\(\int \frac {e^{x^2} (-60 x^3+2 x^4)-2 x^3 \log (-30+x)+(30 x^2-x^3+e^{x^2} (120 x^3-4 x^4)) \log ^2(-30+x)+(30 x-31 x^2+x^3+e^{x^2} (-60 x^3+2 x^4)) \log ^4(-30+x)+(e^{x^2} (120 x^2-4 x^3) \log ^2(-30+x)+(-60 x+2 x^2+e^{x^2} (-120 x^2+4 x^3)) \log ^4(-30+x)) \log (x)+e^{x^2} (-60 x+2 x^2) \log ^4(-30+x) \log ^2(x)}{-30 x^2+x^3+(60 x^2-2 x^3) \log ^2(-30+x)+(-30 x^2+x^3) \log ^4(-30+x)+((60 x-2 x^2) \log ^2(-30+x)+(-60 x+2 x^2) \log ^4(-30+x)) \log (x)+(-30+x) \log ^4(-30+x) \log ^2(x)} \, dx\) [852]

Optimal result

Integrand size = 279, antiderivative size = 29 \[ \int \frac {e^{x^2} \left (-60 x^3+2 x^4\right )-2 x^3 \log (-30+x)+\left (30 x^2-x^3+e^{x^2} \left (120 x^3-4 x^4\right )\right ) \log ^2(-30+x)+\left (30 x-31 x^2+x^3+e^{x^2} \left (-60 x^3+2 x^4\right )\right ) \log ^4(-30+x)+\left (e^{x^2} \left (120 x^2-4 x^3\right ) \log ^2(-30+x)+\left (-60 x+2 x^2+e^{x^2} \left (-120 x^2+4 x^3\right )\right ) \log ^4(-30+x)\right ) \log (x)+e^{x^2} \left (-60 x+2 x^2\right ) \log ^4(-30+x) \log ^2(x)}{-30 x^2+x^3+\left (60 x^2-2 x^3\right ) \log ^2(-30+x)+\left (-30 x^2+x^3\right ) \log ^4(-30+x)+\left (\left (60 x-2 x^2\right ) \log ^2(-30+x)+\left (-60 x+2 x^2\right ) \log ^4(-30+x)\right ) \log (x)+(-30+x) \log ^4(-30+x) \log ^2(x)} \, dx=e^{x^2}-\frac {x^2}{-x+\frac {x}{\log ^2(-30+x)}-\log (x)} \] Output:

exp(x^2)-x^2/(1/ln(x-30)^2*x-x-ln(x))
                                                                                    
                                                                                    
 

Mathematica [A] (verified)

Time = 0.11 (sec) , antiderivative size = 33, normalized size of antiderivative = 1.14 \[ \int \frac {e^{x^2} \left (-60 x^3+2 x^4\right )-2 x^3 \log (-30+x)+\left (30 x^2-x^3+e^{x^2} \left (120 x^3-4 x^4\right )\right ) \log ^2(-30+x)+\left (30 x-31 x^2+x^3+e^{x^2} \left (-60 x^3+2 x^4\right )\right ) \log ^4(-30+x)+\left (e^{x^2} \left (120 x^2-4 x^3\right ) \log ^2(-30+x)+\left (-60 x+2 x^2+e^{x^2} \left (-120 x^2+4 x^3\right )\right ) \log ^4(-30+x)\right ) \log (x)+e^{x^2} \left (-60 x+2 x^2\right ) \log ^4(-30+x) \log ^2(x)}{-30 x^2+x^3+\left (60 x^2-2 x^3\right ) \log ^2(-30+x)+\left (-30 x^2+x^3\right ) \log ^4(-30+x)+\left (\left (60 x-2 x^2\right ) \log ^2(-30+x)+\left (-60 x+2 x^2\right ) \log ^4(-30+x)\right ) \log (x)+(-30+x) \log ^4(-30+x) \log ^2(x)} \, dx=e^{x^2}+\frac {x^2 \log ^2(-30+x)}{-x+\log ^2(-30+x) (x+\log (x))} \] Input:

Integrate[(E^x^2*(-60*x^3 + 2*x^4) - 2*x^3*Log[-30 + x] + (30*x^2 - x^3 + 
E^x^2*(120*x^3 - 4*x^4))*Log[-30 + x]^2 + (30*x - 31*x^2 + x^3 + E^x^2*(-6 
0*x^3 + 2*x^4))*Log[-30 + x]^4 + (E^x^2*(120*x^2 - 4*x^3)*Log[-30 + x]^2 + 
 (-60*x + 2*x^2 + E^x^2*(-120*x^2 + 4*x^3))*Log[-30 + x]^4)*Log[x] + E^x^2 
*(-60*x + 2*x^2)*Log[-30 + x]^4*Log[x]^2)/(-30*x^2 + x^3 + (60*x^2 - 2*x^3 
)*Log[-30 + x]^2 + (-30*x^2 + x^3)*Log[-30 + x]^4 + ((60*x - 2*x^2)*Log[-3 
0 + x]^2 + (-60*x + 2*x^2)*Log[-30 + x]^4)*Log[x] + (-30 + x)*Log[-30 + x] 
^4*Log[x]^2),x]
 

Output:

E^x^2 + (x^2*Log[-30 + x]^2)/(-x + Log[-30 + x]^2*(x + 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.

\(\displaystyle \int \frac {-2 x^3 \log (x-30)+e^{x^2} \left (2 x^2-60 x\right ) \log ^2(x) \log ^4(x-30)+\left (\left (2 x^2+e^{x^2} \left (4 x^3-120 x^2\right )-60 x\right ) \log ^4(x-30)+e^{x^2} \left (120 x^2-4 x^3\right ) \log ^2(x-30)\right ) \log (x)+e^{x^2} \left (2 x^4-60 x^3\right )+\left (x^3-31 x^2+e^{x^2} \left (2 x^4-60 x^3\right )+30 x\right ) \log ^4(x-30)+\left (-x^3+30 x^2+e^{x^2} \left (120 x^3-4 x^4\right )\right ) \log ^2(x-30)}{x^3-30 x^2+\left (\left (2 x^2-60 x\right ) \log ^4(x-30)+\left (60 x-2 x^2\right ) \log ^2(x-30)\right ) \log (x)+\left (x^3-30 x^2\right ) \log ^4(x-30)+\left (60 x^2-2 x^3\right ) \log ^2(x-30)+(x-30) \log ^2(x) \log ^4(x-30)} \, dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {x \left (-2 e^{x^2} (x-30) x^2+(x-30) x \left (4 e^{x^2} x+4 e^{x^2} \log (x)+1\right ) \log ^2(x-30)-\left ((x-30) \left (2 e^{x^2} x^2+2 e^{x^2} \log ^2(x)+\left (4 e^{x^2} x+2\right ) \log (x)+x-1\right ) \log ^4(x-30)\right )+2 x^2 \log (x-30)\right )}{(30-x) \left (x-\log ^2(x-30) (x+\log (x))\right )^2}dx\)

\(\Big \downarrow \) 7293

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

\(\Big \downarrow \) 2009

\(\displaystyle -2 \int \frac {x^2 \log (x-30)}{\left (x \log ^2(x-30)+\log (x) \log ^2(x-30)-x\right )^2}dx+\int \frac {x^2 \log ^2(x-30)}{\left (x \log ^2(x-30)+\log (x) \log ^2(x-30)-x\right )^2}dx-\int \frac {x^2 \log ^4(x-30)}{\left (x \log ^2(x-30)+\log (x) \log ^2(x-30)-x\right )^2}dx-1800 \int \frac {\log (x-30)}{\left (x \log ^2(x-30)+\log (x) \log ^2(x-30)-x\right )^2}dx-54000 \int \frac {\log (x-30)}{(x-30) \left (x \log ^2(x-30)+\log (x) \log ^2(x-30)-x\right )^2}dx-60 \int \frac {x \log (x-30)}{\left (x \log ^2(x-30)+\log (x) \log ^2(x-30)-x\right )^2}dx+2 \int \frac {x \log ^2(x-30)}{x \log ^2(x-30)+\log (x) \log ^2(x-30)-x}dx-\int \frac {x \log ^4(x-30)}{\left (x \log ^2(x-30)+\log (x) \log ^2(x-30)-x\right )^2}dx+e^{x^2}\)

Input:

Int[(E^x^2*(-60*x^3 + 2*x^4) - 2*x^3*Log[-30 + x] + (30*x^2 - x^3 + E^x^2* 
(120*x^3 - 4*x^4))*Log[-30 + x]^2 + (30*x - 31*x^2 + x^3 + E^x^2*(-60*x^3 
+ 2*x^4))*Log[-30 + x]^4 + (E^x^2*(120*x^2 - 4*x^3)*Log[-30 + x]^2 + (-60* 
x + 2*x^2 + E^x^2*(-120*x^2 + 4*x^3))*Log[-30 + x]^4)*Log[x] + E^x^2*(-60* 
x + 2*x^2)*Log[-30 + x]^4*Log[x]^2)/(-30*x^2 + x^3 + (60*x^2 - 2*x^3)*Log[ 
-30 + x]^2 + (-30*x^2 + x^3)*Log[-30 + x]^4 + ((60*x - 2*x^2)*Log[-30 + x] 
^2 + (-60*x + 2*x^2)*Log[-30 + x]^4)*Log[x] + (-30 + x)*Log[-30 + x]^4*Log 
[x]^2),x]
 

Output:

$Aborted
 

Maple [B] (verified)

Leaf count of result is larger than twice the leaf count of optimal. \(58\) vs. \(2(28)=56\).

Time = 0.28 (sec) , antiderivative size = 59, normalized size of antiderivative = 2.03

\[\frac {x^{2}+{\mathrm e}^{x^{2}} x +{\mathrm e}^{x^{2}} \ln \left (x \right )}{x +\ln \left (x \right )}+\frac {x^{3}}{\left (x +\ln \left (x \right )\right ) \left (\ln \left (x -30\right )^{2} \ln \left (x \right )+x \ln \left (x -30\right )^{2}-x \right )}\]

Input:

int(((2*x^2-60*x)*exp(x^2)*ln(x-30)^4*ln(x)^2+(((4*x^3-120*x^2)*exp(x^2)+2 
*x^2-60*x)*ln(x-30)^4+(-4*x^3+120*x^2)*exp(x^2)*ln(x-30)^2)*ln(x)+((2*x^4- 
60*x^3)*exp(x^2)+x^3-31*x^2+30*x)*ln(x-30)^4+((-4*x^4+120*x^3)*exp(x^2)-x^ 
3+30*x^2)*ln(x-30)^2-2*x^3*ln(x-30)+(2*x^4-60*x^3)*exp(x^2))/((x-30)*ln(x- 
30)^4*ln(x)^2+((2*x^2-60*x)*ln(x-30)^4+(-2*x^2+60*x)*ln(x-30)^2)*ln(x)+(x^ 
3-30*x^2)*ln(x-30)^4+(-2*x^3+60*x^2)*ln(x-30)^2+x^3-30*x^2),x)
 

Output:

(x^2+exp(x^2)*x+exp(x^2)*ln(x))/(x+ln(x))+x^3/(x+ln(x))/(ln(x-30)^2*ln(x)+ 
x*ln(x-30)^2-x)
 

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 62 vs. \(2 (24) = 48\).

Time = 0.10 (sec) , antiderivative size = 62, normalized size of antiderivative = 2.14 \[ \int \frac {e^{x^2} \left (-60 x^3+2 x^4\right )-2 x^3 \log (-30+x)+\left (30 x^2-x^3+e^{x^2} \left (120 x^3-4 x^4\right )\right ) \log ^2(-30+x)+\left (30 x-31 x^2+x^3+e^{x^2} \left (-60 x^3+2 x^4\right )\right ) \log ^4(-30+x)+\left (e^{x^2} \left (120 x^2-4 x^3\right ) \log ^2(-30+x)+\left (-60 x+2 x^2+e^{x^2} \left (-120 x^2+4 x^3\right )\right ) \log ^4(-30+x)\right ) \log (x)+e^{x^2} \left (-60 x+2 x^2\right ) \log ^4(-30+x) \log ^2(x)}{-30 x^2+x^3+\left (60 x^2-2 x^3\right ) \log ^2(-30+x)+\left (-30 x^2+x^3\right ) \log ^4(-30+x)+\left (\left (60 x-2 x^2\right ) \log ^2(-30+x)+\left (-60 x+2 x^2\right ) \log ^4(-30+x)\right ) \log (x)+(-30+x) \log ^4(-30+x) \log ^2(x)} \, dx=\frac {e^{\left (x^{2}\right )} \log \left (x - 30\right )^{2} \log \left (x\right ) + {\left (x^{2} + x e^{\left (x^{2}\right )}\right )} \log \left (x - 30\right )^{2} - x e^{\left (x^{2}\right )}}{x \log \left (x - 30\right )^{2} + \log \left (x - 30\right )^{2} \log \left (x\right ) - x} \] Input:

integrate(((2*x^2-60*x)*exp(x^2)*log(x-30)^4*log(x)^2+(((4*x^3-120*x^2)*ex 
p(x^2)+2*x^2-60*x)*log(x-30)^4+(-4*x^3+120*x^2)*exp(x^2)*log(x-30)^2)*log( 
x)+((2*x^4-60*x^3)*exp(x^2)+x^3-31*x^2+30*x)*log(x-30)^4+((-4*x^4+120*x^3) 
*exp(x^2)-x^3+30*x^2)*log(x-30)^2-2*x^3*log(x-30)+(2*x^4-60*x^3)*exp(x^2)) 
/((x-30)*log(x-30)^4*log(x)^2+((2*x^2-60*x)*log(x-30)^4+(-2*x^2+60*x)*log( 
x-30)^2)*log(x)+(x^3-30*x^2)*log(x-30)^4+(-2*x^3+60*x^2)*log(x-30)^2+x^3-3 
0*x^2),x, algorithm="fricas")
 

Output:

(e^(x^2)*log(x - 30)^2*log(x) + (x^2 + x*e^(x^2))*log(x - 30)^2 - x*e^(x^2 
))/(x*log(x - 30)^2 + log(x - 30)^2*log(x) - x)
 

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 46 vs. \(2 (20) = 40\).

Time = 0.34 (sec) , antiderivative size = 46, normalized size of antiderivative = 1.59 \[ \int \frac {e^{x^2} \left (-60 x^3+2 x^4\right )-2 x^3 \log (-30+x)+\left (30 x^2-x^3+e^{x^2} \left (120 x^3-4 x^4\right )\right ) \log ^2(-30+x)+\left (30 x-31 x^2+x^3+e^{x^2} \left (-60 x^3+2 x^4\right )\right ) \log ^4(-30+x)+\left (e^{x^2} \left (120 x^2-4 x^3\right ) \log ^2(-30+x)+\left (-60 x+2 x^2+e^{x^2} \left (-120 x^2+4 x^3\right )\right ) \log ^4(-30+x)\right ) \log (x)+e^{x^2} \left (-60 x+2 x^2\right ) \log ^4(-30+x) \log ^2(x)}{-30 x^2+x^3+\left (60 x^2-2 x^3\right ) \log ^2(-30+x)+\left (-30 x^2+x^3\right ) \log ^4(-30+x)+\left (\left (60 x-2 x^2\right ) \log ^2(-30+x)+\left (-60 x+2 x^2\right ) \log ^4(-30+x)\right ) \log (x)+(-30+x) \log ^4(-30+x) \log ^2(x)} \, dx=\frac {x^{3}}{- x^{2} - x \log {\left (x \right )} + \left (x^{2} + 2 x \log {\left (x \right )} + \log {\left (x \right )}^{2}\right ) \log {\left (x - 30 \right )}^{2}} + \frac {x^{2}}{x + \log {\left (x \right )}} + e^{x^{2}} \] Input:

integrate(((2*x**2-60*x)*exp(x**2)*ln(x-30)**4*ln(x)**2+(((4*x**3-120*x**2 
)*exp(x**2)+2*x**2-60*x)*ln(x-30)**4+(-4*x**3+120*x**2)*exp(x**2)*ln(x-30) 
**2)*ln(x)+((2*x**4-60*x**3)*exp(x**2)+x**3-31*x**2+30*x)*ln(x-30)**4+((-4 
*x**4+120*x**3)*exp(x**2)-x**3+30*x**2)*ln(x-30)**2-2*x**3*ln(x-30)+(2*x** 
4-60*x**3)*exp(x**2))/((x-30)*ln(x-30)**4*ln(x)**2+((2*x**2-60*x)*ln(x-30) 
**4+(-2*x**2+60*x)*ln(x-30)**2)*ln(x)+(x**3-30*x**2)*ln(x-30)**4+(-2*x**3+ 
60*x**2)*ln(x-30)**2+x**3-30*x**2),x)
 

Output:

x**3/(-x**2 - x*log(x) + (x**2 + 2*x*log(x) + log(x)**2)*log(x - 30)**2) + 
 x**2/(x + log(x)) + exp(x**2)
 

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 49 vs. \(2 (24) = 48\).

Time = 0.15 (sec) , antiderivative size = 49, normalized size of antiderivative = 1.69 \[ \int \frac {e^{x^2} \left (-60 x^3+2 x^4\right )-2 x^3 \log (-30+x)+\left (30 x^2-x^3+e^{x^2} \left (120 x^3-4 x^4\right )\right ) \log ^2(-30+x)+\left (30 x-31 x^2+x^3+e^{x^2} \left (-60 x^3+2 x^4\right )\right ) \log ^4(-30+x)+\left (e^{x^2} \left (120 x^2-4 x^3\right ) \log ^2(-30+x)+\left (-60 x+2 x^2+e^{x^2} \left (-120 x^2+4 x^3\right )\right ) \log ^4(-30+x)\right ) \log (x)+e^{x^2} \left (-60 x+2 x^2\right ) \log ^4(-30+x) \log ^2(x)}{-30 x^2+x^3+\left (60 x^2-2 x^3\right ) \log ^2(-30+x)+\left (-30 x^2+x^3\right ) \log ^4(-30+x)+\left (\left (60 x-2 x^2\right ) \log ^2(-30+x)+\left (-60 x+2 x^2\right ) \log ^4(-30+x)\right ) \log (x)+(-30+x) \log ^4(-30+x) \log ^2(x)} \, dx=\frac {x^{2} \log \left (x - 30\right )^{2} + {\left ({\left (x + \log \left (x\right )\right )} \log \left (x - 30\right )^{2} - x\right )} e^{\left (x^{2}\right )}}{{\left (x + \log \left (x\right )\right )} \log \left (x - 30\right )^{2} - x} \] Input:

integrate(((2*x^2-60*x)*exp(x^2)*log(x-30)^4*log(x)^2+(((4*x^3-120*x^2)*ex 
p(x^2)+2*x^2-60*x)*log(x-30)^4+(-4*x^3+120*x^2)*exp(x^2)*log(x-30)^2)*log( 
x)+((2*x^4-60*x^3)*exp(x^2)+x^3-31*x^2+30*x)*log(x-30)^4+((-4*x^4+120*x^3) 
*exp(x^2)-x^3+30*x^2)*log(x-30)^2-2*x^3*log(x-30)+(2*x^4-60*x^3)*exp(x^2)) 
/((x-30)*log(x-30)^4*log(x)^2+((2*x^2-60*x)*log(x-30)^4+(-2*x^2+60*x)*log( 
x-30)^2)*log(x)+(x^3-30*x^2)*log(x-30)^4+(-2*x^3+60*x^2)*log(x-30)^2+x^3-3 
0*x^2),x, algorithm="maxima")
 

Output:

(x^2*log(x - 30)^2 + ((x + log(x))*log(x - 30)^2 - x)*e^(x^2))/((x + log(x 
))*log(x - 30)^2 - x)
 

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 67 vs. \(2 (24) = 48\).

Time = 0.43 (sec) , antiderivative size = 67, normalized size of antiderivative = 2.31 \[ \int \frac {e^{x^2} \left (-60 x^3+2 x^4\right )-2 x^3 \log (-30+x)+\left (30 x^2-x^3+e^{x^2} \left (120 x^3-4 x^4\right )\right ) \log ^2(-30+x)+\left (30 x-31 x^2+x^3+e^{x^2} \left (-60 x^3+2 x^4\right )\right ) \log ^4(-30+x)+\left (e^{x^2} \left (120 x^2-4 x^3\right ) \log ^2(-30+x)+\left (-60 x+2 x^2+e^{x^2} \left (-120 x^2+4 x^3\right )\right ) \log ^4(-30+x)\right ) \log (x)+e^{x^2} \left (-60 x+2 x^2\right ) \log ^4(-30+x) \log ^2(x)}{-30 x^2+x^3+\left (60 x^2-2 x^3\right ) \log ^2(-30+x)+\left (-30 x^2+x^3\right ) \log ^4(-30+x)+\left (\left (60 x-2 x^2\right ) \log ^2(-30+x)+\left (-60 x+2 x^2\right ) \log ^4(-30+x)\right ) \log (x)+(-30+x) \log ^4(-30+x) \log ^2(x)} \, dx=\frac {x^{2} \log \left (x - 30\right )^{2} + x e^{\left (x^{2}\right )} \log \left (x - 30\right )^{2} + e^{\left (x^{2}\right )} \log \left (x - 30\right )^{2} \log \left (x\right ) - x e^{\left (x^{2}\right )}}{x \log \left (x - 30\right )^{2} + \log \left (x - 30\right )^{2} \log \left (x\right ) - x} \] Input:

integrate(((2*x^2-60*x)*exp(x^2)*log(x-30)^4*log(x)^2+(((4*x^3-120*x^2)*ex 
p(x^2)+2*x^2-60*x)*log(x-30)^4+(-4*x^3+120*x^2)*exp(x^2)*log(x-30)^2)*log( 
x)+((2*x^4-60*x^3)*exp(x^2)+x^3-31*x^2+30*x)*log(x-30)^4+((-4*x^4+120*x^3) 
*exp(x^2)-x^3+30*x^2)*log(x-30)^2-2*x^3*log(x-30)+(2*x^4-60*x^3)*exp(x^2)) 
/((x-30)*log(x-30)^4*log(x)^2+((2*x^2-60*x)*log(x-30)^4+(-2*x^2+60*x)*log( 
x-30)^2)*log(x)+(x^3-30*x^2)*log(x-30)^4+(-2*x^3+60*x^2)*log(x-30)^2+x^3-3 
0*x^2),x, algorithm="giac")
 

Output:

(x^2*log(x - 30)^2 + x*e^(x^2)*log(x - 30)^2 + e^(x^2)*log(x - 30)^2*log(x 
) - x*e^(x^2))/(x*log(x - 30)^2 + log(x - 30)^2*log(x) - x)
 

Mupad [B] (verification not implemented)

Time = 8.01 (sec) , antiderivative size = 317, normalized size of antiderivative = 10.93 \[ \int \frac {e^{x^2} \left (-60 x^3+2 x^4\right )-2 x^3 \log (-30+x)+\left (30 x^2-x^3+e^{x^2} \left (120 x^3-4 x^4\right )\right ) \log ^2(-30+x)+\left (30 x-31 x^2+x^3+e^{x^2} \left (-60 x^3+2 x^4\right )\right ) \log ^4(-30+x)+\left (e^{x^2} \left (120 x^2-4 x^3\right ) \log ^2(-30+x)+\left (-60 x+2 x^2+e^{x^2} \left (-120 x^2+4 x^3\right )\right ) \log ^4(-30+x)\right ) \log (x)+e^{x^2} \left (-60 x+2 x^2\right ) \log ^4(-30+x) \log ^2(x)}{-30 x^2+x^3+\left (60 x^2-2 x^3\right ) \log ^2(-30+x)+\left (-30 x^2+x^3\right ) \log ^4(-30+x)+\left (\left (60 x-2 x^2\right ) \log ^2(-30+x)+\left (-60 x+2 x^2\right ) \log ^4(-30+x)\right ) \log (x)+(-30+x) \log ^4(-30+x) \log ^2(x)} \, dx=2\,x+{\mathrm {e}}^{x^2}+\frac {2}{x+1}-\frac {\frac {x^2\,\left (x-1\right )}{x+1}+\frac {2\,x^2\,\ln \left (x\right )}{x+1}}{x+\ln \left (x\right )}+\frac {x^2\,{\left (30\,x-x^2\right )}^2\,\left (4\,x^4+12\,x^3\,\ln \left (x\right )+11\,x^2\,{\ln \left (x\right )}^2+2\,x^2\,\ln \left (x\right )-x^2+4\,x\,{\ln \left (x\right )}^3+60\,x\,{\ln \left (x\right )}^2-120\,x\,\ln \left (x\right )+60\,x-900\,{\ln \left (x\right )}^2+1800\,\ln \left (x\right )-900\right )}{\left (x-{\ln \left (x-30\right )}^2\,\left (x+\ln \left (x\right )\right )\right )\,\left (x-30\right )\,\left (-4\,x^7-16\,x^6\,\ln \left (x\right )+120\,x^6-23\,x^5\,{\ln \left (x\right )}^2+478\,x^5\,\ln \left (x\right )+x^5-15\,x^4\,{\ln \left (x\right )}^3+628\,x^4\,{\ln \left (x\right )}^2+181\,x^4\,\ln \left (x\right )-90\,x^4-4\,x^3\,{\ln \left (x\right )}^4+390\,x^3\,{\ln \left (x\right )}^3+2880\,x^3\,{\ln \left (x\right )}^2-5490\,x^3\,\ln \left (x\right )+2700\,x^3+120\,x^2\,{\ln \left (x\right )}^4+2700\,x^2\,{\ln \left (x\right )}^3-32400\,x^2\,{\ln \left (x\right )}^2+56700\,x^2\,\ln \left (x\right )-27000\,x^2-27000\,x\,{\ln \left (x\right )}^3+54000\,x\,{\ln \left (x\right )}^2-27000\,x\,\ln \left (x\right )\right )} \] Input:

int(-(exp(x^2)*(60*x^3 - 2*x^4) - log(x - 30)^2*(exp(x^2)*(120*x^3 - 4*x^4 
) + 30*x^2 - x^3) + 2*x^3*log(x - 30) + log(x)*(log(x - 30)^4*(60*x + exp( 
x^2)*(120*x^2 - 4*x^3) - 2*x^2) - log(x - 30)^2*exp(x^2)*(120*x^2 - 4*x^3) 
) - log(x - 30)^4*(30*x - exp(x^2)*(60*x^3 - 2*x^4) - 31*x^2 + x^3) + log( 
x - 30)^4*exp(x^2)*log(x)^2*(60*x - 2*x^2))/(log(x)*(log(x - 30)^2*(60*x - 
 2*x^2) - log(x - 30)^4*(60*x - 2*x^2)) - log(x - 30)^4*(30*x^2 - x^3) + l 
og(x - 30)^2*(60*x^2 - 2*x^3) - 30*x^2 + x^3 + log(x - 30)^4*log(x)^2*(x - 
 30)),x)
 

Output:

2*x + exp(x^2) + 2/(x + 1) - ((x^2*(x - 1))/(x + 1) + (2*x^2*log(x))/(x + 
1))/(x + log(x)) + (x^2*(30*x - x^2)^2*(60*x + 1800*log(x) + 60*x*log(x)^2 
 + 2*x^2*log(x) + 4*x*log(x)^3 + 12*x^3*log(x) - 900*log(x)^2 + 11*x^2*log 
(x)^2 - 120*x*log(x) - x^2 + 4*x^4 - 900))/((x - log(x - 30)^2*(x + log(x) 
))*(x - 30)*(54000*x*log(x)^2 + 56700*x^2*log(x) - 27000*x*log(x)^3 - 5490 
*x^3*log(x) + 181*x^4*log(x) + 478*x^5*log(x) - 16*x^6*log(x) - 32400*x^2* 
log(x)^2 + 2700*x^2*log(x)^3 + 2880*x^3*log(x)^2 + 120*x^2*log(x)^4 + 390* 
x^3*log(x)^3 + 628*x^4*log(x)^2 - 4*x^3*log(x)^4 - 15*x^4*log(x)^3 - 23*x^ 
5*log(x)^2 - 27000*x*log(x) - 27000*x^2 + 2700*x^3 - 90*x^4 + x^5 + 120*x^ 
6 - 4*x^7))
 

Reduce [B] (verification not implemented)

Time = 0.18 (sec) , antiderivative size = 70, normalized size of antiderivative = 2.41 \[ \int \frac {e^{x^2} \left (-60 x^3+2 x^4\right )-2 x^3 \log (-30+x)+\left (30 x^2-x^3+e^{x^2} \left (120 x^3-4 x^4\right )\right ) \log ^2(-30+x)+\left (30 x-31 x^2+x^3+e^{x^2} \left (-60 x^3+2 x^4\right )\right ) \log ^4(-30+x)+\left (e^{x^2} \left (120 x^2-4 x^3\right ) \log ^2(-30+x)+\left (-60 x+2 x^2+e^{x^2} \left (-120 x^2+4 x^3\right )\right ) \log ^4(-30+x)\right ) \log (x)+e^{x^2} \left (-60 x+2 x^2\right ) \log ^4(-30+x) \log ^2(x)}{-30 x^2+x^3+\left (60 x^2-2 x^3\right ) \log ^2(-30+x)+\left (-30 x^2+x^3\right ) \log ^4(-30+x)+\left (\left (60 x-2 x^2\right ) \log ^2(-30+x)+\left (-60 x+2 x^2\right ) \log ^4(-30+x)\right ) \log (x)+(-30+x) \log ^4(-30+x) \log ^2(x)} \, dx=\frac {e^{x^{2}} \mathrm {log}\left (x -30\right )^{2} \mathrm {log}\left (x \right )+e^{x^{2}} \mathrm {log}\left (x -30\right )^{2} x -e^{x^{2}} x +\mathrm {log}\left (x -30\right )^{2} x^{2}}{\mathrm {log}\left (x -30\right )^{2} \mathrm {log}\left (x \right )+\mathrm {log}\left (x -30\right )^{2} x -x} \] Input:

int(((2*x^2-60*x)*exp(x^2)*log(x-30)^4*log(x)^2+(((4*x^3-120*x^2)*exp(x^2) 
+2*x^2-60*x)*log(x-30)^4+(-4*x^3+120*x^2)*exp(x^2)*log(x-30)^2)*log(x)+((2 
*x^4-60*x^3)*exp(x^2)+x^3-31*x^2+30*x)*log(x-30)^4+((-4*x^4+120*x^3)*exp(x 
^2)-x^3+30*x^2)*log(x-30)^2-2*x^3*log(x-30)+(2*x^4-60*x^3)*exp(x^2))/((x-3 
0)*log(x-30)^4*log(x)^2+((2*x^2-60*x)*log(x-30)^4+(-2*x^2+60*x)*log(x-30)^ 
2)*log(x)+(x^3-30*x^2)*log(x-30)^4+(-2*x^3+60*x^2)*log(x-30)^2+x^3-30*x^2) 
,x)
 

Output:

(e**(x**2)*log(x - 30)**2*log(x) + e**(x**2)*log(x - 30)**2*x - e**(x**2)* 
x + log(x - 30)**2*x**2)/(log(x - 30)**2*log(x) + log(x - 30)**2*x - x)