\(\int \frac {-12000-15601 x-12 e^{\frac {4}{5} (1+5 x)} x-3960 x^2-372 x^3-12 x^4+e^{\frac {3}{5} (1+5 x)} (-12-372 x-36 x^2)+e^{\frac {2}{5} (1+5 x)} (-360-3996 x-756 x^2-36 x^3)+e^{\frac {1}{5} (1+5 x)} (-3600-16320 x-4356 x^2-396 x^3-12 x^4)+(-3600-4320 x-36 e^{\frac {3}{5} (1+5 x)} x-756 x^2-36 x^3+e^{\frac {2}{5} (1+5 x)} (-36-756 x-72 x^2)+e^{\frac {1}{5} (1+5 x)} (-720-4392 x-792 x^2-36 x^3)) \log (x)+(-360-396 x-36 e^{\frac {2}{5} (1+5 x)} x-36 x^2+e^{\frac {1}{5} (1+5 x)} (-36-396 x-36 x^2)) \log ^2(x)+(-12-12 x-12 e^{\frac {1}{5} (1+5 x)} x) \log ^3(x)}{x} \, dx\) [1302]

Optimal result

Integrand size = 275, antiderivative size = 26 \[ \int \frac {-12000-15601 x-12 e^{\frac {4}{5} (1+5 x)} x-3960 x^2-372 x^3-12 x^4+e^{\frac {3}{5} (1+5 x)} \left (-12-372 x-36 x^2\right )+e^{\frac {2}{5} (1+5 x)} \left (-360-3996 x-756 x^2-36 x^3\right )+e^{\frac {1}{5} (1+5 x)} \left (-3600-16320 x-4356 x^2-396 x^3-12 x^4\right )+\left (-3600-4320 x-36 e^{\frac {3}{5} (1+5 x)} x-756 x^2-36 x^3+e^{\frac {2}{5} (1+5 x)} \left (-36-756 x-72 x^2\right )+e^{\frac {1}{5} (1+5 x)} \left (-720-4392 x-792 x^2-36 x^3\right )\right ) \log (x)+\left (-360-396 x-36 e^{\frac {2}{5} (1+5 x)} x-36 x^2+e^{\frac {1}{5} (1+5 x)} \left (-36-396 x-36 x^2\right )\right ) \log ^2(x)+\left (-12-12 x-12 e^{\frac {1}{5} (1+5 x)} x\right ) \log ^3(x)}{x} \, dx=1-x \left (1+\frac {3 \left (10+e^{\frac {1}{5}+x}+x+\log (x)\right )^4}{x}\right ) \] Output:

1-(1+3*(ln(x)+10+exp(1/5+x)+x)^4/x)*x
                                                                                    
                                                                                    
 

Mathematica [B] (verified)

Leaf count is larger than twice the leaf count of optimal. \(130\) vs. \(2(26)=52\).

Time = 0.18 (sec) , antiderivative size = 130, normalized size of antiderivative = 5.00 \[ \int \frac {-12000-15601 x-12 e^{\frac {4}{5} (1+5 x)} x-3960 x^2-372 x^3-12 x^4+e^{\frac {3}{5} (1+5 x)} \left (-12-372 x-36 x^2\right )+e^{\frac {2}{5} (1+5 x)} \left (-360-3996 x-756 x^2-36 x^3\right )+e^{\frac {1}{5} (1+5 x)} \left (-3600-16320 x-4356 x^2-396 x^3-12 x^4\right )+\left (-3600-4320 x-36 e^{\frac {3}{5} (1+5 x)} x-756 x^2-36 x^3+e^{\frac {2}{5} (1+5 x)} \left (-36-756 x-72 x^2\right )+e^{\frac {1}{5} (1+5 x)} \left (-720-4392 x-792 x^2-36 x^3\right )\right ) \log (x)+\left (-360-396 x-36 e^{\frac {2}{5} (1+5 x)} x-36 x^2+e^{\frac {1}{5} (1+5 x)} \left (-36-396 x-36 x^2\right )\right ) \log ^2(x)+\left (-12-12 x-12 e^{\frac {1}{5} (1+5 x)} x\right ) \log ^3(x)}{x} \, dx=-3 e^{\frac {4}{5}+4 x}-12 e^{\frac {3}{5}+3 x} (10+x)-18 e^{\frac {2}{5}+2 x} (10+x)^2-12 e^{\frac {1}{5}+x} (10+x)^3-x \left (12001+1800 x+120 x^2+3 x^3\right )-12 \left (10+e^{\frac {1}{5}+x}+x\right )^3 \log (x)-18 \left (10+e^{\frac {1}{5}+x}+x\right )^2 \log ^2(x)-12 \left (10+e^{\frac {1}{5}+x}+x\right ) \log ^3(x)-3 \log ^4(x) \] Input:

Integrate[(-12000 - 15601*x - 12*E^((4*(1 + 5*x))/5)*x - 3960*x^2 - 372*x^ 
3 - 12*x^4 + E^((3*(1 + 5*x))/5)*(-12 - 372*x - 36*x^2) + E^((2*(1 + 5*x)) 
/5)*(-360 - 3996*x - 756*x^2 - 36*x^3) + E^((1 + 5*x)/5)*(-3600 - 16320*x 
- 4356*x^2 - 396*x^3 - 12*x^4) + (-3600 - 4320*x - 36*E^((3*(1 + 5*x))/5)* 
x - 756*x^2 - 36*x^3 + E^((2*(1 + 5*x))/5)*(-36 - 756*x - 72*x^2) + E^((1 
+ 5*x)/5)*(-720 - 4392*x - 792*x^2 - 36*x^3))*Log[x] + (-360 - 396*x - 36* 
E^((2*(1 + 5*x))/5)*x - 36*x^2 + E^((1 + 5*x)/5)*(-36 - 396*x - 36*x^2))*L 
og[x]^2 + (-12 - 12*x - 12*E^((1 + 5*x)/5)*x)*Log[x]^3)/x,x]
 

Output:

-3*E^(4/5 + 4*x) - 12*E^(3/5 + 3*x)*(10 + x) - 18*E^(2/5 + 2*x)*(10 + x)^2 
 - 12*E^(1/5 + x)*(10 + x)^3 - x*(12001 + 1800*x + 120*x^2 + 3*x^3) - 12*( 
10 + E^(1/5 + x) + x)^3*Log[x] - 18*(10 + E^(1/5 + x) + x)^2*Log[x]^2 - 12 
*(10 + E^(1/5 + x) + x)*Log[x]^3 - 3*Log[x]^4
 

Rubi [F]

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.

\(\displaystyle \int \frac {-12 x^4-372 x^3-3960 x^2+e^{\frac {3}{5} (5 x+1)} \left (-36 x^2-372 x-12\right )+\left (-36 x^2+e^{\frac {1}{5} (5 x+1)} \left (-36 x^2-396 x-36\right )-36 e^{\frac {2}{5} (5 x+1)} x-396 x-360\right ) \log ^2(x)+e^{\frac {2}{5} (5 x+1)} \left (-36 x^3-756 x^2-3996 x-360\right )+\left (-36 x^3-756 x^2+e^{\frac {2}{5} (5 x+1)} \left (-72 x^2-756 x-36\right )+e^{\frac {1}{5} (5 x+1)} \left (-36 x^3-792 x^2-4392 x-720\right )-36 e^{\frac {3}{5} (5 x+1)} x-4320 x-3600\right ) \log (x)+e^{\frac {1}{5} (5 x+1)} \left (-12 x^4-396 x^3-4356 x^2-16320 x-3600\right )-12 e^{\frac {4}{5} (5 x+1)} x-15601 x+\left (-12 e^{\frac {1}{5} (5 x+1)} x-12 x-12\right ) \log ^3(x)-12000}{x} \, dx\)

\(\Big \downarrow \) 2010

\(\displaystyle \int \left (-\frac {12 e^{x+\frac {1}{5}} \left (x^2+13 x+x \log (x)+3\right ) (x+\log (x)+10)^2}{x}-\frac {12 e^{3 x+\frac {3}{5}} \left (3 x^2+31 x+3 x \log (x)+1\right )}{x}-\frac {36 e^{2 x+\frac {2}{5}} \left (x^3+21 x^2+2 x^2 \log (x)+111 x+x \log ^2(x)+21 x \log (x)+\log (x)+10\right )}{x}+\frac {-12 x^4-372 x^3-36 x^3 \log (x)-3960 x^2-36 x^2 \log ^2(x)-756 x^2 \log (x)-15601 x-12 x \log ^3(x)-12 \log ^3(x)-396 x \log ^2(x)-360 \log ^2(x)-4320 x \log (x)-3600 \log (x)-12000}{x}-12 e^{4 x+\frac {4}{5}}\right )dx\)

\(\Big \downarrow \) 2009

\(\displaystyle -12 \int e^{x+\frac {1}{5}} \log ^3(x)dx-396 \int e^{x+\frac {1}{5}} \log ^2(x)dx-36 \int e^{2 x+\frac {2}{5}} \log ^2(x)dx-36 \int \frac {e^{x+\frac {1}{5}} \log ^2(x)}{x}dx-36 \int e^{x+\frac {1}{5}} x \log ^2(x)dx+720 \sqrt [5]{e} x \, _3F_3(1,1,1;2,2,2;x)+72 e^{2/5} x \, _3F_3(1,1,1;2,2,2;2 x)+720 \sqrt [5]{e} \log (x) (\operatorname {ExpIntegralE}(1,-x)+\operatorname {ExpIntegralEi}(x))+36 e^{2/5} \log (x) (\operatorname {ExpIntegralE}(1,-2 x)+\operatorname {ExpIntegralEi}(2 x))+72 \sqrt [5]{e} \operatorname {ExpIntegralEi}(x)-720 \sqrt [5]{e} \operatorname {ExpIntegralEi}(x) \log (x)-36 e^{2/5} \operatorname {ExpIntegralEi}(2 x) \log (x)-3 x^4-12 e^{x+\frac {1}{5}} x^3-120 x^3-12 x^3 \log (x)-360 e^{x+\frac {1}{5}} x^2-18 e^{2 x+\frac {2}{5}} x^2-1800 x^2-18 x^2 \log ^2(x)-36 e^{x+\frac {1}{5}} x^2 \log (x)-360 x^2 \log (x)-3600 e^{x+\frac {1}{5}} x-360 e^{2 x+\frac {2}{5}} x-12 e^{3 x+\frac {3}{5}} x-12001 x-12000 e^{x+\frac {1}{5}}-1800 e^{2 x+\frac {2}{5}}-120 e^{3 x+\frac {3}{5}}-3 e^{4 x+\frac {4}{5}}-3 \log ^4(x)-12 x \log ^3(x)-120 \log ^3(x)-360 x \log ^2(x)+18 e^{2/5} \log ^2(-2 x)+360 \sqrt [5]{e} \log ^2(-x)-1800 \log ^2(x)-720 e^{x+\frac {1}{5}} x \log (x)-36 e^{2 x+\frac {2}{5}} x \log (x)-3600 x \log (x)-3672 e^{x+\frac {1}{5}} \log (x)-360 e^{2 x+\frac {2}{5}} \log (x)-12 e^{3 x+\frac {3}{5}} \log (x)+36 e^{2/5} \gamma \log (x)+720 \sqrt [5]{e} \gamma \log (x)-12000 \log (x)\)

Input:

Int[(-12000 - 15601*x - 12*E^((4*(1 + 5*x))/5)*x - 3960*x^2 - 372*x^3 - 12 
*x^4 + E^((3*(1 + 5*x))/5)*(-12 - 372*x - 36*x^2) + E^((2*(1 + 5*x))/5)*(- 
360 - 3996*x - 756*x^2 - 36*x^3) + E^((1 + 5*x)/5)*(-3600 - 16320*x - 4356 
*x^2 - 396*x^3 - 12*x^4) + (-3600 - 4320*x - 36*E^((3*(1 + 5*x))/5)*x - 75 
6*x^2 - 36*x^3 + E^((2*(1 + 5*x))/5)*(-36 - 756*x - 72*x^2) + E^((1 + 5*x) 
/5)*(-720 - 4392*x - 792*x^2 - 36*x^3))*Log[x] + (-360 - 396*x - 36*E^((2* 
(1 + 5*x))/5)*x - 36*x^2 + E^((1 + 5*x)/5)*(-36 - 396*x - 36*x^2))*Log[x]^ 
2 + (-12 - 12*x - 12*E^((1 + 5*x)/5)*x)*Log[x]^3)/x,x]
 

Output:

$Aborted
 

Maple [B] (verified)

Leaf count of result is larger than twice the leaf count of optimal. \(226\) vs. \(2(23)=46\).

Time = 0.05 (sec) , antiderivative size = 227, normalized size of antiderivative = 8.73

\[-3 \ln \left (x \right )^{4}+\left (-12 x -12 \,{\mathrm e}^{\frac {1}{5}+x}-120\right ) \ln \left (x \right )^{3}+\left (-18 x^{2}-36 x \,{\mathrm e}^{\frac {1}{5}+x}-18 \,{\mathrm e}^{\frac {2}{5}+2 x}-360 x -360 \,{\mathrm e}^{\frac {1}{5}+x}-1800\right ) \ln \left (x \right )^{2}+\left (-12 x^{3}-36 \,{\mathrm e}^{\frac {1}{5}+x} x^{2}-36 x \,{\mathrm e}^{\frac {2}{5}+2 x}-12 \,{\mathrm e}^{\frac {3}{5}+3 x}-360 x^{2}-720 x \,{\mathrm e}^{\frac {1}{5}+x}-360 \,{\mathrm e}^{\frac {2}{5}+2 x}-3600 x -3600 \,{\mathrm e}^{\frac {1}{5}+x}-12000\right ) \ln \left (x \right )-3 x^{4}-12 \,{\mathrm e}^{\frac {1}{5}+x} x^{3}-18 \,{\mathrm e}^{\frac {2}{5}+2 x} x^{2}-12 x \,{\mathrm e}^{\frac {3}{5}+3 x}-3 \,{\mathrm e}^{\frac {4}{5}+4 x}-120 x^{3}-360 \,{\mathrm e}^{\frac {1}{5}+x} x^{2}-360 x \,{\mathrm e}^{\frac {2}{5}+2 x}-120 \,{\mathrm e}^{\frac {3}{5}+3 x}-1800 x^{2}-3600 x \,{\mathrm e}^{\frac {1}{5}+x}-1800 \,{\mathrm e}^{\frac {2}{5}+2 x}-12001 x -12000 \,{\mathrm e}^{\frac {1}{5}+x}\]

Input:

int(((-12*x*exp(1/5+x)-12*x-12)*ln(x)^3+(-36*x*exp(1/5+x)^2+(-36*x^2-396*x 
-36)*exp(1/5+x)-36*x^2-396*x-360)*ln(x)^2+(-36*x*exp(1/5+x)^3+(-72*x^2-756 
*x-36)*exp(1/5+x)^2+(-36*x^3-792*x^2-4392*x-720)*exp(1/5+x)-36*x^3-756*x^2 
-4320*x-3600)*ln(x)-12*x*exp(1/5+x)^4+(-36*x^2-372*x-12)*exp(1/5+x)^3+(-36 
*x^3-756*x^2-3996*x-360)*exp(1/5+x)^2+(-12*x^4-396*x^3-4356*x^2-16320*x-36 
00)*exp(1/5+x)-12*x^4-372*x^3-3960*x^2-15601*x-12000)/x,x)
 

Output:

-3*ln(x)^4+(-12*x-12*exp(1/5+x)-120)*ln(x)^3+(-18*x^2-36*x*exp(1/5+x)-18*e 
xp(2/5+2*x)-360*x-360*exp(1/5+x)-1800)*ln(x)^2+(-12*x^3-36*exp(1/5+x)*x^2- 
36*x*exp(2/5+2*x)-12*exp(3/5+3*x)-360*x^2-720*x*exp(1/5+x)-360*exp(2/5+2*x 
)-3600*x-3600*exp(1/5+x)-12000)*ln(x)-3*x^4-12*exp(1/5+x)*x^3-18*exp(2/5+2 
*x)*x^2-12*x*exp(3/5+3*x)-3*exp(4/5+4*x)-120*x^3-360*exp(1/5+x)*x^2-360*x* 
exp(2/5+2*x)-120*exp(3/5+3*x)-1800*x^2-3600*x*exp(1/5+x)-1800*exp(2/5+2*x) 
-12001*x-12000*exp(1/5+x)
 

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 169 vs. \(2 (23) = 46\).

Time = 0.08 (sec) , antiderivative size = 169, normalized size of antiderivative = 6.50 \[ \int \frac {-12000-15601 x-12 e^{\frac {4}{5} (1+5 x)} x-3960 x^2-372 x^3-12 x^4+e^{\frac {3}{5} (1+5 x)} \left (-12-372 x-36 x^2\right )+e^{\frac {2}{5} (1+5 x)} \left (-360-3996 x-756 x^2-36 x^3\right )+e^{\frac {1}{5} (1+5 x)} \left (-3600-16320 x-4356 x^2-396 x^3-12 x^4\right )+\left (-3600-4320 x-36 e^{\frac {3}{5} (1+5 x)} x-756 x^2-36 x^3+e^{\frac {2}{5} (1+5 x)} \left (-36-756 x-72 x^2\right )+e^{\frac {1}{5} (1+5 x)} \left (-720-4392 x-792 x^2-36 x^3\right )\right ) \log (x)+\left (-360-396 x-36 e^{\frac {2}{5} (1+5 x)} x-36 x^2+e^{\frac {1}{5} (1+5 x)} \left (-36-396 x-36 x^2\right )\right ) \log ^2(x)+\left (-12-12 x-12 e^{\frac {1}{5} (1+5 x)} x\right ) \log ^3(x)}{x} \, dx=-3 \, x^{4} - 12 \, {\left (x + e^{\left (x + \frac {1}{5}\right )} + 10\right )} \log \left (x\right )^{3} - 3 \, \log \left (x\right )^{4} - 120 \, x^{3} - 18 \, {\left (x^{2} + 2 \, {\left (x + 10\right )} e^{\left (x + \frac {1}{5}\right )} + 20 \, x + e^{\left (2 \, x + \frac {2}{5}\right )} + 100\right )} \log \left (x\right )^{2} - 1800 \, x^{2} - 12 \, {\left (x + 10\right )} e^{\left (3 \, x + \frac {3}{5}\right )} - 18 \, {\left (x^{2} + 20 \, x + 100\right )} e^{\left (2 \, x + \frac {2}{5}\right )} - 12 \, {\left (x^{3} + 30 \, x^{2} + 300 \, x + 1000\right )} e^{\left (x + \frac {1}{5}\right )} - 12 \, {\left (x^{3} + 30 \, x^{2} + 3 \, {\left (x + 10\right )} e^{\left (2 \, x + \frac {2}{5}\right )} + 3 \, {\left (x^{2} + 20 \, x + 100\right )} e^{\left (x + \frac {1}{5}\right )} + 300 \, x + e^{\left (3 \, x + \frac {3}{5}\right )} + 1000\right )} \log \left (x\right ) - 12001 \, x - 3 \, e^{\left (4 \, x + \frac {4}{5}\right )} \] Input:

integrate(((-12*x*exp(1/5+x)-12*x-12)*log(x)^3+(-36*x*exp(1/5+x)^2+(-36*x^ 
2-396*x-36)*exp(1/5+x)-36*x^2-396*x-360)*log(x)^2+(-36*x*exp(1/5+x)^3+(-72 
*x^2-756*x-36)*exp(1/5+x)^2+(-36*x^3-792*x^2-4392*x-720)*exp(1/5+x)-36*x^3 
-756*x^2-4320*x-3600)*log(x)-12*x*exp(1/5+x)^4+(-36*x^2-372*x-12)*exp(1/5+ 
x)^3+(-36*x^3-756*x^2-3996*x-360)*exp(1/5+x)^2+(-12*x^4-396*x^3-4356*x^2-1 
6320*x-3600)*exp(1/5+x)-12*x^4-372*x^3-3960*x^2-15601*x-12000)/x,x, algori 
thm="fricas")
 

Output:

-3*x^4 - 12*(x + e^(x + 1/5) + 10)*log(x)^3 - 3*log(x)^4 - 120*x^3 - 18*(x 
^2 + 2*(x + 10)*e^(x + 1/5) + 20*x + e^(2*x + 2/5) + 100)*log(x)^2 - 1800* 
x^2 - 12*(x + 10)*e^(3*x + 3/5) - 18*(x^2 + 20*x + 100)*e^(2*x + 2/5) - 12 
*(x^3 + 30*x^2 + 300*x + 1000)*e^(x + 1/5) - 12*(x^3 + 30*x^2 + 3*(x + 10) 
*e^(2*x + 2/5) + 3*(x^2 + 20*x + 100)*e^(x + 1/5) + 300*x + e^(3*x + 3/5) 
+ 1000)*log(x) - 12001*x - 3*e^(4*x + 4/5)
 

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 212 vs. \(2 (22) = 44\).

Time = 0.41 (sec) , antiderivative size = 212, normalized size of antiderivative = 8.15 \[ \int \frac {-12000-15601 x-12 e^{\frac {4}{5} (1+5 x)} x-3960 x^2-372 x^3-12 x^4+e^{\frac {3}{5} (1+5 x)} \left (-12-372 x-36 x^2\right )+e^{\frac {2}{5} (1+5 x)} \left (-360-3996 x-756 x^2-36 x^3\right )+e^{\frac {1}{5} (1+5 x)} \left (-3600-16320 x-4356 x^2-396 x^3-12 x^4\right )+\left (-3600-4320 x-36 e^{\frac {3}{5} (1+5 x)} x-756 x^2-36 x^3+e^{\frac {2}{5} (1+5 x)} \left (-36-756 x-72 x^2\right )+e^{\frac {1}{5} (1+5 x)} \left (-720-4392 x-792 x^2-36 x^3\right )\right ) \log (x)+\left (-360-396 x-36 e^{\frac {2}{5} (1+5 x)} x-36 x^2+e^{\frac {1}{5} (1+5 x)} \left (-36-396 x-36 x^2\right )\right ) \log ^2(x)+\left (-12-12 x-12 e^{\frac {1}{5} (1+5 x)} x\right ) \log ^3(x)}{x} \, dx=- 3 x^{4} - 120 x^{3} - 1800 x^{2} - 12001 x + \left (- 12 x - 120\right ) \log {\left (x \right )}^{3} + \left (- 12 x - 12 \log {\left (x \right )} - 120\right ) e^{3 x + \frac {3}{5}} + \left (- 18 x^{2} - 360 x - 1800\right ) \log {\left (x \right )}^{2} + \left (- 12 x^{3} - 360 x^{2} - 3600 x\right ) \log {\left (x \right )} + \left (- 18 x^{2} - 36 x \log {\left (x \right )} - 360 x - 18 \log {\left (x \right )}^{2} - 360 \log {\left (x \right )} - 1800\right ) e^{2 x + \frac {2}{5}} + \left (- 12 x^{3} - 36 x^{2} \log {\left (x \right )} - 360 x^{2} - 36 x \log {\left (x \right )}^{2} - 720 x \log {\left (x \right )} - 3600 x - 12 \log {\left (x \right )}^{3} - 360 \log {\left (x \right )}^{2} - 3600 \log {\left (x \right )} - 12000\right ) e^{x + \frac {1}{5}} - 3 e^{4 x + \frac {4}{5}} - 3 \log {\left (x \right )}^{4} - 12000 \log {\left (x \right )} \] Input:

integrate(((-12*x*exp(1/5+x)-12*x-12)*ln(x)**3+(-36*x*exp(1/5+x)**2+(-36*x 
**2-396*x-36)*exp(1/5+x)-36*x**2-396*x-360)*ln(x)**2+(-36*x*exp(1/5+x)**3+ 
(-72*x**2-756*x-36)*exp(1/5+x)**2+(-36*x**3-792*x**2-4392*x-720)*exp(1/5+x 
)-36*x**3-756*x**2-4320*x-3600)*ln(x)-12*x*exp(1/5+x)**4+(-36*x**2-372*x-1 
2)*exp(1/5+x)**3+(-36*x**3-756*x**2-3996*x-360)*exp(1/5+x)**2+(-12*x**4-39 
6*x**3-4356*x**2-16320*x-3600)*exp(1/5+x)-12*x**4-372*x**3-3960*x**2-15601 
*x-12000)/x,x)
 

Output:

-3*x**4 - 120*x**3 - 1800*x**2 - 12001*x + (-12*x - 120)*log(x)**3 + (-12* 
x - 12*log(x) - 120)*exp(3*x + 3/5) + (-18*x**2 - 360*x - 1800)*log(x)**2 
+ (-12*x**3 - 360*x**2 - 3600*x)*log(x) + (-18*x**2 - 36*x*log(x) - 360*x 
- 18*log(x)**2 - 360*log(x) - 1800)*exp(2*x + 2/5) + (-12*x**3 - 36*x**2*l 
og(x) - 360*x**2 - 36*x*log(x)**2 - 720*x*log(x) - 3600*x - 12*log(x)**3 - 
 360*log(x)**2 - 3600*log(x) - 12000)*exp(x + 1/5) - 3*exp(4*x + 4/5) - 3* 
log(x)**4 - 12000*log(x)
 

Maxima [F]

\[ \int \frac {-12000-15601 x-12 e^{\frac {4}{5} (1+5 x)} x-3960 x^2-372 x^3-12 x^4+e^{\frac {3}{5} (1+5 x)} \left (-12-372 x-36 x^2\right )+e^{\frac {2}{5} (1+5 x)} \left (-360-3996 x-756 x^2-36 x^3\right )+e^{\frac {1}{5} (1+5 x)} \left (-3600-16320 x-4356 x^2-396 x^3-12 x^4\right )+\left (-3600-4320 x-36 e^{\frac {3}{5} (1+5 x)} x-756 x^2-36 x^3+e^{\frac {2}{5} (1+5 x)} \left (-36-756 x-72 x^2\right )+e^{\frac {1}{5} (1+5 x)} \left (-720-4392 x-792 x^2-36 x^3\right )\right ) \log (x)+\left (-360-396 x-36 e^{\frac {2}{5} (1+5 x)} x-36 x^2+e^{\frac {1}{5} (1+5 x)} \left (-36-396 x-36 x^2\right )\right ) \log ^2(x)+\left (-12-12 x-12 e^{\frac {1}{5} (1+5 x)} x\right ) \log ^3(x)}{x} \, dx=\int { -\frac {12 \, x^{4} + 12 \, {\left (x e^{\left (x + \frac {1}{5}\right )} + x + 1\right )} \log \left (x\right )^{3} + 372 \, x^{3} + 36 \, {\left (x^{2} + x e^{\left (2 \, x + \frac {2}{5}\right )} + {\left (x^{2} + 11 \, x + 1\right )} e^{\left (x + \frac {1}{5}\right )} + 11 \, x + 10\right )} \log \left (x\right )^{2} + 3960 \, x^{2} + 12 \, x e^{\left (4 \, x + \frac {4}{5}\right )} + 12 \, {\left (3 \, x^{2} + 31 \, x + 1\right )} e^{\left (3 \, x + \frac {3}{5}\right )} + 36 \, {\left (x^{3} + 21 \, x^{2} + 111 \, x + 10\right )} e^{\left (2 \, x + \frac {2}{5}\right )} + 12 \, {\left (x^{4} + 33 \, x^{3} + 363 \, x^{2} + 1360 \, x + 300\right )} e^{\left (x + \frac {1}{5}\right )} + 36 \, {\left (x^{3} + 21 \, x^{2} + x e^{\left (3 \, x + \frac {3}{5}\right )} + {\left (2 \, x^{2} + 21 \, x + 1\right )} e^{\left (2 \, x + \frac {2}{5}\right )} + {\left (x^{3} + 22 \, x^{2} + 122 \, x + 20\right )} e^{\left (x + \frac {1}{5}\right )} + 120 \, x + 100\right )} \log \left (x\right ) + 15601 \, x + 12000}{x} \,d x } \] Input:

integrate(((-12*x*exp(1/5+x)-12*x-12)*log(x)^3+(-36*x*exp(1/5+x)^2+(-36*x^ 
2-396*x-36)*exp(1/5+x)-36*x^2-396*x-360)*log(x)^2+(-36*x*exp(1/5+x)^3+(-72 
*x^2-756*x-36)*exp(1/5+x)^2+(-36*x^3-792*x^2-4392*x-720)*exp(1/5+x)-36*x^3 
-756*x^2-4320*x-3600)*log(x)-12*x*exp(1/5+x)^4+(-36*x^2-372*x-12)*exp(1/5+ 
x)^3+(-36*x^3-756*x^2-3996*x-360)*exp(1/5+x)^2+(-12*x^4-396*x^3-4356*x^2-1 
6320*x-3600)*exp(1/5+x)-12*x^4-372*x^3-3960*x^2-15601*x-12000)/x,x, algori 
thm="maxima")
 

Output:

-3*x^4 - 12*x^3*log(x) - 12*(x + 10)*log(x)^3 - 3*log(x)^4 - 120*x^3 - 378 
*x^2*log(x) - 18*(x^2 + 20*x)*log(x)^2 - 1800*x^2 - 12*Ei(3*x)*e^(3/5) - 3 
60*Ei(2*x)*e^(2/5) + 792*Ei(x)*e^(1/5) - 4*(3*x*e^(3/5) - e^(3/5))*e^(3*x) 
 - 9*(2*x^2*e^(2/5) - 2*x*e^(2/5) + e^(2/5))*e^(2*x) - 18*(e^(2/5)*log(x)^ 
2 + 2*(x*e^(2/5) + 10*e^(2/5))*log(x))*e^(2*x) - 189*(2*x*e^(2/5) - e^(2/5 
))*e^(2*x) - 12*(x^3*e^(1/5) - 3*x^2*e^(1/5) + 6*x*e^(1/5) - 6*e^(1/5))*e^ 
x - 12*(e^(1/5)*log(x)^3 + 3*(x*e^(1/5) + 10*e^(1/5))*log(x)^2 + 3*(x^2*e^ 
(1/5) + 20*x*e^(1/5) - 22*e^(1/5))*log(x))*e^x - 396*(x^2*e^(1/5) - 2*x*e^ 
(1/5) + 2*e^(1/5))*e^x - 4356*(x*e^(1/5) - e^(1/5))*e^x + 18*(x^2 + 40*x)* 
log(x) - 4320*x*log(x) - 12*e^(3*x + 3/5)*log(x) - 4392*e^(x + 1/5)*log(x) 
 - 1800*log(x)^2 - 12001*x - 3*e^(4*x + 4/5) - 124*e^(3*x + 3/5) - 1998*e^ 
(2*x + 2/5) - 16320*e^(x + 1/5) + integrate(36*(x*e^(2/5) + 10*e^(2/5))*e^ 
(2*x)/x, x) + integrate(36*(x^2*e^(1/5) + 20*x*e^(1/5) - 22*e^(1/5))*e^x/x 
, x) + 12*integrate(e^(3*x + 3/5)/x, x) - 12000*log(x)
 

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 759 vs. \(2 (23) = 46\).

Time = 0.16 (sec) , antiderivative size = 759, normalized size of antiderivative = 29.19 \[ \int \frac {-12000-15601 x-12 e^{\frac {4}{5} (1+5 x)} x-3960 x^2-372 x^3-12 x^4+e^{\frac {3}{5} (1+5 x)} \left (-12-372 x-36 x^2\right )+e^{\frac {2}{5} (1+5 x)} \left (-360-3996 x-756 x^2-36 x^3\right )+e^{\frac {1}{5} (1+5 x)} \left (-3600-16320 x-4356 x^2-396 x^3-12 x^4\right )+\left (-3600-4320 x-36 e^{\frac {3}{5} (1+5 x)} x-756 x^2-36 x^3+e^{\frac {2}{5} (1+5 x)} \left (-36-756 x-72 x^2\right )+e^{\frac {1}{5} (1+5 x)} \left (-720-4392 x-792 x^2-36 x^3\right )\right ) \log (x)+\left (-360-396 x-36 e^{\frac {2}{5} (1+5 x)} x-36 x^2+e^{\frac {1}{5} (1+5 x)} \left (-36-396 x-36 x^2\right )\right ) \log ^2(x)+\left (-12-12 x-12 e^{\frac {1}{5} (1+5 x)} x\right ) \log ^3(x)}{x} \, dx=\text {Too large to display} \] Input:

integrate(((-12*x*exp(1/5+x)-12*x-12)*log(x)^3+(-36*x*exp(1/5+x)^2+(-36*x^ 
2-396*x-36)*exp(1/5+x)-36*x^2-396*x-360)*log(x)^2+(-36*x*exp(1/5+x)^3+(-72 
*x^2-756*x-36)*exp(1/5+x)^2+(-36*x^3-792*x^2-4392*x-720)*exp(1/5+x)-36*x^3 
-756*x^2-4320*x-3600)*log(x)-12*x*exp(1/5+x)^4+(-36*x^2-372*x-12)*exp(1/5+ 
x)^3+(-36*x^3-756*x^2-3996*x-360)*exp(1/5+x)^2+(-12*x^4-396*x^3-4356*x^2-1 
6320*x-3600)*exp(1/5+x)-12*x^4-372*x^3-3960*x^2-15601*x-12000)/x,x, algori 
thm="giac")
 

Output:

-3/625*(5*x + 1)^4 - 12/125*(5*x + 1)^3*e^(x + 1/5) + 12/125*(5*x + 1)^3*l 
og(5) + 36/25*(5*x + 1)^2*e^(x + 1/5)*log(5) - 18/25*(5*x + 1)^2*log(5)^2 
- 36/5*(5*x + 1)*e^(x + 1/5)*log(5)^2 + 12/5*(5*x + 1)*log(5)^3 + 12*e^(x 
+ 1/5)*log(5)^3 - 12/125*(5*x + 1)^3*log(5*x) - 36/25*(5*x + 1)^2*e^(x + 1 
/5)*log(5*x) + 36/25*(5*x + 1)^2*log(5)*log(5*x) + 72/5*(5*x + 1)*e^(x + 1 
/5)*log(5)*log(5*x) - 36/5*(5*x + 1)*log(5)^2*log(5*x) - 36*e^(x + 1/5)*lo 
g(5)^2*log(5*x) + 12*log(5)^3*log(5*x) - 18/25*(5*x + 1)^2*log(5*x)^2 - 36 
/5*(5*x + 1)*e^(x + 1/5)*log(5*x)^2 + 36/5*(5*x + 1)*log(5)*log(5*x)^2 + 3 
6*e^(x + 1/5)*log(5)*log(5*x)^2 - 18*log(5)^2*log(5*x)^2 - 12/5*(5*x + 1)* 
log(5*x)^3 - 12*e^(x + 1/5)*log(5*x)^3 + 12*log(5)*log(5*x)^3 - 3*log(5*x) 
^4 - 588/625*(5*x + 1)^3 - 18/25*(5*x + 1)^2*e^(2*x + 2/5) - 1764/125*(5*x 
 + 1)^2*e^(x + 1/5) + 1764/125*(5*x + 1)^2*log(5) + 36/5*(5*x + 1)*e^(2*x 
+ 2/5)*log(5) + 3528/25*(5*x + 1)*e^(x + 1/5)*log(5) - 1764/25*(5*x + 1)*l 
og(5)^2 - 18*e^(2*x + 2/5)*log(5)^2 - 1764/5*e^(x + 1/5)*log(5)^2 - 1764/1 
25*(5*x + 1)^2*log(5*x) - 36/5*(5*x + 1)*e^(2*x + 2/5)*log(5*x) - 3528/25* 
(5*x + 1)*e^(x + 1/5)*log(5*x) + 3528/25*(5*x + 1)*log(5)*log(5*x) + 36*e^ 
(2*x + 2/5)*log(5)*log(5*x) + 3528/5*e^(x + 1/5)*log(5)*log(5*x) - 1764/5* 
log(5)^2*log(5*x) - 1764/25*(5*x + 1)*log(5*x)^2 - 18*e^(2*x + 2/5)*log(5* 
x)^2 - 1764/5*e^(x + 1/5)*log(5*x)^2 + 1764/5*log(5)*log(5*x)^2 - 588/5*lo 
g(5*x)^3 - 43218/625*(5*x + 1)^2 - 12/5*(5*x + 1)*e^(3*x + 3/5) - 1764/...
 

Mupad [B] (verification not implemented)

Time = 3.90 (sec) , antiderivative size = 269, normalized size of antiderivative = 10.35 \[ \int \frac {-12000-15601 x-12 e^{\frac {4}{5} (1+5 x)} x-3960 x^2-372 x^3-12 x^4+e^{\frac {3}{5} (1+5 x)} \left (-12-372 x-36 x^2\right )+e^{\frac {2}{5} (1+5 x)} \left (-360-3996 x-756 x^2-36 x^3\right )+e^{\frac {1}{5} (1+5 x)} \left (-3600-16320 x-4356 x^2-396 x^3-12 x^4\right )+\left (-3600-4320 x-36 e^{\frac {3}{5} (1+5 x)} x-756 x^2-36 x^3+e^{\frac {2}{5} (1+5 x)} \left (-36-756 x-72 x^2\right )+e^{\frac {1}{5} (1+5 x)} \left (-720-4392 x-792 x^2-36 x^3\right )\right ) \log (x)+\left (-360-396 x-36 e^{\frac {2}{5} (1+5 x)} x-36 x^2+e^{\frac {1}{5} (1+5 x)} \left (-36-396 x-36 x^2\right )\right ) \log ^2(x)+\left (-12-12 x-12 e^{\frac {1}{5} (1+5 x)} x\right ) \log ^3(x)}{x} \, dx=-12001\,x-12000\,{\mathrm {e}}^{x+\frac {1}{5}}-1800\,{\mathrm {e}}^{2\,x+\frac {2}{5}}-120\,{\mathrm {e}}^{3\,x+\frac {3}{5}}-3\,{\mathrm {e}}^{4\,x+\frac {4}{5}}-12000\,\ln \left (x\right )-3600\,x\,{\mathrm {e}}^{x+\frac {1}{5}}-360\,x\,{\ln \left (x\right )}^2-360\,x^2\,\ln \left (x\right )-12\,x\,{\ln \left (x\right )}^3-12\,x^3\,\ln \left (x\right )-18\,{\mathrm {e}}^{2\,x+\frac {2}{5}}\,{\ln \left (x\right )}^2-1800\,{\ln \left (x\right )}^2-120\,{\ln \left (x\right )}^3-3\,{\ln \left (x\right )}^4-360\,x\,{\mathrm {e}}^{2\,x+\frac {2}{5}}-12\,x\,{\mathrm {e}}^{3\,x+\frac {3}{5}}-360\,x^2\,{\mathrm {e}}^{x+\frac {1}{5}}-12\,x^3\,{\mathrm {e}}^{x+\frac {1}{5}}-18\,x^2\,{\ln \left (x\right )}^2-3600\,{\mathrm {e}}^{x+\frac {1}{5}}\,\ln \left (x\right )-3600\,x\,\ln \left (x\right )-18\,x^2\,{\mathrm {e}}^{2\,x+\frac {2}{5}}-1800\,x^2-120\,x^3-3\,x^4-360\,{\mathrm {e}}^{2\,x+\frac {2}{5}}\,\ln \left (x\right )-12\,{\mathrm {e}}^{3\,x+\frac {3}{5}}\,\ln \left (x\right )-360\,{\mathrm {e}}^{x+\frac {1}{5}}\,{\ln \left (x\right )}^2-12\,{\mathrm {e}}^{x+\frac {1}{5}}\,{\ln \left (x\right )}^3-36\,x\,{\mathrm {e}}^{2\,x+\frac {2}{5}}\,\ln \left (x\right )-36\,x\,{\mathrm {e}}^{x+\frac {1}{5}}\,{\ln \left (x\right )}^2-36\,x^2\,{\mathrm {e}}^{x+\frac {1}{5}}\,\ln \left (x\right )-720\,x\,{\mathrm {e}}^{x+\frac {1}{5}}\,\ln \left (x\right ) \] Input:

int(-(15601*x + log(x)*(4320*x + exp(x + 1/5)*(4392*x + 792*x^2 + 36*x^3 + 
 720) + exp(2*x + 2/5)*(756*x + 72*x^2 + 36) + 36*x*exp(3*x + 3/5) + 756*x 
^2 + 36*x^3 + 3600) + exp(3*x + 3/5)*(372*x + 36*x^2 + 12) + 12*x*exp(4*x 
+ 4/5) + exp(x + 1/5)*(16320*x + 4356*x^2 + 396*x^3 + 12*x^4 + 3600) + log 
(x)^2*(396*x + exp(x + 1/5)*(396*x + 36*x^2 + 36) + 36*x*exp(2*x + 2/5) + 
36*x^2 + 360) + exp(2*x + 2/5)*(3996*x + 756*x^2 + 36*x^3 + 360) + 3960*x^ 
2 + 372*x^3 + 12*x^4 + log(x)^3*(12*x + 12*x*exp(x + 1/5) + 12) + 12000)/x 
,x)
 

Output:

- 12001*x - 12000*exp(x + 1/5) - 1800*exp(2*x + 2/5) - 120*exp(3*x + 3/5) 
- 3*exp(4*x + 4/5) - 12000*log(x) - 3600*x*exp(x + 1/5) - 360*x*log(x)^2 - 
 360*x^2*log(x) - 12*x*log(x)^3 - 12*x^3*log(x) - 18*exp(2*x + 2/5)*log(x) 
^2 - 1800*log(x)^2 - 120*log(x)^3 - 3*log(x)^4 - 360*x*exp(2*x + 2/5) - 12 
*x*exp(3*x + 3/5) - 360*x^2*exp(x + 1/5) - 12*x^3*exp(x + 1/5) - 18*x^2*lo 
g(x)^2 - 3600*exp(x + 1/5)*log(x) - 3600*x*log(x) - 18*x^2*exp(2*x + 2/5) 
- 1800*x^2 - 120*x^3 - 3*x^4 - 360*exp(2*x + 2/5)*log(x) - 12*exp(3*x + 3/ 
5)*log(x) - 360*exp(x + 1/5)*log(x)^2 - 12*exp(x + 1/5)*log(x)^3 - 36*x*ex 
p(2*x + 2/5)*log(x) - 36*x*exp(x + 1/5)*log(x)^2 - 36*x^2*exp(x + 1/5)*log 
(x) - 720*x*exp(x + 1/5)*log(x)
 

Reduce [B] (verification not implemented)

Time = 0.21 (sec) , antiderivative size = 289, normalized size of antiderivative = 11.12 \[ \int \frac {-12000-15601 x-12 e^{\frac {4}{5} (1+5 x)} x-3960 x^2-372 x^3-12 x^4+e^{\frac {3}{5} (1+5 x)} \left (-12-372 x-36 x^2\right )+e^{\frac {2}{5} (1+5 x)} \left (-360-3996 x-756 x^2-36 x^3\right )+e^{\frac {1}{5} (1+5 x)} \left (-3600-16320 x-4356 x^2-396 x^3-12 x^4\right )+\left (-3600-4320 x-36 e^{\frac {3}{5} (1+5 x)} x-756 x^2-36 x^3+e^{\frac {2}{5} (1+5 x)} \left (-36-756 x-72 x^2\right )+e^{\frac {1}{5} (1+5 x)} \left (-720-4392 x-792 x^2-36 x^3\right )\right ) \log (x)+\left (-360-396 x-36 e^{\frac {2}{5} (1+5 x)} x-36 x^2+e^{\frac {1}{5} (1+5 x)} \left (-36-396 x-36 x^2\right )\right ) \log ^2(x)+\left (-12-12 x-12 e^{\frac {1}{5} (1+5 x)} x\right ) \log ^3(x)}{x} \, dx=-12001 x -18 \mathrm {log}\left (x \right )^{2} x^{2}-1800 x^{2}-36 e^{2 x +\frac {2}{5}} \mathrm {log}\left (x \right ) x -36 e^{x +\frac {1}{5}} \mathrm {log}\left (x \right )^{2} x -36 e^{x +\frac {1}{5}} \mathrm {log}\left (x \right ) x^{2}-720 e^{x +\frac {1}{5}} \mathrm {log}\left (x \right ) x -120 x^{3}-12000 \,\mathrm {log}\left (x \right )-360 \,\mathrm {log}\left (x \right ) x^{2}-12 e^{3 x +\frac {3}{5}} \mathrm {log}\left (x \right )-12 e^{3 x +\frac {3}{5}} x -18 e^{2 x +\frac {2}{5}} \mathrm {log}\left (x \right )^{2}-360 e^{2 x +\frac {2}{5}} \mathrm {log}\left (x \right )-18 e^{2 x +\frac {2}{5}} x^{2}-360 e^{2 x +\frac {2}{5}} x -12 e^{x +\frac {1}{5}} \mathrm {log}\left (x \right )^{3}-360 e^{x +\frac {1}{5}} \mathrm {log}\left (x \right )^{2}-3600 e^{x +\frac {1}{5}} \mathrm {log}\left (x \right )-12 e^{x +\frac {1}{5}} x^{3}-360 e^{x +\frac {1}{5}} x^{2}-3600 e^{x +\frac {1}{5}} x -12 \,\mathrm {log}\left (x \right ) x^{3}-12 \mathrm {log}\left (x \right )^{3} x -3 \mathrm {log}\left (x \right )^{4}-3 x^{4}-1800 \mathrm {log}\left (x \right )^{2}-3600 \,\mathrm {log}\left (x \right ) x -360 \mathrm {log}\left (x \right )^{2} x -120 \mathrm {log}\left (x \right )^{3}-3 e^{4 x +\frac {4}{5}}-120 e^{3 x +\frac {3}{5}}-1800 e^{2 x +\frac {2}{5}}-12000 e^{x +\frac {1}{5}} \] Input:

int(((-12*x*exp(1/5+x)-12*x-12)*log(x)^3+(-36*x*exp(1/5+x)^2+(-36*x^2-396* 
x-36)*exp(1/5+x)-36*x^2-396*x-360)*log(x)^2+(-36*x*exp(1/5+x)^3+(-72*x^2-7 
56*x-36)*exp(1/5+x)^2+(-36*x^3-792*x^2-4392*x-720)*exp(1/5+x)-36*x^3-756*x 
^2-4320*x-3600)*log(x)-12*x*exp(1/5+x)^4+(-36*x^2-372*x-12)*exp(1/5+x)^3+( 
-36*x^3-756*x^2-3996*x-360)*exp(1/5+x)^2+(-12*x^4-396*x^3-4356*x^2-16320*x 
-3600)*exp(1/5+x)-12*x^4-372*x^3-3960*x^2-15601*x-12000)/x,x)
 

Output:

 - 3*e**((20*x + 4)/5) - 12*e**((15*x + 3)/5)*log(x) - 12*e**((15*x + 3)/5 
)*x - 120*e**((15*x + 3)/5) - 18*e**((10*x + 2)/5)*log(x)**2 - 36*e**((10* 
x + 2)/5)*log(x)*x - 360*e**((10*x + 2)/5)*log(x) - 18*e**((10*x + 2)/5)*x 
**2 - 360*e**((10*x + 2)/5)*x - 1800*e**((10*x + 2)/5) - 12*e**((5*x + 1)/ 
5)*log(x)**3 - 36*e**((5*x + 1)/5)*log(x)**2*x - 360*e**((5*x + 1)/5)*log( 
x)**2 - 36*e**((5*x + 1)/5)*log(x)*x**2 - 720*e**((5*x + 1)/5)*log(x)*x - 
3600*e**((5*x + 1)/5)*log(x) - 12*e**((5*x + 1)/5)*x**3 - 360*e**((5*x + 1 
)/5)*x**2 - 3600*e**((5*x + 1)/5)*x - 12000*e**((5*x + 1)/5) - 3*log(x)**4 
 - 12*log(x)**3*x - 120*log(x)**3 - 18*log(x)**2*x**2 - 360*log(x)**2*x - 
1800*log(x)**2 - 12*log(x)*x**3 - 360*log(x)*x**2 - 3600*log(x)*x - 12000* 
log(x) - 3*x**4 - 120*x**3 - 1800*x**2 - 12001*x