\(\int \frac {-140 x+130 x^3+20 x^4+10 x^6+(40 x-40 x^3) \log (x)+e^{e^x} (-70 x+10 x^4+e^x (-30 x^2-10 x^5)+(20 x+10 e^x x^2) \log (x))}{9+6 x^3+x^6+(-6-2 x^3) \log (x)+\log ^2(x)} \, dx\) [2770]

Optimal result

Integrand size = 103, antiderivative size = 28 \[ \int \frac {-140 x+130 x^3+20 x^4+10 x^6+\left (40 x-40 x^3\right ) \log (x)+e^{e^x} \left (-70 x+10 x^4+e^x \left (-30 x^2-10 x^5\right )+\left (20 x+10 e^x x^2\right ) \log (x)\right )}{9+6 x^3+x^6+\left (-6-2 x^3\right ) \log (x)+\log ^2(x)} \, dx=\frac {10 x^2 \left (2+e^{e^x}-x^2\right )}{-3-x^3+\log (x)} \] Output:

10*(2+exp(exp(x))-x^2)*x^2/(ln(x)-x^3-3)
                                                                                    
                                                                                    
 

Mathematica [A] (verified)

Time = 0.05 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.00 \[ \int \frac {-140 x+130 x^3+20 x^4+10 x^6+\left (40 x-40 x^3\right ) \log (x)+e^{e^x} \left (-70 x+10 x^4+e^x \left (-30 x^2-10 x^5\right )+\left (20 x+10 e^x x^2\right ) \log (x)\right )}{9+6 x^3+x^6+\left (-6-2 x^3\right ) \log (x)+\log ^2(x)} \, dx=\frac {10 x^2 \left (-2-e^{e^x}+x^2\right )}{3+x^3-\log (x)} \] Input:

Integrate[(-140*x + 130*x^3 + 20*x^4 + 10*x^6 + (40*x - 40*x^3)*Log[x] + E 
^E^x*(-70*x + 10*x^4 + E^x*(-30*x^2 - 10*x^5) + (20*x + 10*E^x*x^2)*Log[x] 
))/(9 + 6*x^3 + x^6 + (-6 - 2*x^3)*Log[x] + Log[x]^2),x]
 

Output:

(10*x^2*(-2 - E^E^x + x^2))/(3 + x^3 - Log[x])
 

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.

\(\displaystyle \int \frac {10 x^6+20 x^4+130 x^3+\left (40 x-40 x^3\right ) \log (x)+e^{e^x} \left (10 x^4+\left (10 e^x x^2+20 x\right ) \log (x)+e^x \left (-10 x^5-30 x^2\right )-70 x\right )-140 x}{x^6+6 x^3+\left (-2 x^3-6\right ) \log (x)+\log ^2(x)+9} \, dx\)

\(\Big \downarrow \) 7292

\(\displaystyle \int \frac {10 x^6+20 x^4+130 x^3+\left (40 x-40 x^3\right ) \log (x)+e^{e^x} \left (10 x^4+\left (10 e^x x^2+20 x\right ) \log (x)+e^x \left (-10 x^5-30 x^2\right )-70 x\right )-140 x}{\left (x^3-\log (x)+3\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (\frac {130 x^3}{\left (x^3-\log (x)+3\right )^2}+\frac {20 e^{e^x} x \log (x)}{\left (x^3-\log (x)+3\right )^2}-\frac {40 (x-1) (x+1) x \log (x)}{\left (x^3-\log (x)+3\right )^2}-\frac {70 e^{e^x} x}{\left (x^3-\log (x)+3\right )^2}-\frac {140 x}{\left (x^3-\log (x)+3\right )^2}+\frac {10 x^6}{\left (x^3-\log (x)+3\right )^2}+\frac {10 e^{e^x} x^4}{\left (x^3-\log (x)+3\right )^2}+\frac {20 x^4}{\left (x^3-\log (x)+3\right )^2}-\frac {10 e^{x+e^x} x^2}{x^3-\log (x)+3}\right )dx\)

\(\Big \downarrow \) 2009

\(\displaystyle -20 \int \frac {x}{\left (x^3-\log (x)+3\right )^2}dx-10 \int \frac {e^{e^x} x}{\left (x^3-\log (x)+3\right )^2}dx+10 \int \frac {x^3}{\left (x^3-\log (x)+3\right )^2}dx-40 \int \frac {x}{x^3-\log (x)+3}dx-20 \int \frac {e^{e^x} x}{x^3-\log (x)+3}dx+40 \int \frac {x^3}{x^3-\log (x)+3}dx-30 \int \frac {x^6}{\left (x^3-\log (x)+3\right )^2}dx+60 \int \frac {x^4}{\left (x^3-\log (x)+3\right )^2}dx+30 \int \frac {e^{e^x} x^4}{\left (x^3-\log (x)+3\right )^2}dx-10 \int \frac {e^{x+e^x} x^2}{x^3-\log (x)+3}dx\)

Input:

Int[(-140*x + 130*x^3 + 20*x^4 + 10*x^6 + (40*x - 40*x^3)*Log[x] + E^E^x*( 
-70*x + 10*x^4 + E^x*(-30*x^2 - 10*x^5) + (20*x + 10*E^x*x^2)*Log[x]))/(9 
+ 6*x^3 + x^6 + (-6 - 2*x^3)*Log[x] + Log[x]^2),x]
 

Output:

$Aborted
 

Maple [A] (verified)

Time = 4.68 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.14

method	result	size
parallelrisch	\(\frac {10 x^{4}-10 \,{\mathrm e}^{{\mathrm e}^{x}} x^{2}-20 x^{2}}{x^{3}-\ln \left (x \right )+3}\)	\(32\)

Input:

int((((10*exp(x)*x^2+20*x)*ln(x)+(-10*x^5-30*x^2)*exp(x)+10*x^4-70*x)*exp( 
exp(x))+(-40*x^3+40*x)*ln(x)+10*x^6+20*x^4+130*x^3-140*x)/(ln(x)^2+(-2*x^3 
-6)*ln(x)+x^6+6*x^3+9),x,method=_RETURNVERBOSE)
 

Output:

(10*x^4-10*exp(exp(x))*x^2-20*x^2)/(x^3-ln(x)+3)
 

Fricas [A] (verification not implemented)

Time = 0.13 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.07 \[ \int \frac {-140 x+130 x^3+20 x^4+10 x^6+\left (40 x-40 x^3\right ) \log (x)+e^{e^x} \left (-70 x+10 x^4+e^x \left (-30 x^2-10 x^5\right )+\left (20 x+10 e^x x^2\right ) \log (x)\right )}{9+6 x^3+x^6+\left (-6-2 x^3\right ) \log (x)+\log ^2(x)} \, dx=\frac {10 \, {\left (x^{4} - x^{2} e^{\left (e^{x}\right )} - 2 \, x^{2}\right )}}{x^{3} - \log \left (x\right ) + 3} \] Input:

integrate((((10*exp(x)*x^2+20*x)*log(x)+(-10*x^5-30*x^2)*exp(x)+10*x^4-70* 
x)*exp(exp(x))+(-40*x^3+40*x)*log(x)+10*x^6+20*x^4+130*x^3-140*x)/(log(x)^ 
2+(-2*x^3-6)*log(x)+x^6+6*x^3+9),x, algorithm="fricas")
 

Output:

10*(x^4 - x^2*e^(e^x) - 2*x^2)/(x^3 - log(x) + 3)
 

Sympy [A] (verification not implemented)

Time = 0.15 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.29 \[ \int \frac {-140 x+130 x^3+20 x^4+10 x^6+\left (40 x-40 x^3\right ) \log (x)+e^{e^x} \left (-70 x+10 x^4+e^x \left (-30 x^2-10 x^5\right )+\left (20 x+10 e^x x^2\right ) \log (x)\right )}{9+6 x^3+x^6+\left (-6-2 x^3\right ) \log (x)+\log ^2(x)} \, dx=- \frac {10 x^{2} e^{e^{x}}}{x^{3} - \log {\left (x \right )} + 3} + \frac {- 10 x^{4} + 20 x^{2}}{- x^{3} + \log {\left (x \right )} - 3} \] Input:

integrate((((10*exp(x)*x**2+20*x)*ln(x)+(-10*x**5-30*x**2)*exp(x)+10*x**4- 
70*x)*exp(exp(x))+(-40*x**3+40*x)*ln(x)+10*x**6+20*x**4+130*x**3-140*x)/(l 
n(x)**2+(-2*x**3-6)*ln(x)+x**6+6*x**3+9),x)
 

Output:

-10*x**2*exp(exp(x))/(x**3 - log(x) + 3) + (-10*x**4 + 20*x**2)/(-x**3 + l 
og(x) - 3)
 

Maxima [A] (verification not implemented)

Time = 0.07 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.07 \[ \int \frac {-140 x+130 x^3+20 x^4+10 x^6+\left (40 x-40 x^3\right ) \log (x)+e^{e^x} \left (-70 x+10 x^4+e^x \left (-30 x^2-10 x^5\right )+\left (20 x+10 e^x x^2\right ) \log (x)\right )}{9+6 x^3+x^6+\left (-6-2 x^3\right ) \log (x)+\log ^2(x)} \, dx=\frac {10 \, {\left (x^{4} - x^{2} e^{\left (e^{x}\right )} - 2 \, x^{2}\right )}}{x^{3} - \log \left (x\right ) + 3} \] Input:

integrate((((10*exp(x)*x^2+20*x)*log(x)+(-10*x^5-30*x^2)*exp(x)+10*x^4-70* 
x)*exp(exp(x))+(-40*x^3+40*x)*log(x)+10*x^6+20*x^4+130*x^3-140*x)/(log(x)^ 
2+(-2*x^3-6)*log(x)+x^6+6*x^3+9),x, algorithm="maxima")
 

Output:

10*(x^4 - x^2*e^(e^x) - 2*x^2)/(x^3 - log(x) + 3)
 

Giac [A] (verification not implemented)

Time = 0.12 (sec) , antiderivative size = 45, normalized size of antiderivative = 1.61 \[ \int \frac {-140 x+130 x^3+20 x^4+10 x^6+\left (40 x-40 x^3\right ) \log (x)+e^{e^x} \left (-70 x+10 x^4+e^x \left (-30 x^2-10 x^5\right )+\left (20 x+10 e^x x^2\right ) \log (x)\right )}{9+6 x^3+x^6+\left (-6-2 x^3\right ) \log (x)+\log ^2(x)} \, dx=\frac {10 \, {\left (x^{4} e^{x} - x^{2} e^{\left (x + e^{x}\right )} - 2 \, x^{2} e^{x}\right )}}{x^{3} e^{x} - e^{x} \log \left (x\right ) + 3 \, e^{x}} \] Input:

integrate((((10*exp(x)*x^2+20*x)*log(x)+(-10*x^5-30*x^2)*exp(x)+10*x^4-70* 
x)*exp(exp(x))+(-40*x^3+40*x)*log(x)+10*x^6+20*x^4+130*x^3-140*x)/(log(x)^ 
2+(-2*x^3-6)*log(x)+x^6+6*x^3+9),x, algorithm="giac")
 

Output:

10*(x^4*e^x - x^2*e^(x + e^x) - 2*x^2*e^x)/(x^3*e^x - e^x*log(x) + 3*e^x)
 

Mupad [B] (verification not implemented)

Time = 3.68 (sec) , antiderivative size = 104, normalized size of antiderivative = 3.71 \[ \int \frac {-140 x+130 x^3+20 x^4+10 x^6+\left (40 x-40 x^3\right ) \log (x)+e^{e^x} \left (-70 x+10 x^4+e^x \left (-30 x^2-10 x^5\right )+\left (20 x+10 e^x x^2\right ) \log (x)\right )}{9+6 x^3+x^6+\left (-6-2 x^3\right ) \log (x)+\log ^2(x)} \, dx=\frac {40\,x}{3}+\frac {\frac {40\,x}{9}-\frac {40\,x^2}{3}}{x^3-\frac {1}{3}}-\frac {\frac {10\,x^2\,\left (x^5+2\,x^3+13\,x^2-14\right )}{3\,x^3-1}-\frac {40\,x^2\,\ln \left (x\right )\,\left (x^2-1\right )}{3\,x^3-1}}{x^3-\ln \left (x\right )+3}-\frac {10\,x^2\,{\mathrm {e}}^{{\mathrm {e}}^x}}{x^3-\ln \left (x\right )+3} \] Input:

int((log(x)*(40*x - 40*x^3) - exp(exp(x))*(70*x + exp(x)*(30*x^2 + 10*x^5) 
 - log(x)*(20*x + 10*x^2*exp(x)) - 10*x^4) - 140*x + 130*x^3 + 20*x^4 + 10 
*x^6)/(log(x)^2 + 6*x^3 + x^6 - log(x)*(2*x^3 + 6) + 9),x)
 

Output:

(40*x)/3 + ((40*x)/9 - (40*x^2)/3)/(x^3 - 1/3) - ((10*x^2*(13*x^2 + 2*x^3 
+ x^5 - 14))/(3*x^3 - 1) - (40*x^2*log(x)*(x^2 - 1))/(3*x^3 - 1))/(x^3 - l 
og(x) + 3) - (10*x^2*exp(exp(x)))/(x^3 - log(x) + 3)
 

Reduce [F]

\[ \int \frac {-140 x+130 x^3+20 x^4+10 x^6+\left (40 x-40 x^3\right ) \log (x)+e^{e^x} \left (-70 x+10 x^4+e^x \left (-30 x^2-10 x^5\right )+\left (20 x+10 e^x x^2\right ) \log (x)\right )}{9+6 x^3+x^6+\left (-6-2 x^3\right ) \log (x)+\log ^2(x)} \, dx =\text {Too large to display} \] Input:

int((((10*exp(x)*x^2+20*x)*log(x)+(-10*x^5-30*x^2)*exp(x)+10*x^4-70*x)*exp 
(exp(x))+(-40*x^3+40*x)*log(x)+10*x^6+20*x^4+130*x^3-140*x)/(log(x)^2+(-2* 
x^3-6)*log(x)+x^6+6*x^3+9),x)
 

Output:

10*(int(x**6/(log(x)**2 - 2*log(x)*x**3 - 6*log(x) + x**6 + 6*x**3 + 9),x) 
 + 2*int(x**4/(log(x)**2 - 2*log(x)*x**3 - 6*log(x) + x**6 + 6*x**3 + 9),x 
) + 13*int(x**3/(log(x)**2 - 2*log(x)*x**3 - 6*log(x) + x**6 + 6*x**3 + 9) 
,x) + int((e**(e**x)*x**4)/(log(x)**2 - 2*log(x)*x**3 - 6*log(x) + x**6 + 
6*x**3 + 9),x) + 2*int((e**(e**x)*log(x)*x)/(log(x)**2 - 2*log(x)*x**3 - 6 
*log(x) + x**6 + 6*x**3 + 9),x) - 7*int((e**(e**x)*x)/(log(x)**2 - 2*log(x 
)*x**3 - 6*log(x) + x**6 + 6*x**3 + 9),x) - int((e**(e**x + x)*x**5)/(log( 
x)**2 - 2*log(x)*x**3 - 6*log(x) + x**6 + 6*x**3 + 9),x) - 3*int((e**(e**x 
 + x)*x**2)/(log(x)**2 - 2*log(x)*x**3 - 6*log(x) + x**6 + 6*x**3 + 9),x) 
+ int((e**(e**x + x)*log(x)*x**2)/(log(x)**2 - 2*log(x)*x**3 - 6*log(x) + 
x**6 + 6*x**3 + 9),x) - 4*int((log(x)*x**3)/(log(x)**2 - 2*log(x)*x**3 - 6 
*log(x) + x**6 + 6*x**3 + 9),x) + 4*int((log(x)*x)/(log(x)**2 - 2*log(x)*x 
**3 - 6*log(x) + x**6 + 6*x**3 + 9),x) - 14*int(x/(log(x)**2 - 2*log(x)*x* 
*3 - 6*log(x) + x**6 + 6*x**3 + 9),x))