{3}+\pi \,\operatorname {csgn}\left (i \left (x^{2}-1\right )^{2}\right ) \operatorname {csgn}\left (i {\mathrm e}^{\frac {x}{-2+x}}\right ) \operatorname {csgn}\left (i {\mathrm e}^{\frac {x}{-2+x}} \left (x^{2}-1\right )^{2}\right )-\pi \,\operatorname {csgn}\left (i \left (x^{2}-1\right )^{2}\right ) \operatorname {csgn}\left (i {\mathrm e}^{\frac {x}{-2+x}} \left (x^{2}-1\right )^{2}\right )^{2}-\pi \,\operatorname {csgn}\left (i {\mathrm e}^{\frac {x}{-2+x}}\right ) \operatorname {csgn}\left (i {\mathrm e}^{\frac {x}{-2+x}} \left (x^{2}-1\right )^{2}\right )^{2}+\pi \operatorname {csgn}\left (i {\mathrm e}^{\frac {x}{-2+x}} \left (x^{2}-1\right )^{2}\right )^{3}-\pi \,\operatorname {csgn}\left (i {\mathrm e}^{\frac {x}{-2+x}} \left (x^{2}-1\right )^{2}\right ) {\operatorname {csgn}\left (\frac {i \left (x^{2}-1\right )^{2} {\mathrm e}^{\frac {x}{-2+x}}}{x}\right )}^{2}+\pi {\operatorname {csgn}\left (\frac {i \left (x^{2}-1\right )^{2} {\mathrm e}^{\frac {x}{-2+x}}}{x}\right )}^{3}-2 i \ln \left (x \right )+4 i \ln \left (x^{2}-1\right )+2 i \ln \left ({\mathrm e}^{\frac {x}{-2+x}}\right )\right )}^{2}}\) | \(393\) |
Input:
int(((-x^4+4*x^3-3*x^2-4*x+4)*ln((x^4-2*x^2+1)*exp(x/(-2+x))/x)-6*x^4+28*x ^3-26*x^2+4*x-8)/(x^6-4*x^5+3*x^4+4*x^3-4*x^2)/ln((x^4-2*x^2+1)*exp(x/(-2+ x))/x)^3,x,method=_RETURNVERBOSE)
Output:
-1/192/x*(384-192*x)/ln((x^4-2*x^2+1)*exp(x/(-2+x))/x)^2/(-2+x)
Time = 0.09 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.07 \[ \int \frac {-8+4 x-26 x^2+28 x^3-6 x^4+\left (4-4 x-3 x^2+4 x^3-x^4\right ) \log \left (\frac {e^{\frac {x}{-2+x}} \left (1-2 x^2+x^4\right )}{x}\right )}{\left (-4 x^2+4 x^3+3 x^4-4 x^5+x^6\right ) \log ^3\left (\frac {e^{\frac {x}{-2+x}} \left (1-2 x^2+x^4\right )}{x}\right )} \, dx=\frac {1}{x \log \left (\frac {{\left (x^{4} - 2 \, x^{2} + 1\right )} e^{\left (\frac {x}{x - 2}\right )}}{x}\right )^{2}} \] Input:
integrate(((-x^4+4*x^3-3*x^2-4*x+4)*log((x^4-2*x^2+1)*exp(x/(-2+x))/x)-6*x ^4+28*x^3-26*x^2+4*x-8)/(x^6-4*x^5+3*x^4+4*x^3-4*x^2)/log((x^4-2*x^2+1)*ex p(x/(-2+x))/x)^3,x, algorithm="fricas")
Output:
1/(x*log((x^4 - 2*x^2 + 1)*e^(x/(x - 2))/x)^2)
Time = 0.15 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.89 \[ \int \frac {-8+4 x-26 x^2+28 x^3-6 x^4+\left (4-4 x-3 x^2+4 x^3-x^4\right ) \log \left (\frac {e^{\frac {x}{-2+x}} \left (1-2 x^2+x^4\right )}{x}\right )}{\left (-4 x^2+4 x^3+3 x^4-4 x^5+x^6\right ) \log ^3\left (\frac {e^{\frac {x}{-2+x}} \left (1-2 x^2+x^4\right )}{x}\right )} \, dx=\frac {1}{x \log {\left (\frac {\left (x^{4} - 2 x^{2} + 1\right ) e^{\frac {x}{x - 2}}}{x} \right )}^{2}} \] Input:
integrate(((-x**4+4*x**3-3*x**2-4*x+4)*ln((x**4-2*x**2+1)*exp(x/(-2+x))/x) -6*x**4+28*x**3-26*x**2+4*x-8)/(x**6-4*x**5+3*x**4+4*x**3-4*x**2)/ln((x**4 -2*x**2+1)*exp(x/(-2+x))/x)**3,x)
Output:
1/(x*log((x**4 - 2*x**2 + 1)*exp(x/(x - 2))/x)**2)
Leaf count of result is larger than twice the leaf count of optimal. 165 vs. \(2 (26) = 52\).
Time = 0.15 (sec) , antiderivative size = 165, normalized size of antiderivative = 6.11 \[ \int \frac {-8+4 x-26 x^2+28 x^3-6 x^4+\left (4-4 x-3 x^2+4 x^3-x^4\right ) \log \left (\frac {e^{\frac {x}{-2+x}} \left (1-2 x^2+x^4\right )}{x}\right )}{\left (-4 x^2+4 x^3+3 x^4-4 x^5+x^6\right ) \log ^3\left (\frac {e^{\frac {x}{-2+x}} \left (1-2 x^2+x^4\right )}{x}\right )} \, dx=\frac {x^{2} - 4 \, x + 4}{x^{3} + 4 \, {\left (x^{3} - 4 \, x^{2} + 4 \, x\right )} \log \left (x + 1\right )^{2} + 4 \, {\left (x^{3} - 4 \, x^{2} + 4 \, x\right )} \log \left (x - 1\right )^{2} + {\left (x^{3} - 4 \, x^{2} + 4 \, x\right )} \log \left (x\right )^{2} + 4 \, {\left (x^{3} - 2 \, x^{2} + 2 \, {\left (x^{3} - 4 \, x^{2} + 4 \, x\right )} \log \left (x - 1\right ) - {\left (x^{3} - 4 \, x^{2} + 4 \, x\right )} \log \left (x\right )\right )} \log \left (x + 1\right ) + 4 \, {\left (x^{3} - 2 \, x^{2} - {\left (x^{3} - 4 \, x^{2} + 4 \, x\right )} \log \left (x\right )\right )} \log \left (x - 1\right ) - 2 \, {\left (x^{3} - 2 \, x^{2}\right )} \log \left (x\right )} \] Input:
integrate(((-x^4+4*x^3-3*x^2-4*x+4)*log((x^4-2*x^2+1)*exp(x/(-2+x))/x)-6*x ^4+28*x^3-26*x^2+4*x-8)/(x^6-4*x^5+3*x^4+4*x^3-4*x^2)/log((x^4-2*x^2+1)*ex p(x/(-2+x))/x)^3,x, algorithm="maxima")
Output:
(x^2 - 4*x + 4)/(x^3 + 4*(x^3 - 4*x^2 + 4*x)*log(x + 1)^2 + 4*(x^3 - 4*x^2 + 4*x)*log(x - 1)^2 + (x^3 - 4*x^2 + 4*x)*log(x)^2 + 4*(x^3 - 2*x^2 + 2*( x^3 - 4*x^2 + 4*x)*log(x - 1) - (x^3 - 4*x^2 + 4*x)*log(x))*log(x + 1) + 4 *(x^3 - 2*x^2 - (x^3 - 4*x^2 + 4*x)*log(x))*log(x - 1) - 2*(x^3 - 2*x^2)*l og(x))
Leaf count of result is larger than twice the leaf count of optimal. 331 vs. \(2 (26) = 52\).
Time = 0.75 (sec) , antiderivative size = 331, normalized size of antiderivative = 12.26 \[ \int \frac {-8+4 x-26 x^2+28 x^3-6 x^4+\left (4-4 x-3 x^2+4 x^3-x^4\right ) \log \left (\frac {e^{\frac {x}{-2+x}} \left (1-2 x^2+x^4\right )}{x}\right )}{\left (-4 x^2+4 x^3+3 x^4-4 x^5+x^6\right ) \log ^3\left (\frac {e^{\frac {x}{-2+x}} \left (1-2 x^2+x^4\right )}{x}\right )} \, dx=\frac {3 \, x^{6} - 26 \, x^{5} + 81 \, x^{4} - 110 \, x^{3} + 64 \, x^{2} - 24 \, x + 16}{3 \, x^{7} \log \left (\frac {x^{4} - 2 \, x^{2} + 1}{x}\right )^{2} + 6 \, x^{7} \log \left (\frac {x^{4} - 2 \, x^{2} + 1}{x}\right ) - 26 \, x^{6} \log \left (\frac {x^{4} - 2 \, x^{2} + 1}{x}\right )^{2} + 3 \, x^{7} - 40 \, x^{6} \log \left (\frac {x^{4} - 2 \, x^{2} + 1}{x}\right ) + 81 \, x^{5} \log \left (\frac {x^{4} - 2 \, x^{2} + 1}{x}\right )^{2} - 14 \, x^{6} + 82 \, x^{5} \log \left (\frac {x^{4} - 2 \, x^{2} + 1}{x}\right ) - 110 \, x^{4} \log \left (\frac {x^{4} - 2 \, x^{2} + 1}{x}\right )^{2} + 13 \, x^{5} - 56 \, x^{4} \log \left (\frac {x^{4} - 2 \, x^{2} + 1}{x}\right ) + 64 \, x^{3} \log \left (\frac {x^{4} - 2 \, x^{2} + 1}{x}\right )^{2} - 2 \, x^{4} + 16 \, x^{3} \log \left (\frac {x^{4} - 2 \, x^{2} + 1}{x}\right ) - 24 \, x^{2} \log \left (\frac {x^{4} - 2 \, x^{2} + 1}{x}\right )^{2} + 4 \, x^{3} - 16 \, x^{2} \log \left (\frac {x^{4} - 2 \, x^{2} + 1}{x}\right ) + 16 \, x \log \left (\frac {x^{4} - 2 \, x^{2} + 1}{x}\right )^{2}} \] Input:
integrate(((-x^4+4*x^3-3*x^2-4*x+4)*log((x^4-2*x^2+1)*exp(x/(-2+x))/x)-6*x ^4+28*x^3-26*x^2+4*x-8)/(x^6-4*x^5+3*x^4+4*x^3-4*x^2)/log((x^4-2*x^2+1)*ex p(x/(-2+x))/x)^3,x, algorithm="giac")
Output:
(3*x^6 - 26*x^5 + 81*x^4 - 110*x^3 + 64*x^2 - 24*x + 16)/(3*x^7*log((x^4 - 2*x^2 + 1)/x)^2 + 6*x^7*log((x^4 - 2*x^2 + 1)/x) - 26*x^6*log((x^4 - 2*x^ 2 + 1)/x)^2 + 3*x^7 - 40*x^6*log((x^4 - 2*x^2 + 1)/x) + 81*x^5*log((x^4 - 2*x^2 + 1)/x)^2 - 14*x^6 + 82*x^5*log((x^4 - 2*x^2 + 1)/x) - 110*x^4*log(( x^4 - 2*x^2 + 1)/x)^2 + 13*x^5 - 56*x^4*log((x^4 - 2*x^2 + 1)/x) + 64*x^3* log((x^4 - 2*x^2 + 1)/x)^2 - 2*x^4 + 16*x^3*log((x^4 - 2*x^2 + 1)/x) - 24* x^2*log((x^4 - 2*x^2 + 1)/x)^2 + 4*x^3 - 16*x^2*log((x^4 - 2*x^2 + 1)/x) + 16*x*log((x^4 - 2*x^2 + 1)/x)^2)
Time = 2.61 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.07 \[ \int \frac {-8+4 x-26 x^2+28 x^3-6 x^4+\left (4-4 x-3 x^2+4 x^3-x^4\right ) \log \left (\frac {e^{\frac {x}{-2+x}} \left (1-2 x^2+x^4\right )}{x}\right )}{\left (-4 x^2+4 x^3+3 x^4-4 x^5+x^6\right ) \log ^3\left (\frac {e^{\frac {x}{-2+x}} \left (1-2 x^2+x^4\right )}{x}\right )} \, dx=\frac {1}{x\,{\ln \left (\frac {{\mathrm {e}}^{\frac {x}{x-2}}\,\left (x^4-2\,x^2+1\right )}{x}\right )}^2} \] Input:
int(-(log((exp(x/(x - 2))*(x^4 - 2*x^2 + 1))/x)*(4*x + 3*x^2 - 4*x^3 + x^4 - 4) - 4*x + 26*x^2 - 28*x^3 + 6*x^4 + 8)/(log((exp(x/(x - 2))*(x^4 - 2*x ^2 + 1))/x)^3*(4*x^3 - 4*x^2 + 3*x^4 - 4*x^5 + x^6)),x)
Output:
1/(x*log((exp(x/(x - 2))*(x^4 - 2*x^2 + 1))/x)^2)
\[ \int \frac {-8+4 x-26 x^2+28 x^3-6 x^4+\left (4-4 x-3 x^2+4 x^3-x^4\right ) \log \left (\frac {e^{\frac {x}{-2+x}} \left (1-2 x^2+x^4\right )}{x}\right )}{\left (-4 x^2+4 x^3+3 x^4-4 x^5+x^6\right ) \log ^3\left (\frac {e^{\frac {x}{-2+x}} \left (1-2 x^2+x^4\right )}{x}\right )} \, dx=\text {too large to display} \] Input:
int(((-x^4+4*x^3-3*x^2-4*x+4)*log((x^4-2*x^2+1)*exp(x/(-2+x))/x)-6*x^4+28* x^3-26*x^2+4*x-8)/(x^6-4*x^5+3*x^4+4*x^3-4*x^2)/log((x^4-2*x^2+1)*exp(x/(- 2+x))/x)^3,x)
Output:
- 6*int(x**2/(log((e**(2/(x - 2))*e*x**4 - 2*e**(2/(x - 2))*e*x**2 + e**( 2/(x - 2))*e)/x)**3*x**4 - 4*log((e**(2/(x - 2))*e*x**4 - 2*e**(2/(x - 2)) *e*x**2 + e**(2/(x - 2))*e)/x)**3*x**3 + 3*log((e**(2/(x - 2))*e*x**4 - 2* e**(2/(x - 2))*e*x**2 + e**(2/(x - 2))*e)/x)**3*x**2 + 4*log((e**(2/(x - 2 ))*e*x**4 - 2*e**(2/(x - 2))*e*x**2 + e**(2/(x - 2))*e)/x)**3*x - 4*log((e **(2/(x - 2))*e*x**4 - 2*e**(2/(x - 2))*e*x**2 + e**(2/(x - 2))*e)/x)**3), x) - int(x**2/(log((e**(2/(x - 2))*e*x**4 - 2*e**(2/(x - 2))*e*x**2 + e**( 2/(x - 2))*e)/x)**2*x**4 - 4*log((e**(2/(x - 2))*e*x**4 - 2*e**(2/(x - 2)) *e*x**2 + e**(2/(x - 2))*e)/x)**2*x**3 + 3*log((e**(2/(x - 2))*e*x**4 - 2* e**(2/(x - 2))*e*x**2 + e**(2/(x - 2))*e)/x)**2*x**2 + 4*log((e**(2/(x - 2 ))*e*x**4 - 2*e**(2/(x - 2))*e*x**2 + e**(2/(x - 2))*e)/x)**2*x - 4*log((e **(2/(x - 2))*e*x**4 - 2*e**(2/(x - 2))*e*x**2 + e**(2/(x - 2))*e)/x)**2), x) + 28*int(x/(log((e**(2/(x - 2))*e*x**4 - 2*e**(2/(x - 2))*e*x**2 + e**( 2/(x - 2))*e)/x)**3*x**4 - 4*log((e**(2/(x - 2))*e*x**4 - 2*e**(2/(x - 2)) *e*x**2 + e**(2/(x - 2))*e)/x)**3*x**3 + 3*log((e**(2/(x - 2))*e*x**4 - 2* e**(2/(x - 2))*e*x**2 + e**(2/(x - 2))*e)/x)**3*x**2 + 4*log((e**(2/(x - 2 ))*e*x**4 - 2*e**(2/(x - 2))*e*x**2 + e**(2/(x - 2))*e)/x)**3*x - 4*log((e **(2/(x - 2))*e*x**4 - 2*e**(2/(x - 2))*e*x**2 + e**(2/(x - 2))*e)/x)**3), x) + 4*int(x/(log((e**(2/(x - 2))*e*x**4 - 2*e**(2/(x - 2))*e*x**2 + e**(2 /(x - 2))*e)/x)**2*x**4 - 4*log((e**(2/(x - 2))*e*x**4 - 2*e**(2/(x - 2...