Integrand size = 258, antiderivative size = 33 \[ \int \frac {-36 e^x x^3+\left (-1500-1500 x+e^x (500+500 x)\right ) \log \left (3-e^x\right )+\left (900+e^x (-300-300 x)+900 x\right ) \log \left (3-e^x\right ) \log \left (\log \left (3-e^x\right )\right )+\left (-180-180 x+e^x (60+60 x)\right ) \log \left (3-e^x\right ) \log ^2\left (\log \left (3-e^x\right )\right )+\left (12+e^x (-4-4 x)+12 x\right ) \log \left (3-e^x\right ) \log ^3\left (\log \left (3-e^x\right )\right )}{\left (375 x^3-125 e^x x^3\right ) \log \left (3-e^x\right )+\left (-225 x^3+75 e^x x^3\right ) \log \left (3-e^x\right ) \log \left (\log \left (3-e^x\right )\right )+\left (45 x^3-15 e^x x^3\right ) \log \left (3-e^x\right ) \log ^2\left (\log \left (3-e^x\right )\right )+\left (-3 x^3+e^x x^3\right ) \log \left (3-e^x\right ) \log ^3\left (\log \left (3-e^x\right )\right )} \, dx=3+\frac {1}{2} \left (\left (2+\frac {2}{x}\right )^2+\frac {36}{\left (5-\log \left (\log \left (3-e^x\right )\right )\right )^2}\right ) \] Output:
18/(5-ln(ln(-exp(x)+3)))^2+1/2*(2/x+2)^2+3
Time = 0.04 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.79 \[ \int \frac {-36 e^x x^3+\left (-1500-1500 x+e^x (500+500 x)\right ) \log \left (3-e^x\right )+\left (900+e^x (-300-300 x)+900 x\right ) \log \left (3-e^x\right ) \log \left (\log \left (3-e^x\right )\right )+\left (-180-180 x+e^x (60+60 x)\right ) \log \left (3-e^x\right ) \log ^2\left (\log \left (3-e^x\right )\right )+\left (12+e^x (-4-4 x)+12 x\right ) \log \left (3-e^x\right ) \log ^3\left (\log \left (3-e^x\right )\right )}{\left (375 x^3-125 e^x x^3\right ) \log \left (3-e^x\right )+\left (-225 x^3+75 e^x x^3\right ) \log \left (3-e^x\right ) \log \left (\log \left (3-e^x\right )\right )+\left (45 x^3-15 e^x x^3\right ) \log \left (3-e^x\right ) \log ^2\left (\log \left (3-e^x\right )\right )+\left (-3 x^3+e^x x^3\right ) \log \left (3-e^x\right ) \log ^3\left (\log \left (3-e^x\right )\right )} \, dx=\frac {2}{x^2}+\frac {4}{x}+\frac {18}{\left (-5+\log \left (\log \left (3-e^x\right )\right )\right )^2} \] Input:
Integrate[(-36*E^x*x^3 + (-1500 - 1500*x + E^x*(500 + 500*x))*Log[3 - E^x] + (900 + E^x*(-300 - 300*x) + 900*x)*Log[3 - E^x]*Log[Log[3 - E^x]] + (-1 80 - 180*x + E^x*(60 + 60*x))*Log[3 - E^x]*Log[Log[3 - E^x]]^2 + (12 + E^x *(-4 - 4*x) + 12*x)*Log[3 - E^x]*Log[Log[3 - E^x]]^3)/((375*x^3 - 125*E^x* x^3)*Log[3 - E^x] + (-225*x^3 + 75*E^x*x^3)*Log[3 - E^x]*Log[Log[3 - E^x]] + (45*x^3 - 15*E^x*x^3)*Log[3 - E^x]*Log[Log[3 - E^x]]^2 + (-3*x^3 + E^x* x^3)*Log[3 - E^x]*Log[Log[3 - E^x]]^3),x]
Output:
2/x^2 + 4/x + 18/(-5 + Log[Log[3 - E^x]])^2
Time = 0.74 (sec) , antiderivative size = 28, normalized size of antiderivative = 0.85, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.008, Rules used = {7239, 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.
| \(\displaystyle \int \frac {-36 e^x x^3+\left (e^x (-4 x-4)+12 x+12\right ) \log \left (3-e^x\right ) \log ^3\left (\log \left (3-e^x\right )\right )+\left (-180 x+e^x (60 x+60)-180\right ) \log \left (3-e^x\right ) \log ^2\left (\log \left (3-e^x\right )\right )+\left (-1500 x+e^x (500 x+500)-1500\right ) \log \left (3-e^x\right )+\left (e^x (-300 x-300)+900 x+900\right ) \log \left (3-e^x\right ) \log \left (\log \left (3-e^x\right )\right )}{\left (e^x x^3-3 x^3\right ) \log \left (3-e^x\right ) \log ^3\left (\log \left (3-e^x\right )\right )+\left (45 x^3-15 e^x x^3\right ) \log \left (3-e^x\right ) \log ^2\left (\log \left (3-e^x\right )\right )+\left (75 e^x x^3-225 x^3\right ) \log \left (3-e^x\right ) \log \left (\log \left (3-e^x\right )\right )+\left (375 x^3-125 e^x x^3\right ) \log \left (3-e^x\right )} \, dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \left (-\frac {4 (x+1)}{x^3}-\frac {36 e^x}{\left (e^x-3\right ) \log \left (3-e^x\right ) \left (\log \left (\log \left (3-e^x\right )\right )-5\right )^3}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle \frac {2 (x+1)^2}{x^2}+\frac {18}{\left (5-\log \left (\log \left (3-e^x\right )\right )\right )^2}\) |
Input:
Int[(-36*E^x*x^3 + (-1500 - 1500*x + E^x*(500 + 500*x))*Log[3 - E^x] + (90 0 + E^x*(-300 - 300*x) + 900*x)*Log[3 - E^x]*Log[Log[3 - E^x]] + (-180 - 1 80*x + E^x*(60 + 60*x))*Log[3 - E^x]*Log[Log[3 - E^x]]^2 + (12 + E^x*(-4 - 4*x) + 12*x)*Log[3 - E^x]*Log[Log[3 - E^x]]^3)/((375*x^3 - 125*E^x*x^3)*L og[3 - E^x] + (-225*x^3 + 75*E^x*x^3)*Log[3 - E^x]*Log[Log[3 - E^x]] + (45 *x^3 - 15*E^x*x^3)*Log[3 - E^x]*Log[Log[3 - E^x]]^2 + (-3*x^3 + E^x*x^3)*L og[3 - E^x]*Log[Log[3 - E^x]]^3),x]
Output:
(2*(1 + x)^2)/x^2 + 18/(5 - Log[Log[3 - E^x]])^2
Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; Simpl erIntegrandQ[v, u, x]]
Time = 29.99 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.79
| method | result | size |
| risch | \(\frac {4 x +2}{x^{2}}+\frac {18}{{\left (\ln \left (\ln \left (-{\mathrm e}^{x}+3\right )\right )-5\right )}^{2}}\) | \(26\) |
| parallelrisch | \(\frac {3000+240 {\ln \left (\ln \left (-{\mathrm e}^{x}+3\right )\right )}^{2} x +1080 x^{2}-2400 \ln \left (\ln \left (-{\mathrm e}^{x}+3\right )\right ) x +120 {\ln \left (\ln \left (-{\mathrm e}^{x}+3\right )\right )}^{2}+6000 x -1200 \ln \left (\ln \left (-{\mathrm e}^{x}+3\right )\right )}{60 x^{2} \left ({\ln \left (\ln \left (-{\mathrm e}^{x}+3\right )\right )}^{2}-10 \ln \left (\ln \left (-{\mathrm e}^{x}+3\right )\right )+25\right )}\) | \(86\) |
Input:
int((((-4-4*x)*exp(x)+12*x+12)*ln(-exp(x)+3)*ln(ln(-exp(x)+3))^3+((60*x+60 )*exp(x)-180*x-180)*ln(-exp(x)+3)*ln(ln(-exp(x)+3))^2+((-300*x-300)*exp(x) +900*x+900)*ln(-exp(x)+3)*ln(ln(-exp(x)+3))+((500*x+500)*exp(x)-1500*x-150 0)*ln(-exp(x)+3)-36*exp(x)*x^3)/((exp(x)*x^3-3*x^3)*ln(-exp(x)+3)*ln(ln(-e xp(x)+3))^3+(-15*exp(x)*x^3+45*x^3)*ln(-exp(x)+3)*ln(ln(-exp(x)+3))^2+(75* exp(x)*x^3-225*x^3)*ln(-exp(x)+3)*ln(ln(-exp(x)+3))+(-125*exp(x)*x^3+375*x ^3)*ln(-exp(x)+3)),x,method=_RETURNVERBOSE)
Output:
2*(1+2*x)/x^2+18/(ln(ln(-exp(x)+3))-5)^2
Leaf count of result is larger than twice the leaf count of optimal. 78 vs. \(2 (25) = 50\).
Time = 0.07 (sec) , antiderivative size = 78, normalized size of antiderivative = 2.36 \[ \int \frac {-36 e^x x^3+\left (-1500-1500 x+e^x (500+500 x)\right ) \log \left (3-e^x\right )+\left (900+e^x (-300-300 x)+900 x\right ) \log \left (3-e^x\right ) \log \left (\log \left (3-e^x\right )\right )+\left (-180-180 x+e^x (60+60 x)\right ) \log \left (3-e^x\right ) \log ^2\left (\log \left (3-e^x\right )\right )+\left (12+e^x (-4-4 x)+12 x\right ) \log \left (3-e^x\right ) \log ^3\left (\log \left (3-e^x\right )\right )}{\left (375 x^3-125 e^x x^3\right ) \log \left (3-e^x\right )+\left (-225 x^3+75 e^x x^3\right ) \log \left (3-e^x\right ) \log \left (\log \left (3-e^x\right )\right )+\left (45 x^3-15 e^x x^3\right ) \log \left (3-e^x\right ) \log ^2\left (\log \left (3-e^x\right )\right )+\left (-3 x^3+e^x x^3\right ) \log \left (3-e^x\right ) \log ^3\left (\log \left (3-e^x\right )\right )} \, dx=\frac {2 \, {\left ({\left (2 \, x + 1\right )} \log \left (\log \left (-e^{x} + 3\right )\right )^{2} + 9 \, x^{2} - 10 \, {\left (2 \, x + 1\right )} \log \left (\log \left (-e^{x} + 3\right )\right ) + 50 \, x + 25\right )}}{x^{2} \log \left (\log \left (-e^{x} + 3\right )\right )^{2} - 10 \, x^{2} \log \left (\log \left (-e^{x} + 3\right )\right ) + 25 \, x^{2}} \] Input:
integrate((((-4-4*x)*exp(x)+12*x+12)*log(-exp(x)+3)*log(log(-exp(x)+3))^3+ ((60*x+60)*exp(x)-180*x-180)*log(-exp(x)+3)*log(log(-exp(x)+3))^2+((-300*x -300)*exp(x)+900*x+900)*log(-exp(x)+3)*log(log(-exp(x)+3))+((500*x+500)*ex p(x)-1500*x-1500)*log(-exp(x)+3)-36*exp(x)*x^3)/((exp(x)*x^3-3*x^3)*log(-e xp(x)+3)*log(log(-exp(x)+3))^3+(-15*exp(x)*x^3+45*x^3)*log(-exp(x)+3)*log( log(-exp(x)+3))^2+(75*exp(x)*x^3-225*x^3)*log(-exp(x)+3)*log(log(-exp(x)+3 ))+(-125*exp(x)*x^3+375*x^3)*log(-exp(x)+3)),x, algorithm="fricas")
Output:
2*((2*x + 1)*log(log(-e^x + 3))^2 + 9*x^2 - 10*(2*x + 1)*log(log(-e^x + 3) ) + 50*x + 25)/(x^2*log(log(-e^x + 3))^2 - 10*x^2*log(log(-e^x + 3)) + 25* x^2)
Time = 0.22 (sec) , antiderivative size = 32, normalized size of antiderivative = 0.97 \[ \int \frac {-36 e^x x^3+\left (-1500-1500 x+e^x (500+500 x)\right ) \log \left (3-e^x\right )+\left (900+e^x (-300-300 x)+900 x\right ) \log \left (3-e^x\right ) \log \left (\log \left (3-e^x\right )\right )+\left (-180-180 x+e^x (60+60 x)\right ) \log \left (3-e^x\right ) \log ^2\left (\log \left (3-e^x\right )\right )+\left (12+e^x (-4-4 x)+12 x\right ) \log \left (3-e^x\right ) \log ^3\left (\log \left (3-e^x\right )\right )}{\left (375 x^3-125 e^x x^3\right ) \log \left (3-e^x\right )+\left (-225 x^3+75 e^x x^3\right ) \log \left (3-e^x\right ) \log \left (\log \left (3-e^x\right )\right )+\left (45 x^3-15 e^x x^3\right ) \log \left (3-e^x\right ) \log ^2\left (\log \left (3-e^x\right )\right )+\left (-3 x^3+e^x x^3\right ) \log \left (3-e^x\right ) \log ^3\left (\log \left (3-e^x\right )\right )} \, dx=\frac {18}{\log {\left (\log {\left (3 - e^{x} \right )} \right )}^{2} - 10 \log {\left (\log {\left (3 - e^{x} \right )} \right )} + 25} - \frac {- 4 x - 2}{x^{2}} \] Input:
integrate((((-4-4*x)*exp(x)+12*x+12)*ln(-exp(x)+3)*ln(ln(-exp(x)+3))**3+(( 60*x+60)*exp(x)-180*x-180)*ln(-exp(x)+3)*ln(ln(-exp(x)+3))**2+((-300*x-300 )*exp(x)+900*x+900)*ln(-exp(x)+3)*ln(ln(-exp(x)+3))+((500*x+500)*exp(x)-15 00*x-1500)*ln(-exp(x)+3)-36*exp(x)*x**3)/((exp(x)*x**3-3*x**3)*ln(-exp(x)+ 3)*ln(ln(-exp(x)+3))**3+(-15*exp(x)*x**3+45*x**3)*ln(-exp(x)+3)*ln(ln(-exp (x)+3))**2+(75*exp(x)*x**3-225*x**3)*ln(-exp(x)+3)*ln(ln(-exp(x)+3))+(-125 *exp(x)*x**3+375*x**3)*ln(-exp(x)+3)),x)
Output:
18/(log(log(3 - exp(x)))**2 - 10*log(log(3 - exp(x))) + 25) - (-4*x - 2)/x **2
Time = 0.34 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.12 \[ \int \frac {-36 e^x x^3+\left (-1500-1500 x+e^x (500+500 x)\right ) \log \left (3-e^x\right )+\left (900+e^x (-300-300 x)+900 x\right ) \log \left (3-e^x\right ) \log \left (\log \left (3-e^x\right )\right )+\left (-180-180 x+e^x (60+60 x)\right ) \log \left (3-e^x\right ) \log ^2\left (\log \left (3-e^x\right )\right )+\left (12+e^x (-4-4 x)+12 x\right ) \log \left (3-e^x\right ) \log ^3\left (\log \left (3-e^x\right )\right )}{\left (375 x^3-125 e^x x^3\right ) \log \left (3-e^x\right )+\left (-225 x^3+75 e^x x^3\right ) \log \left (3-e^x\right ) \log \left (\log \left (3-e^x\right )\right )+\left (45 x^3-15 e^x x^3\right ) \log \left (3-e^x\right ) \log ^2\left (\log \left (3-e^x\right )\right )+\left (-3 x^3+e^x x^3\right ) \log \left (3-e^x\right ) \log ^3\left (\log \left (3-e^x\right )\right )} \, dx=\frac {18}{\log \left (\log \left (-e^{x} + 3\right )\right )^{2} - 10 \, \log \left (\log \left (-e^{x} + 3\right )\right ) + 25} + \frac {2 \, {\left (2 \, x + 1\right )}}{x^{2}} \] Input:
integrate((((-4-4*x)*exp(x)+12*x+12)*log(-exp(x)+3)*log(log(-exp(x)+3))^3+ ((60*x+60)*exp(x)-180*x-180)*log(-exp(x)+3)*log(log(-exp(x)+3))^2+((-300*x -300)*exp(x)+900*x+900)*log(-exp(x)+3)*log(log(-exp(x)+3))+((500*x+500)*ex p(x)-1500*x-1500)*log(-exp(x)+3)-36*exp(x)*x^3)/((exp(x)*x^3-3*x^3)*log(-e xp(x)+3)*log(log(-exp(x)+3))^3+(-15*exp(x)*x^3+45*x^3)*log(-exp(x)+3)*log( log(-exp(x)+3))^2+(75*exp(x)*x^3-225*x^3)*log(-exp(x)+3)*log(log(-exp(x)+3 ))+(-125*exp(x)*x^3+375*x^3)*log(-exp(x)+3)),x, algorithm="maxima")
Output:
18/(log(log(-e^x + 3))^2 - 10*log(log(-e^x + 3)) + 25) + 2*(2*x + 1)/x^2
Leaf count of result is larger than twice the leaf count of optimal. 91 vs. \(2 (25) = 50\).
Time = 0.54 (sec) , antiderivative size = 91, normalized size of antiderivative = 2.76 \[ \int \frac {-36 e^x x^3+\left (-1500-1500 x+e^x (500+500 x)\right ) \log \left (3-e^x\right )+\left (900+e^x (-300-300 x)+900 x\right ) \log \left (3-e^x\right ) \log \left (\log \left (3-e^x\right )\right )+\left (-180-180 x+e^x (60+60 x)\right ) \log \left (3-e^x\right ) \log ^2\left (\log \left (3-e^x\right )\right )+\left (12+e^x (-4-4 x)+12 x\right ) \log \left (3-e^x\right ) \log ^3\left (\log \left (3-e^x\right )\right )}{\left (375 x^3-125 e^x x^3\right ) \log \left (3-e^x\right )+\left (-225 x^3+75 e^x x^3\right ) \log \left (3-e^x\right ) \log \left (\log \left (3-e^x\right )\right )+\left (45 x^3-15 e^x x^3\right ) \log \left (3-e^x\right ) \log ^2\left (\log \left (3-e^x\right )\right )+\left (-3 x^3+e^x x^3\right ) \log \left (3-e^x\right ) \log ^3\left (\log \left (3-e^x\right )\right )} \, dx=\frac {2 \, {\left (2 \, x \log \left (\log \left (-e^{x} + 3\right )\right )^{2} + 9 \, x^{2} - 20 \, x \log \left (\log \left (-e^{x} + 3\right )\right ) + \log \left (\log \left (-e^{x} + 3\right )\right )^{2} + 50 \, x - 10 \, \log \left (\log \left (-e^{x} + 3\right )\right ) + 25\right )}}{x^{2} \log \left (\log \left (-e^{x} + 3\right )\right )^{2} - 10 \, x^{2} \log \left (\log \left (-e^{x} + 3\right )\right ) + 25 \, x^{2}} \] Input:
integrate((((-4-4*x)*exp(x)+12*x+12)*log(-exp(x)+3)*log(log(-exp(x)+3))^3+ ((60*x+60)*exp(x)-180*x-180)*log(-exp(x)+3)*log(log(-exp(x)+3))^2+((-300*x -300)*exp(x)+900*x+900)*log(-exp(x)+3)*log(log(-exp(x)+3))+((500*x+500)*ex p(x)-1500*x-1500)*log(-exp(x)+3)-36*exp(x)*x^3)/((exp(x)*x^3-3*x^3)*log(-e xp(x)+3)*log(log(-exp(x)+3))^3+(-15*exp(x)*x^3+45*x^3)*log(-exp(x)+3)*log( log(-exp(x)+3))^2+(75*exp(x)*x^3-225*x^3)*log(-exp(x)+3)*log(log(-exp(x)+3 ))+(-125*exp(x)*x^3+375*x^3)*log(-exp(x)+3)),x, algorithm="giac")
Output:
2*(2*x*log(log(-e^x + 3))^2 + 9*x^2 - 20*x*log(log(-e^x + 3)) + log(log(-e ^x + 3))^2 + 50*x - 10*log(log(-e^x + 3)) + 25)/(x^2*log(log(-e^x + 3))^2 - 10*x^2*log(log(-e^x + 3)) + 25*x^2)
Time = 0.29 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.09 \[ \int \frac {-36 e^x x^3+\left (-1500-1500 x+e^x (500+500 x)\right ) \log \left (3-e^x\right )+\left (900+e^x (-300-300 x)+900 x\right ) \log \left (3-e^x\right ) \log \left (\log \left (3-e^x\right )\right )+\left (-180-180 x+e^x (60+60 x)\right ) \log \left (3-e^x\right ) \log ^2\left (\log \left (3-e^x\right )\right )+\left (12+e^x (-4-4 x)+12 x\right ) \log \left (3-e^x\right ) \log ^3\left (\log \left (3-e^x\right )\right )}{\left (375 x^3-125 e^x x^3\right ) \log \left (3-e^x\right )+\left (-225 x^3+75 e^x x^3\right ) \log \left (3-e^x\right ) \log \left (\log \left (3-e^x\right )\right )+\left (45 x^3-15 e^x x^3\right ) \log \left (3-e^x\right ) \log ^2\left (\log \left (3-e^x\right )\right )+\left (-3 x^3+e^x x^3\right ) \log \left (3-e^x\right ) \log ^3\left (\log \left (3-e^x\right )\right )} \, dx=\frac {18}{{\ln \left (\ln \left (3-{\mathrm {e}}^x\right )\right )}^2-10\,\ln \left (\ln \left (3-{\mathrm {e}}^x\right )\right )+25}+\frac {4\,x+2}{x^2} \] Input:
int((log(3 - exp(x))*(1500*x - exp(x)*(500*x + 500) + 1500) + 36*x^3*exp(x ) - log(3 - exp(x))*log(log(3 - exp(x)))*(900*x - exp(x)*(300*x + 300) + 9 00) - log(3 - exp(x))*log(log(3 - exp(x)))^3*(12*x - exp(x)*(4*x + 4) + 12 ) + log(3 - exp(x))*log(log(3 - exp(x)))^2*(180*x - exp(x)*(60*x + 60) + 1 80))/(log(3 - exp(x))*(125*x^3*exp(x) - 375*x^3) - log(3 - exp(x))*log(log (3 - exp(x)))*(75*x^3*exp(x) - 225*x^3) - log(3 - exp(x))*log(log(3 - exp( x)))^3*(x^3*exp(x) - 3*x^3) + log(3 - exp(x))*log(log(3 - exp(x)))^2*(15*x ^3*exp(x) - 45*x^3)),x)
Output:
18/(log(log(3 - exp(x)))^2 - 10*log(log(3 - exp(x))) + 25) + (4*x + 2)/x^2
Time = 0.25 (sec) , antiderivative size = 89, normalized size of antiderivative = 2.70 \[ \int \frac {-36 e^x x^3+\left (-1500-1500 x+e^x (500+500 x)\right ) \log \left (3-e^x\right )+\left (900+e^x (-300-300 x)+900 x\right ) \log \left (3-e^x\right ) \log \left (\log \left (3-e^x\right )\right )+\left (-180-180 x+e^x (60+60 x)\right ) \log \left (3-e^x\right ) \log ^2\left (\log \left (3-e^x\right )\right )+\left (12+e^x (-4-4 x)+12 x\right ) \log \left (3-e^x\right ) \log ^3\left (\log \left (3-e^x\right )\right )}{\left (375 x^3-125 e^x x^3\right ) \log \left (3-e^x\right )+\left (-225 x^3+75 e^x x^3\right ) \log \left (3-e^x\right ) \log \left (\log \left (3-e^x\right )\right )+\left (45 x^3-15 e^x x^3\right ) \log \left (3-e^x\right ) \log ^2\left (\log \left (3-e^x\right )\right )+\left (-3 x^3+e^x x^3\right ) \log \left (3-e^x\right ) \log ^3\left (\log \left (3-e^x\right )\right )} \, dx=\frac {4 {\mathrm {log}\left (\mathrm {log}\left (-e^{x}+3\right )\right )}^{2} x +2 {\mathrm {log}\left (\mathrm {log}\left (-e^{x}+3\right )\right )}^{2}-40 \,\mathrm {log}\left (\mathrm {log}\left (-e^{x}+3\right )\right ) x -20 \,\mathrm {log}\left (\mathrm {log}\left (-e^{x}+3\right )\right )+18 x^{2}+100 x +50}{x^{2} \left ({\mathrm {log}\left (\mathrm {log}\left (-e^{x}+3\right )\right )}^{2}-10 \,\mathrm {log}\left (\mathrm {log}\left (-e^{x}+3\right )\right )+25\right )} \] Input:
int((((-4-4*x)*exp(x)+12*x+12)*log(-exp(x)+3)*log(log(-exp(x)+3))^3+((60*x +60)*exp(x)-180*x-180)*log(-exp(x)+3)*log(log(-exp(x)+3))^2+((-300*x-300)* exp(x)+900*x+900)*log(-exp(x)+3)*log(log(-exp(x)+3))+((500*x+500)*exp(x)-1 500*x-1500)*log(-exp(x)+3)-36*exp(x)*x^3)/((exp(x)*x^3-3*x^3)*log(-exp(x)+ 3)*log(log(-exp(x)+3))^3+(-15*exp(x)*x^3+45*x^3)*log(-exp(x)+3)*log(log(-e xp(x)+3))^2+(75*exp(x)*x^3-225*x^3)*log(-exp(x)+3)*log(log(-exp(x)+3))+(-1 25*exp(x)*x^3+375*x^3)*log(-exp(x)+3)),x)
Output:
(2*(2*log(log( - e**x + 3))**2*x + log(log( - e**x + 3))**2 - 20*log(log( - e**x + 3))*x - 10*log(log( - e**x + 3)) + 9*x**2 + 50*x + 25))/(x**2*(lo g(log( - e**x + 3))**2 - 10*log(log( - e**x + 3)) + 25))