Integrand size = 206, antiderivative size = 29 \[ \int \frac {e^{\frac {-1+\log (5)}{\log \left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )}} \left (-9 x+9 x \log (5)+(-6 x+6 x \log (5)) \log (x)+(-x+x \log (5)) \log ^2(x)+e^{\frac {75+28 x+x \log (x)}{3+\log (x)}} \left (-75+59 x+(75-59 x) \log (5)+(31 x-31 x \log (5)) \log (x)+(x-x \log (5)) \log ^2(x)\right )\right )}{\left (-9 x^2-6 x^2 \log (x)-x^2 \log ^2(x)+e^{\frac {75+28 x+x \log (x)}{3+\log (x)}} \left (9 x+6 x \log (x)+x \log ^2(x)\right )\right ) \log ^2\left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )} \, dx=e^{\frac {-1+\log (5)}{\log \left (-e^{x+\frac {25 (3+x)}{3+\log (x)}}+x\right )}} \]
Time = 0.40 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.07 \[ \int \frac {e^{\frac {-1+\log (5)}{\log \left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )}} \left (-9 x+9 x \log (5)+(-6 x+6 x \log (5)) \log (x)+(-x+x \log (5)) \log ^2(x)+e^{\frac {75+28 x+x \log (x)}{3+\log (x)}} \left (-75+59 x+(75-59 x) \log (5)+(31 x-31 x \log (5)) \log (x)+(x-x \log (5)) \log ^2(x)\right )\right )}{\left (-9 x^2-6 x^2 \log (x)-x^2 \log ^2(x)+e^{\frac {75+28 x+x \log (x)}{3+\log (x)}} \left (9 x+6 x \log (x)+x \log ^2(x)\right )\right ) \log ^2\left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )} \, dx=\left (\frac {5}{e}\right )^{\frac {1}{\log \left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )}} \]
Integrate[(E^((-1 + Log[5])/Log[-E^((75 + 28*x + x*Log[x])/(3 + Log[x])) + x])*(-9*x + 9*x*Log[5] + (-6*x + 6*x*Log[5])*Log[x] + (-x + x*Log[5])*Log [x]^2 + E^((75 + 28*x + x*Log[x])/(3 + Log[x]))*(-75 + 59*x + (75 - 59*x)* Log[5] + (31*x - 31*x*Log[5])*Log[x] + (x - x*Log[5])*Log[x]^2)))/((-9*x^2 - 6*x^2*Log[x] - x^2*Log[x]^2 + E^((75 + 28*x + x*Log[x])/(3 + Log[x]))*( 9*x + 6*x*Log[x] + x*Log[x]^2))*Log[-E^((75 + 28*x + x*Log[x])/(3 + Log[x] )) + x]^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.
| \(\displaystyle \int \frac {\left (-9 x+(x \log (5)-x) \log ^2(x)+e^{\frac {28 x+x \log (x)+75}{\log (x)+3}} \left (59 x+(x-x \log (5)) \log ^2(x)+(31 x-31 x \log (5)) \log (x)+(75-59 x) \log (5)-75\right )+(6 x \log (5)-6 x) \log (x)+9 x \log (5)\right ) \exp \left (\frac {\log (5)-1}{\log \left (x-e^{\frac {28 x+x \log (x)+75}{\log (x)+3}}\right )}\right )}{\left (-9 x^2+x^2 \left (-\log ^2(x)\right )-6 x^2 \log (x)+e^{\frac {28 x+x \log (x)+75}{\log (x)+3}} \left (9 x+x \log ^2(x)+6 x \log (x)\right )\right ) \log ^2\left (x-e^{\frac {28 x+x \log (x)+75}{\log (x)+3}}\right )} \, dx\) |
| \(\Big \downarrow \) 6 |
| \(\displaystyle \int \frac {\left ((x \log (5)-x) \log ^2(x)+e^{\frac {28 x+x \log (x)+75}{\log (x)+3}} \left (59 x+(x-x \log (5)) \log ^2(x)+(31 x-31 x \log (5)) \log (x)+(75-59 x) \log (5)-75\right )+(6 x \log (5)-6 x) \log (x)+x (9 \log (5)-9)\right ) \exp \left (\frac {\log (5)-1}{\log \left (x-e^{\frac {28 x+x \log (x)+75}{\log (x)+3}}\right )}\right )}{\left (-9 x^2+x^2 \left (-\log ^2(x)\right )-6 x^2 \log (x)+e^{\frac {28 x+x \log (x)+75}{\log (x)+3}} \left (9 x+x \log ^2(x)+6 x \log (x)\right )\right ) \log ^2\left (x-e^{\frac {28 x+x \log (x)+75}{\log (x)+3}}\right )}dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {\left (-\left ((x \log (5)-x) \log ^2(x)\right )-e^{\frac {28 x+x \log (x)+75}{\log (x)+3}} \left (59 x+(x-x \log (5)) \log ^2(x)+(31 x-31 x \log (5)) \log (x)+(75-59 x) \log (5)-75\right )-(6 x \log (5)-6 x) \log (x)-x (9 \log (5)-9)\right ) \exp \left (\frac {\log (5)-1}{\log \left (x-e^{\frac {28 x+x \log (x)+75}{\log (x)+3}}\right )}\right )}{x \left (x-e^{\frac {28 x}{\log (x)+3}+\frac {75}{\log (x)+3}} x^{\frac {x}{\log (x)+3}}\right ) (\log (x)+3)^2 \log ^2\left (x-e^{\frac {28 x+x \log (x)+75}{\log (x)+3}}\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {e^{\frac {28 x+75}{\log (x)+3}+\frac {-1+\log (5)}{\log \left (x-e^{\frac {\log (x) x+28 x+75}{\log (x)+3}}\right )}} (1-\log (5)) \log ^2(x) x^{\frac {x}{\log (x)+3}}}{\left (e^{\frac {28 x}{\log (x)+3}+\frac {75}{\log (x)+3}} x^{\frac {x}{\log (x)+3}}-x\right ) (\log (x)+3)^2 \log ^2\left (x-e^{\frac {\log (x) x+28 x+75}{\log (x)+3}}\right )}+\frac {31 e^{\frac {28 x+75}{\log (x)+3}+\frac {-1+\log (5)}{\log \left (x-e^{\frac {\log (x) x+28 x+75}{\log (x)+3}}\right )}} (1-\log (5)) \log (x) x^{\frac {x}{\log (x)+3}}}{\left (e^{\frac {28 x}{\log (x)+3}+\frac {75}{\log (x)+3}} x^{\frac {x}{\log (x)+3}}-x\right ) (\log (x)+3)^2 \log ^2\left (x-e^{\frac {\log (x) x+28 x+75}{\log (x)+3}}\right )}+\frac {59 e^{\frac {28 x+75}{\log (x)+3}+\frac {-1+\log (5)}{\log \left (x-e^{\frac {\log (x) x+28 x+75}{\log (x)+3}}\right )}} (1-\log (5)) x^{\frac {x}{\log (x)+3}}}{\left (e^{\frac {28 x}{\log (x)+3}+\frac {75}{\log (x)+3}} x^{\frac {x}{\log (x)+3}}-x\right ) (\log (x)+3)^2 \log ^2\left (x-e^{\frac {\log (x) x+28 x+75}{\log (x)+3}}\right )}+\frac {75 e^{\frac {28 x+75}{\log (x)+3}+\frac {-1+\log (5)}{\log \left (x-e^{\frac {\log (x) x+28 x+75}{\log (x)+3}}\right )}} (1-\log (5)) x^{\frac {x}{\log (x)+3}-1}}{\left (x-e^{\frac {28 x}{\log (x)+3}+\frac {75}{\log (x)+3}} x^{\frac {x}{\log (x)+3}}\right ) (\log (x)+3)^2 \log ^2\left (x-e^{\frac {\log (x) x+28 x+75}{\log (x)+3}}\right )}-\frac {e^{\frac {-1+\log (5)}{\log \left (x-e^{\frac {\log (x) x+28 x+75}{\log (x)+3}}\right )}} (1-\log (5)) \log ^2(x)}{\left (e^{\frac {28 x}{\log (x)+3}+\frac {75}{\log (x)+3}} x^{\frac {x}{\log (x)+3}}-x\right ) (\log (x)+3)^2 \log ^2\left (x-e^{\frac {\log (x) x+28 x+75}{\log (x)+3}}\right )}-\frac {6 e^{\frac {-1+\log (5)}{\log \left (x-e^{\frac {\log (x) x+28 x+75}{\log (x)+3}}\right )}} (1-\log (5)) \log (x)}{\left (e^{\frac {28 x}{\log (x)+3}+\frac {75}{\log (x)+3}} x^{\frac {x}{\log (x)+3}}-x\right ) (\log (x)+3)^2 \log ^2\left (x-e^{\frac {\log (x) x+28 x+75}{\log (x)+3}}\right )}+\frac {9 e^{\frac {-1+\log (5)}{\log \left (x-e^{\frac {\log (x) x+28 x+75}{\log (x)+3}}\right )}} (-1+\log (5))}{\left (e^{\frac {28 x}{\log (x)+3}+\frac {75}{\log (x)+3}} x^{\frac {x}{\log (x)+3}}-x\right ) (\log (x)+3)^2 \log ^2\left (x-e^{\frac {\log (x) x+28 x+75}{\log (x)+3}}\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {(1-\log (5)) \left (\frac {5}{e}\right )^{\frac {1}{\log \left (x-e^{\frac {28 x+x \log (x)+75}{\log (x)+3}}\right )}} \left (-59 e^{\frac {28 x+75}{\log (x)+3}} x^{\frac {x}{\log (x)+3}+1}-x \left (e^{\frac {28 x+75}{\log (x)+3}} x^{\frac {x}{\log (x)+3}}-1\right ) \log ^2(x)+75 e^{\frac {28 x+75}{\log (x)+3}} x^{\frac {x}{\log (x)+3}}-x \left (31 e^{\frac {28 x+75}{\log (x)+3}} x^{\frac {x}{\log (x)+3}}-6\right ) \log (x)+9 x\right )}{x \left (x-e^{\frac {28 x+75}{\log (x)+3}} x^{\frac {x}{\log (x)+3}}\right ) (\log (x)+3)^2 \log ^2\left (x-e^{\frac {28 x+x \log (x)+75}{\log (x)+3}}\right )}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle (1-\log (5)) \int \frac {\left (\frac {5}{e}\right )^{\frac {1}{\log \left (x-e^{\frac {28 x+75}{\log (x)+3}} x^{\frac {x}{\log (x)+3}}\right )}} \left (75 e^{\frac {28 x+75}{\log (x)+3}} x^{\frac {x}{\log (x)+3}}-59 e^{\frac {28 x+75}{\log (x)+3}} x^{\frac {x}{\log (x)+3}+1}+\left (1-e^{\frac {28 x+75}{\log (x)+3}} x^{\frac {x}{\log (x)+3}}\right ) \log ^2(x) x+\left (6-31 e^{\frac {28 x+75}{\log (x)+3}} x^{\frac {x}{\log (x)+3}}\right ) \log (x) x+9 x\right )}{x \left (x-e^{\frac {28 x+75}{\log (x)+3}} x^{\frac {x}{\log (x)+3}}\right ) (\log (x)+3)^2 \log ^2\left (x-e^{\frac {28 x+75}{\log (x)+3}} x^{\frac {x}{\log (x)+3}}\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle (1-\log (5)) \int \left (\frac {\left (\frac {5}{e}\right )^{\frac {1}{\log \left (x-e^{\frac {28 x+75}{\log (x)+3}} x^{\frac {x}{\log (x)+3}}\right )}} \left (x \log ^2(x)+31 x \log (x)+59 x-75\right )}{x (\log (x)+3)^2 \log ^2\left (x-e^{\frac {28 x+75}{\log (x)+3}} x^{\frac {x}{\log (x)+3}}\right )}+\frac {\left (\frac {5}{e}\right )^{\frac {1}{\log \left (x-e^{\frac {28 x+75}{\log (x)+3}} x^{\frac {x}{\log (x)+3}}\right )}} \left (x \log ^2(x)-\log ^2(x)+31 x \log (x)-6 \log (x)+59 x-84\right )}{\left (e^{\frac {28 x}{\log (x)+3}+\frac {75}{\log (x)+3}} x^{\frac {x}{\log (x)+3}}-x\right ) (\log (x)+3)^2 \log ^2\left (x-e^{\frac {28 x+75}{\log (x)+3}} x^{\frac {x}{\log (x)+3}}\right )}\right )dx\) |
| \(\Big \downarrow \) 7299 |
| \(\displaystyle (1-\log (5)) \int \left (\frac {\left (\frac {5}{e}\right )^{\frac {1}{\log \left (x-e^{\frac {28 x+75}{\log (x)+3}} x^{\frac {x}{\log (x)+3}}\right )}} \left (x \log ^2(x)+31 x \log (x)+59 x-75\right )}{x (\log (x)+3)^2 \log ^2\left (x-e^{\frac {28 x+75}{\log (x)+3}} x^{\frac {x}{\log (x)+3}}\right )}+\frac {\left (\frac {5}{e}\right )^{\frac {1}{\log \left (x-e^{\frac {28 x+75}{\log (x)+3}} x^{\frac {x}{\log (x)+3}}\right )}} \left (x \log ^2(x)-\log ^2(x)+31 x \log (x)-6 \log (x)+59 x-84\right )}{\left (e^{\frac {28 x}{\log (x)+3}+\frac {75}{\log (x)+3}} x^{\frac {x}{\log (x)+3}}-x\right ) (\log (x)+3)^2 \log ^2\left (x-e^{\frac {28 x+75}{\log (x)+3}} x^{\frac {x}{\log (x)+3}}\right )}\right )dx\) |
Int[(E^((-1 + Log[5])/Log[-E^((75 + 28*x + x*Log[x])/(3 + Log[x])) + x])*( -9*x + 9*x*Log[5] + (-6*x + 6*x*Log[5])*Log[x] + (-x + x*Log[5])*Log[x]^2 + E^((75 + 28*x + x*Log[x])/(3 + Log[x]))*(-75 + 59*x + (75 - 59*x)*Log[5] + (31*x - 31*x*Log[5])*Log[x] + (x - x*Log[5])*Log[x]^2)))/((-9*x^2 - 6*x ^2*Log[x] - x^2*Log[x]^2 + E^((75 + 28*x + x*Log[x])/(3 + Log[x]))*(9*x + 6*x*Log[x] + x*Log[x]^2))*Log[-E^((75 + 28*x + x*Log[x])/(3 + Log[x])) + x ]^2),x]
3.5.12.3.1 Defintions of rubi rules used
Int[(u_.)*((v_.) + (a_.)*(Fx_) + (b_.)*(Fx_))^(p_.), x_Symbol] :> Int[u*(v + (a + b)*Fx)^p, x] /; FreeQ[{a, b}, x] && !FreeQ[Fx, x]
Int[(a_)*(Fx_), x_Symbol] :> Simp[a Int[Fx, x], x] /; FreeQ[a, x] && !Ma tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; Simpl erIntegrandQ[v, u, x]]
Time = 0.04 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.07
\[{\mathrm e}^{\frac {\ln \left (5\right )-1}{\ln \left (-{\mathrm e}^{\frac {x \ln \left (x \right )+28 x +75}{3+\ln \left (x \right )}}+x \right )}}\]
int((((-x*ln(5)+x)*ln(x)^2+(-31*x*ln(5)+31*x)*ln(x)+(-59*x+75)*ln(5)+59*x- 75)*exp((x*ln(x)+28*x+75)/(3+ln(x)))+(x*ln(5)-x)*ln(x)^2+(6*x*ln(5)-6*x)*l n(x)+9*x*ln(5)-9*x)*exp((ln(5)-1)/ln(-exp((x*ln(x)+28*x+75)/(3+ln(x)))+x)) /((x*ln(x)^2+6*x*ln(x)+9*x)*exp((x*ln(x)+28*x+75)/(3+ln(x)))-x^2*ln(x)^2-6 *x^2*ln(x)-9*x^2)/ln(-exp((x*ln(x)+28*x+75)/(3+ln(x)))+x)^2,x)
Time = 0.24 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.03 \[ \int \frac {e^{\frac {-1+\log (5)}{\log \left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )}} \left (-9 x+9 x \log (5)+(-6 x+6 x \log (5)) \log (x)+(-x+x \log (5)) \log ^2(x)+e^{\frac {75+28 x+x \log (x)}{3+\log (x)}} \left (-75+59 x+(75-59 x) \log (5)+(31 x-31 x \log (5)) \log (x)+(x-x \log (5)) \log ^2(x)\right )\right )}{\left (-9 x^2-6 x^2 \log (x)-x^2 \log ^2(x)+e^{\frac {75+28 x+x \log (x)}{3+\log (x)}} \left (9 x+6 x \log (x)+x \log ^2(x)\right )\right ) \log ^2\left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )} \, dx=e^{\left (\frac {\log \left (5\right ) - 1}{\log \left (x - e^{\left (\frac {x \log \left (x\right ) + 28 \, x + 75}{\log \left (x\right ) + 3}\right )}\right )}\right )} \]
integrate((((-x*log(5)+x)*log(x)^2+(-31*x*log(5)+31*x)*log(x)+(-59*x+75)*l og(5)+59*x-75)*exp((x*log(x)+28*x+75)/(3+log(x)))+(x*log(5)-x)*log(x)^2+(6 *x*log(5)-6*x)*log(x)+9*x*log(5)-9*x)*exp((log(5)-1)/log(-exp((x*log(x)+28 *x+75)/(3+log(x)))+x))/((x*log(x)^2+6*x*log(x)+9*x)*exp((x*log(x)+28*x+75) /(3+log(x)))-x^2*log(x)^2-6*x^2*log(x)-9*x^2)/log(-exp((x*log(x)+28*x+75)/ (3+log(x)))+x)^2,x, algorithm=\
Timed out. \[ \int \frac {e^{\frac {-1+\log (5)}{\log \left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )}} \left (-9 x+9 x \log (5)+(-6 x+6 x \log (5)) \log (x)+(-x+x \log (5)) \log ^2(x)+e^{\frac {75+28 x+x \log (x)}{3+\log (x)}} \left (-75+59 x+(75-59 x) \log (5)+(31 x-31 x \log (5)) \log (x)+(x-x \log (5)) \log ^2(x)\right )\right )}{\left (-9 x^2-6 x^2 \log (x)-x^2 \log ^2(x)+e^{\frac {75+28 x+x \log (x)}{3+\log (x)}} \left (9 x+6 x \log (x)+x \log ^2(x)\right )\right ) \log ^2\left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )} \, dx=\text {Timed out} \]
integrate((((-x*ln(5)+x)*ln(x)**2+(-31*x*ln(5)+31*x)*ln(x)+(-59*x+75)*ln(5 )+59*x-75)*exp((x*ln(x)+28*x+75)/(3+ln(x)))+(x*ln(5)-x)*ln(x)**2+(6*x*ln(5 )-6*x)*ln(x)+9*x*ln(5)-9*x)*exp((ln(5)-1)/ln(-exp((x*ln(x)+28*x+75)/(3+ln( x)))+x))/((x*ln(x)**2+6*x*ln(x)+9*x)*exp((x*ln(x)+28*x+75)/(3+ln(x)))-x**2 *ln(x)**2-6*x**2*ln(x)-9*x**2)/ln(-exp((x*ln(x)+28*x+75)/(3+ln(x)))+x)**2, x)
Leaf count of result is larger than twice the leaf count of optimal. 79 vs. \(2 (27) = 54\).
Time = 0.66 (sec) , antiderivative size = 79, normalized size of antiderivative = 2.72 \[ \int \frac {e^{\frac {-1+\log (5)}{\log \left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )}} \left (-9 x+9 x \log (5)+(-6 x+6 x \log (5)) \log (x)+(-x+x \log (5)) \log ^2(x)+e^{\frac {75+28 x+x \log (x)}{3+\log (x)}} \left (-75+59 x+(75-59 x) \log (5)+(31 x-31 x \log (5)) \log (x)+(x-x \log (5)) \log ^2(x)\right )\right )}{\left (-9 x^2-6 x^2 \log (x)-x^2 \log ^2(x)+e^{\frac {75+28 x+x \log (x)}{3+\log (x)}} \left (9 x+6 x \log (x)+x \log ^2(x)\right )\right ) \log ^2\left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )} \, dx=e^{\left (\frac {\log \left (5\right )}{\log \left (x - e^{\left (\frac {x \log \left (x\right )}{\log \left (x\right ) + 3} + \frac {28 \, x}{\log \left (x\right ) + 3} + \frac {75}{\log \left (x\right ) + 3}\right )}\right )} - \frac {1}{\log \left (x - e^{\left (\frac {x \log \left (x\right )}{\log \left (x\right ) + 3} + \frac {28 \, x}{\log \left (x\right ) + 3} + \frac {75}{\log \left (x\right ) + 3}\right )}\right )}\right )} \]
integrate((((-x*log(5)+x)*log(x)^2+(-31*x*log(5)+31*x)*log(x)+(-59*x+75)*l og(5)+59*x-75)*exp((x*log(x)+28*x+75)/(3+log(x)))+(x*log(5)-x)*log(x)^2+(6 *x*log(5)-6*x)*log(x)+9*x*log(5)-9*x)*exp((log(5)-1)/log(-exp((x*log(x)+28 *x+75)/(3+log(x)))+x))/((x*log(x)^2+6*x*log(x)+9*x)*exp((x*log(x)+28*x+75) /(3+log(x)))-x^2*log(x)^2-6*x^2*log(x)-9*x^2)/log(-exp((x*log(x)+28*x+75)/ (3+log(x)))+x)^2,x, algorithm=\
e^(log(5)/log(x - e^(x*log(x)/(log(x) + 3) + 28*x/(log(x) + 3) + 75/(log(x ) + 3))) - 1/log(x - e^(x*log(x)/(log(x) + 3) + 28*x/(log(x) + 3) + 75/(lo g(x) + 3))))
Timed out. \[ \int \frac {e^{\frac {-1+\log (5)}{\log \left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )}} \left (-9 x+9 x \log (5)+(-6 x+6 x \log (5)) \log (x)+(-x+x \log (5)) \log ^2(x)+e^{\frac {75+28 x+x \log (x)}{3+\log (x)}} \left (-75+59 x+(75-59 x) \log (5)+(31 x-31 x \log (5)) \log (x)+(x-x \log (5)) \log ^2(x)\right )\right )}{\left (-9 x^2-6 x^2 \log (x)-x^2 \log ^2(x)+e^{\frac {75+28 x+x \log (x)}{3+\log (x)}} \left (9 x+6 x \log (x)+x \log ^2(x)\right )\right ) \log ^2\left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )} \, dx=\text {Timed out} \]
integrate((((-x*log(5)+x)*log(x)^2+(-31*x*log(5)+31*x)*log(x)+(-59*x+75)*l og(5)+59*x-75)*exp((x*log(x)+28*x+75)/(3+log(x)))+(x*log(5)-x)*log(x)^2+(6 *x*log(5)-6*x)*log(x)+9*x*log(5)-9*x)*exp((log(5)-1)/log(-exp((x*log(x)+28 *x+75)/(3+log(x)))+x))/((x*log(x)^2+6*x*log(x)+9*x)*exp((x*log(x)+28*x+75) /(3+log(x)))-x^2*log(x)^2-6*x^2*log(x)-9*x^2)/log(-exp((x*log(x)+28*x+75)/ (3+log(x)))+x)^2,x, algorithm=\
Time = 8.68 (sec) , antiderivative size = 78, normalized size of antiderivative = 2.69 \[ \int \frac {e^{\frac {-1+\log (5)}{\log \left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )}} \left (-9 x+9 x \log (5)+(-6 x+6 x \log (5)) \log (x)+(-x+x \log (5)) \log ^2(x)+e^{\frac {75+28 x+x \log (x)}{3+\log (x)}} \left (-75+59 x+(75-59 x) \log (5)+(31 x-31 x \log (5)) \log (x)+(x-x \log (5)) \log ^2(x)\right )\right )}{\left (-9 x^2-6 x^2 \log (x)-x^2 \log ^2(x)+e^{\frac {75+28 x+x \log (x)}{3+\log (x)}} \left (9 x+6 x \log (x)+x \log ^2(x)\right )\right ) \log ^2\left (-e^{\frac {75+28 x+x \log (x)}{3+\log (x)}}+x\right )} \, dx=5^{\frac {1}{\ln \left (x-x^{\frac {x}{\ln \left (x\right )+3}}\,{\mathrm {e}}^{\frac {75}{\ln \left (x\right )+3}}\,{\mathrm {e}}^{\frac {28\,x}{\ln \left (x\right )+3}}\right )}}\,{\mathrm {e}}^{-\frac {1}{\ln \left (x-x^{\frac {x}{\ln \left (x\right )+3}}\,{\mathrm {e}}^{\frac {75}{\ln \left (x\right )+3}}\,{\mathrm {e}}^{\frac {28\,x}{\ln \left (x\right )+3}}\right )}} \]
int((exp((log(5) - 1)/log(x - exp((28*x + x*log(x) + 75)/(log(x) + 3))))*( 9*x - 9*x*log(5) - exp((28*x + x*log(x) + 75)/(log(x) + 3))*(59*x - log(5) *(59*x - 75) + log(x)*(31*x - 31*x*log(5)) + log(x)^2*(x - x*log(5)) - 75) + log(x)*(6*x - 6*x*log(5)) + log(x)^2*(x - x*log(5))))/(log(x - exp((28* x + x*log(x) + 75)/(log(x) + 3)))^2*(6*x^2*log(x) + x^2*log(x)^2 - exp((28 *x + x*log(x) + 75)/(log(x) + 3))*(9*x + x*log(x)^2 + 6*x*log(x)) + 9*x^2) ),x)