Integrand size = 79, antiderivative size = 22 \[ \int \frac {-6 e^8 x \log ^4\left (\frac {5}{3}\right )+e^{12} \log ^6\left (\frac {5}{3}\right ) (-6 x+6 x \log (x))}{-1+3 e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)-3 e^8 \log ^4\left (\frac {5}{3}\right ) \log ^2(x)+e^{12} \log ^6\left (\frac {5}{3}\right ) \log ^3(x)} \, dx=\frac {3 x^2}{\left (\frac {1}{e^4 \log ^2\left (\frac {5}{3}\right )}-\log (x)\right )^2} \] Output:
3/(exp(4-2*ln(exp(4)*ln(5/3)))-ln(x))^2*x^2
Time = 0.06 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.36 \[ \int \frac {-6 e^8 x \log ^4\left (\frac {5}{3}\right )+e^{12} \log ^6\left (\frac {5}{3}\right ) (-6 x+6 x \log (x))}{-1+3 e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)-3 e^8 \log ^4\left (\frac {5}{3}\right ) \log ^2(x)+e^{12} \log ^6\left (\frac {5}{3}\right ) \log ^3(x)} \, dx=\frac {3 e^8 x^2 \log ^4\left (\frac {5}{3}\right )}{\left (-1+e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)\right )^2} \] Input:
Integrate[(-6*E^8*x*Log[5/3]^4 + E^12*Log[5/3]^6*(-6*x + 6*x*Log[x]))/(-1 + 3*E^4*Log[5/3]^2*Log[x] - 3*E^8*Log[5/3]^4*Log[x]^2 + E^12*Log[5/3]^6*Lo g[x]^3),x]
Output:
(3*E^8*x^2*Log[5/3]^4)/(-1 + E^4*Log[5/3]^2*Log[x])^2
Time = 0.73 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.41, number of steps used = 3, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.038, Rules used = {7292, 7293, 2009}
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.
| \(\displaystyle \int \frac {e^{12} \log ^6\left (\frac {5}{3}\right ) (6 x \log (x)-6 x)-6 e^8 x \log ^4\left (\frac {5}{3}\right )}{3 e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)+e^{12} \log ^6\left (\frac {5}{3}\right ) \log ^3(x)-3 e^8 \log ^4\left (\frac {5}{3}\right ) \log ^2(x)-1} \, dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {6 e^8 x \log ^4\left (\frac {5}{3}\right )-e^{12} \log ^6\left (\frac {5}{3}\right ) (6 x \log (x)-6 x)}{\left (1-e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {6 e^8 x \log ^4\left (\frac {5}{3}\right )}{\left (e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)-1\right )^2}-\frac {6 e^{12} x \log ^6\left (\frac {5}{3}\right )}{\left (e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)-1\right )^3}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle \frac {3 e^8 x^2 \log ^4\left (\frac {5}{3}\right )}{\left (1-e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)\right )^2}\) |
Input:
Int[(-6*E^8*x*Log[5/3]^4 + E^12*Log[5/3]^6*(-6*x + 6*x*Log[x]))/(-1 + 3*E^ 4*Log[5/3]^2*Log[x] - 3*E^8*Log[5/3]^4*Log[x]^2 + E^12*Log[5/3]^6*Log[x]^3 ),x]
Output:
(3*E^8*x^2*Log[5/3]^4)/(1 - E^4*Log[5/3]^2*Log[x])^2
Leaf count of result is larger than twice the leaf count of optimal. \(55\) vs. \(2(23)=46\).
Time = 0.47 (sec) , antiderivative size = 56, normalized size of antiderivative = 2.55
| method | result | size |
| parallelrisch | \(\frac {3 x^{2} \ln \left (\frac {5}{3}\right )^{4} {\mathrm e}^{8}}{\ln \left (x \right )^{2} \ln \left (\frac {5}{3}\right )^{4} {\mathrm e}^{8}-2 \ln \left (x \right ) {\mathrm e}^{2 \ln \left ({\mathrm e}^{4} \ln \left (\frac {5}{3}\right )\right )-4}+1}\) | \(56\) |
| norman | \(\frac {3 \,{\mathrm e}^{8} \left (\ln \left (3\right )^{4}-4 \ln \left (3\right )^{3} \ln \left (5\right )+6 \ln \left (3\right )^{2} \ln \left (5\right )^{2}-4 \ln \left (3\right ) \ln \left (5\right )^{3}+\ln \left (5\right )^{4}\right ) x^{2}}{\left (\ln \left (x \right ) {\mathrm e}^{4} \ln \left (\frac {5}{3}\right )^{2}-1\right )^{2}}\) | \(58\) |
| risch | \(\frac {3 \left (\ln \left (3\right )^{4}-4 \ln \left (3\right )^{3} \ln \left (5\right )+6 \ln \left (3\right )^{2} \ln \left (5\right )^{2}-4 \ln \left (3\right ) \ln \left (5\right )^{3}+\ln \left (5\right )^{4}\right ) x^{2} {\mathrm e}^{8}}{\left (\ln \left (x \right ) {\mathrm e}^{4} \ln \left (3\right )^{2}-2 \ln \left (x \right ) {\mathrm e}^{4} \ln \left (3\right ) \ln \left (5\right )+\ln \left (x \right ) {\mathrm e}^{4} \ln \left (5\right )^{2}-1\right )^{2}}\) | \(75\) |
| default | \(\frac {3 \,{\mathrm e}^{8} x^{2} \left (\ln \left (3\right )^{4}-4 \ln \left (3\right )^{3} \ln \left (5\right )+6 \ln \left (3\right )^{2} \ln \left (5\right )^{2}-4 \ln \left (3\right ) \ln \left (5\right )^{3}+\ln \left (5\right )^{4}\right )}{\ln \left (x \right )^{2} \ln \left (3\right )^{4} {\mathrm e}^{8}-4 \ln \left (x \right )^{2} \ln \left (3\right )^{3} \ln \left (5\right ) {\mathrm e}^{8}+6 \ln \left (x \right )^{2} \ln \left (3\right )^{2} \ln \left (5\right )^{2} {\mathrm e}^{8}-4 \ln \left (x \right )^{2} \ln \left (3\right ) \ln \left (5\right )^{3} {\mathrm e}^{8}+\ln \left (x \right )^{2} \ln \left (5\right )^{4} {\mathrm e}^{8}-2 \ln \left (x \right ) {\mathrm e}^{4} \ln \left (3\right )^{2}+4 \ln \left (x \right ) {\mathrm e}^{4} \ln \left (3\right ) \ln \left (5\right )-2 \ln \left (x \right ) {\mathrm e}^{4} \ln \left (5\right )^{2}+1}\) | \(155\) |
Input:
int(((6*x*ln(x)-6*x)*exp(2*ln(exp(4)*ln(5/3))-4)^3-6*x*exp(2*ln(exp(4)*ln( 5/3))-4)^2)/(ln(x)^3*exp(2*ln(exp(4)*ln(5/3))-4)^3-3*ln(x)^2*exp(2*ln(exp( 4)*ln(5/3))-4)^2+3*ln(x)*exp(2*ln(exp(4)*ln(5/3))-4)-1),x,method=_RETURNVE RBOSE)
Output:
3*x^2*exp(2*ln(exp(4)*ln(5/3))-4)^2/(ln(x)^2*exp(2*ln(exp(4)*ln(5/3))-4)^2 -2*ln(x)*exp(2*ln(exp(4)*ln(5/3))-4)+1)
Time = 0.08 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.64 \[ \int \frac {-6 e^8 x \log ^4\left (\frac {5}{3}\right )+e^{12} \log ^6\left (\frac {5}{3}\right ) (-6 x+6 x \log (x))}{-1+3 e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)-3 e^8 \log ^4\left (\frac {5}{3}\right ) \log ^2(x)+e^{12} \log ^6\left (\frac {5}{3}\right ) \log ^3(x)} \, dx=\frac {3 \, x^{2} e^{8} \log \left (\frac {5}{3}\right )^{4}}{e^{8} \log \left (\frac {5}{3}\right )^{4} \log \left (x\right )^{2} - 2 \, e^{4} \log \left (\frac {5}{3}\right )^{2} \log \left (x\right ) + 1} \] Input:
integrate(((6*x*log(x)-6*x)*exp(2*log(exp(4)*log(5/3))-4)^3-6*x*exp(2*log( exp(4)*log(5/3))-4)^2)/(log(x)^3*exp(2*log(exp(4)*log(5/3))-4)^3-3*log(x)^ 2*exp(2*log(exp(4)*log(5/3))-4)^2+3*log(x)*exp(2*log(exp(4)*log(5/3))-4)-1 ),x, algorithm="fricas")
Output:
3*x^2*e^8*log(5/3)^4/(e^8*log(5/3)^4*log(x)^2 - 2*e^4*log(5/3)^2*log(x) + 1)
Leaf count of result is larger than twice the leaf count of optimal. 180 vs. \(2 (22) = 44\).
Time = 0.21 (sec) , antiderivative size = 180, normalized size of antiderivative = 8.18 \[ \int \frac {-6 e^8 x \log ^4\left (\frac {5}{3}\right )+e^{12} \log ^6\left (\frac {5}{3}\right ) (-6 x+6 x \log (x))}{-1+3 e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)-3 e^8 \log ^4\left (\frac {5}{3}\right ) \log ^2(x)+e^{12} \log ^6\left (\frac {5}{3}\right ) \log ^3(x)} \, dx=\frac {- 12 x^{2} e^{8} \log {\left (3 \right )} \log {\left (5 \right )}^{3} - 12 x^{2} e^{8} \log {\left (3 \right )}^{3} \log {\left (5 \right )} + 3 x^{2} e^{8} \log {\left (3 \right )}^{4} + 3 x^{2} e^{8} \log {\left (5 \right )}^{4} + 18 x^{2} e^{8} \log {\left (3 \right )}^{2} \log {\left (5 \right )}^{2}}{\left (- 4 e^{8} \log {\left (3 \right )} \log {\left (5 \right )}^{3} - 4 e^{8} \log {\left (3 \right )}^{3} \log {\left (5 \right )} + e^{8} \log {\left (3 \right )}^{4} + e^{8} \log {\left (5 \right )}^{4} + 6 e^{8} \log {\left (3 \right )}^{2} \log {\left (5 \right )}^{2}\right ) \log {\left (x \right )}^{2} + \left (- 2 e^{4} \log {\left (5 \right )}^{2} - 2 e^{4} \log {\left (3 \right )}^{2} + 4 e^{4} \log {\left (3 \right )} \log {\left (5 \right )}\right ) \log {\left (x \right )} + 1} \] Input:
integrate(((6*x*ln(x)-6*x)*exp(2*ln(exp(4)*ln(5/3))-4)**3-6*x*exp(2*ln(exp (4)*ln(5/3))-4)**2)/(ln(x)**3*exp(2*ln(exp(4)*ln(5/3))-4)**3-3*ln(x)**2*ex p(2*ln(exp(4)*ln(5/3))-4)**2+3*ln(x)*exp(2*ln(exp(4)*ln(5/3))-4)-1),x)
Output:
(-12*x**2*exp(8)*log(3)*log(5)**3 - 12*x**2*exp(8)*log(3)**3*log(5) + 3*x* *2*exp(8)*log(3)**4 + 3*x**2*exp(8)*log(5)**4 + 18*x**2*exp(8)*log(3)**2*l og(5)**2)/((-4*exp(8)*log(3)*log(5)**3 - 4*exp(8)*log(3)**3*log(5) + exp(8 )*log(3)**4 + exp(8)*log(5)**4 + 6*exp(8)*log(3)**2*log(5)**2)*log(x)**2 + (-2*exp(4)*log(5)**2 - 2*exp(4)*log(3)**2 + 4*exp(4)*log(3)*log(5))*log(x ) + 1)
\[ \int \frac {-6 e^8 x \log ^4\left (\frac {5}{3}\right )+e^{12} \log ^6\left (\frac {5}{3}\right ) (-6 x+6 x \log (x))}{-1+3 e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)-3 e^8 \log ^4\left (\frac {5}{3}\right ) \log ^2(x)+e^{12} \log ^6\left (\frac {5}{3}\right ) \log ^3(x)} \, dx=\int { \frac {6 \, {\left ({\left (x \log \left (x\right ) - x\right )} e^{\left (6 \, \log \left (e^{4} \log \left (\frac {5}{3}\right )\right ) - 12\right )} - x e^{\left (4 \, \log \left (e^{4} \log \left (\frac {5}{3}\right )\right ) - 8\right )}\right )}}{e^{\left (6 \, \log \left (e^{4} \log \left (\frac {5}{3}\right )\right ) - 12\right )} \log \left (x\right )^{3} - 3 \, e^{\left (4 \, \log \left (e^{4} \log \left (\frac {5}{3}\right )\right ) - 8\right )} \log \left (x\right )^{2} + 3 \, e^{\left (2 \, \log \left (e^{4} \log \left (\frac {5}{3}\right )\right ) - 4\right )} \log \left (x\right ) - 1} \,d x } \] Input:
integrate(((6*x*log(x)-6*x)*exp(2*log(exp(4)*log(5/3))-4)^3-6*x*exp(2*log( exp(4)*log(5/3))-4)^2)/(log(x)^3*exp(2*log(exp(4)*log(5/3))-4)^3-3*log(x)^ 2*exp(2*log(exp(4)*log(5/3))-4)^2+3*log(x)*exp(2*log(exp(4)*log(5/3))-4)-1 ),x, algorithm="maxima")
Output:
3*(4*((log(5)^2 - 2*log(5)*log(3) + log(3)^2)*e^4 + 1)*integrate(x/((log(5 )^8 - 8*log(5)^7*log(3) + 28*log(5)^6*log(3)^2 - 56*log(5)^5*log(3)^3 + 70 *log(5)^4*log(3)^4 - 56*log(5)^3*log(3)^5 + 28*log(5)^2*log(3)^6 - 8*log(5 )*log(3)^7 + log(3)^8)*e^16*log(x) - (log(5)^6 - 6*log(5)^5*log(3) + 15*lo g(5)^4*log(3)^2 - 20*log(5)^3*log(3)^3 + 15*log(5)^2*log(3)^4 - 6*log(5)*l og(3)^5 + log(3)^6)*e^12), x) - (2*((log(5)^4 - 4*log(5)^3*log(3) + 6*log( 5)^2*log(3)^2 - 4*log(5)*log(3)^3 + log(3)^4)*e^8 + (log(5)^2 - 2*log(5)*l og(3) + log(3)^2)*e^4)*x^2*log(x) - ((log(5)^2 - 2*log(5)*log(3) + log(3)^ 2)*e^4 + 2)*x^2)/((log(5)^10 - 10*log(5)^9*log(3) + 45*log(5)^8*log(3)^2 - 120*log(5)^7*log(3)^3 + 210*log(5)^6*log(3)^4 - 252*log(5)^5*log(3)^5 + 2 10*log(5)^4*log(3)^6 - 120*log(5)^3*log(3)^7 + 45*log(5)^2*log(3)^8 - 10*l og(5)*log(3)^9 + log(3)^10)*e^20*log(x)^2 - 2*(log(5)^8 - 8*log(5)^7*log(3 ) + 28*log(5)^6*log(3)^2 - 56*log(5)^5*log(3)^3 + 70*log(5)^4*log(3)^4 - 5 6*log(5)^3*log(3)^5 + 28*log(5)^2*log(3)^6 - 8*log(5)*log(3)^7 + log(3)^8) *e^16*log(x) + (log(5)^6 - 6*log(5)^5*log(3) + 15*log(5)^4*log(3)^2 - 20*l og(5)^3*log(3)^3 + 15*log(5)^2*log(3)^4 - 6*log(5)*log(3)^5 + log(3)^6)*e^ 12))*e^12*log(5/3)^6 + 6*e^(2*e^(-4)/log(5/3)^2 + 8)*exp_integral_e(3, -2* (e^4*log(5/3)^2*log(x) - 1)*e^(-4)/log(5/3)^2)*log(5/3)^4/(e^4*log(5/3)^2* log(x) - 1)^2 + 6*e^(2*e^(-4)/log(5/3)^2 + 4)*exp_integral_e(3, -2*(e^4*lo g(5/3)^2*log(x) - 1)*e^(-4)/log(5/3)^2)*log(5/3)^2/(e^4*log(5/3)^2*log(...
Leaf count of result is larger than twice the leaf count of optimal. 564 vs. \(2 (23) = 46\).
Time = 0.33 (sec) , antiderivative size = 564, normalized size of antiderivative = 25.64 \[ \int \frac {-6 e^8 x \log ^4\left (\frac {5}{3}\right )+e^{12} \log ^6\left (\frac {5}{3}\right ) (-6 x+6 x \log (x))}{-1+3 e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)-3 e^8 \log ^4\left (\frac {5}{3}\right ) \log ^2(x)+e^{12} \log ^6\left (\frac {5}{3}\right ) \log ^3(x)} \, dx =\text {Too large to display} \] Input:
integrate(((6*x*log(x)-6*x)*exp(2*log(exp(4)*log(5/3))-4)^3-6*x*exp(2*log( exp(4)*log(5/3))-4)^2)/(log(x)^3*exp(2*log(exp(4)*log(5/3))-4)^3-3*log(x)^ 2*exp(2*log(exp(4)*log(5/3))-4)^2+3*log(x)*exp(2*log(exp(4)*log(5/3))-4)-1 ),x, algorithm="giac")
Output:
3*x^2*e^8*log(5)^4/(e^8*log(5)^4*log(x)^2 - 4*e^8*log(5)^3*log(3)*log(x)^2 + 6*e^8*log(5)^2*log(3)^2*log(x)^2 - 4*e^8*log(5)*log(3)^3*log(x)^2 + e^8 *log(3)^4*log(x)^2 - 2*e^4*log(5)^2*log(x) + 4*e^4*log(5)*log(3)*log(x) - 2*e^4*log(3)^2*log(x) + 1) - 12*x^2*e^8*log(5)^3*log(3)/(e^8*log(5)^4*log( x)^2 - 4*e^8*log(5)^3*log(3)*log(x)^2 + 6*e^8*log(5)^2*log(3)^2*log(x)^2 - 4*e^8*log(5)*log(3)^3*log(x)^2 + e^8*log(3)^4*log(x)^2 - 2*e^4*log(5)^2*l og(x) + 4*e^4*log(5)*log(3)*log(x) - 2*e^4*log(3)^2*log(x) + 1) + 18*x^2*e ^8*log(5)^2*log(3)^2/(e^8*log(5)^4*log(x)^2 - 4*e^8*log(5)^3*log(3)*log(x) ^2 + 6*e^8*log(5)^2*log(3)^2*log(x)^2 - 4*e^8*log(5)*log(3)^3*log(x)^2 + e ^8*log(3)^4*log(x)^2 - 2*e^4*log(5)^2*log(x) + 4*e^4*log(5)*log(3)*log(x) - 2*e^4*log(3)^2*log(x) + 1) - 12*x^2*e^8*log(5)*log(3)^3/(e^8*log(5)^4*lo g(x)^2 - 4*e^8*log(5)^3*log(3)*log(x)^2 + 6*e^8*log(5)^2*log(3)^2*log(x)^2 - 4*e^8*log(5)*log(3)^3*log(x)^2 + e^8*log(3)^4*log(x)^2 - 2*e^4*log(5)^2 *log(x) + 4*e^4*log(5)*log(3)*log(x) - 2*e^4*log(3)^2*log(x) + 1) + 3*x^2* e^8*log(3)^4/(e^8*log(5)^4*log(x)^2 - 4*e^8*log(5)^3*log(3)*log(x)^2 + 6*e ^8*log(5)^2*log(3)^2*log(x)^2 - 4*e^8*log(5)*log(3)^3*log(x)^2 + e^8*log(3 )^4*log(x)^2 - 2*e^4*log(5)^2*log(x) + 4*e^4*log(5)*log(3)*log(x) - 2*e^4* log(3)^2*log(x) + 1)
Time = 3.21 (sec) , antiderivative size = 102, normalized size of antiderivative = 4.64 \[ \int \frac {-6 e^8 x \log ^4\left (\frac {5}{3}\right )+e^{12} \log ^6\left (\frac {5}{3}\right ) (-6 x+6 x \log (x))}{-1+3 e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)-3 e^8 \log ^4\left (\frac {5}{3}\right ) \log ^2(x)+e^{12} \log ^6\left (\frac {5}{3}\right ) \log ^3(x)} \, dx=\frac {3\,x^2\,{\mathrm {e}}^{24}\,{\left (\ln \left (3\right )-\ln \left (5\right )\right )}^4}{\left ({\mathrm {e}}^{24}\,{\ln \left (3\right )}^4+{\mathrm {e}}^{24}\,{\ln \left (5\right )}^4+6\,{\mathrm {e}}^{24}\,{\ln \left (3\right )}^2\,{\ln \left (5\right )}^2-4\,{\mathrm {e}}^{24}\,\ln \left (3\right )\,{\ln \left (5\right )}^3-4\,{\mathrm {e}}^{24}\,{\ln \left (3\right )}^3\,\ln \left (5\right )\right )\,{\ln \left (x\right )}^2+\left (4\,{\mathrm {e}}^{20}\,\ln \left (3\right )\,\ln \left (5\right )-2\,{\mathrm {e}}^{20}\,{\ln \left (5\right )}^2-2\,{\mathrm {e}}^{20}\,{\ln \left (3\right )}^2\right )\,\ln \left (x\right )+{\mathrm {e}}^{16}} \] Input:
int(-(exp(6*log(exp(4)*log(5/3)) - 12)*(6*x - 6*x*log(x)) + 6*x*exp(4*log( exp(4)*log(5/3)) - 8))/(3*exp(2*log(exp(4)*log(5/3)) - 4)*log(x) - 3*exp(4 *log(exp(4)*log(5/3)) - 8)*log(x)^2 + exp(6*log(exp(4)*log(5/3)) - 12)*log (x)^3 - 1),x)
Output:
(3*x^2*exp(24)*(log(3) - log(5))^4)/(exp(16) - log(x)*(2*exp(20)*log(3)^2 + 2*exp(20)*log(5)^2 - 4*exp(20)*log(3)*log(5)) + log(x)^2*(exp(24)*log(3) ^4 + exp(24)*log(5)^4 + 6*exp(24)*log(3)^2*log(5)^2 - 4*exp(24)*log(3)*log (5)^3 - 4*exp(24)*log(3)^3*log(5)))
Time = 0.46 (sec) , antiderivative size = 39, normalized size of antiderivative = 1.77 \[ \int \frac {-6 e^8 x \log ^4\left (\frac {5}{3}\right )+e^{12} \log ^6\left (\frac {5}{3}\right ) (-6 x+6 x \log (x))}{-1+3 e^4 \log ^2\left (\frac {5}{3}\right ) \log (x)-3 e^8 \log ^4\left (\frac {5}{3}\right ) \log ^2(x)+e^{12} \log ^6\left (\frac {5}{3}\right ) \log ^3(x)} \, dx=\frac {3 \mathrm {log}\left (\frac {5}{3}\right )^{4} e^{8} x^{2}}{\mathrm {log}\left (\frac {5}{3}\right )^{4} \mathrm {log}\left (x \right )^{2} e^{8}-2 \mathrm {log}\left (\frac {5}{3}\right )^{2} \mathrm {log}\left (x \right ) e^{4}+1} \] Input:
int(((6*x*log(x)-6*x)*exp(2*log(exp(4)*log(5/3))-4)^3-6*x*exp(2*log(exp(4) *log(5/3))-4)^2)/(log(x)^3*exp(2*log(exp(4)*log(5/3))-4)^3-3*log(x)^2*exp( 2*log(exp(4)*log(5/3))-4)^2+3*log(x)*exp(2*log(exp(4)*log(5/3))-4)-1),x)
Output:
(3*log(5/3)**4*e**8*x**2)/(log(5/3)**4*log(x)**2*e**8 - 2*log(5/3)**2*log( x)*e**4 + 1)