\(\int \frac {-305156281250-73279658750 x-7328903800 x^2-390814950 x^3-11721300 x^4-187500 x^5-1250 x^6+(-1464781300-234497450 x-14070000 x^2-375100 x^3-3750 x^4) \log (x)+(-2343700-187600 x-3750 x^2) \log ^2(x)-1250 \log ^3(x)}{3813964890624 x^3+916142488128 x^4+91662930072 x^5+4889659851 x^6+146670075 x^7+2345625 x^8+15625 x^9+(18308203200 x^3+2931843600 x^4+175965075 x^5+4691250 x^6+46875 x^7) \log (x)+(29295000 x^3+2345625 x^4+46875 x^5) \log ^2(x)+15625 x^3 \log ^3(x)} \, dx\) [2092]

Optimal result

Integrand size = 172, antiderivative size = 25 \[ \int \frac {-305156281250-73279658750 x-7328903800 x^2-390814950 x^3-11721300 x^4-187500 x^5-1250 x^6+\left (-1464781300-234497450 x-14070000 x^2-375100 x^3-3750 x^4\right ) \log (x)+\left (-2343700-187600 x-3750 x^2\right ) \log ^2(x)-1250 \log ^3(x)}{3813964890624 x^3+916142488128 x^4+91662930072 x^5+4889659851 x^6+146670075 x^7+2345625 x^8+15625 x^9+\left (18308203200 x^3+2931843600 x^4+175965075 x^5+4691250 x^6+46875 x^7\right ) \log (x)+\left (29295000 x^3+2345625 x^4+46875 x^5\right ) \log ^2(x)+15625 x^3 \log ^3(x)} \, dx=\frac {1}{x^2 \left (5+\frac {-1+x}{5 \left ((25+x)^2+\log (x)\right )}\right )^2} \] Output:

1/(1/5*(-1+x)/((x+25)^2+ln(x))+5)^2/x^2
                                                                                    
                                                                                    
 

Mathematica [A] (verified)

Time = 0.03 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.24 \[ \int \frac {-305156281250-73279658750 x-7328903800 x^2-390814950 x^3-11721300 x^4-187500 x^5-1250 x^6+\left (-1464781300-234497450 x-14070000 x^2-375100 x^3-3750 x^4\right ) \log (x)+\left (-2343700-187600 x-3750 x^2\right ) \log ^2(x)-1250 \log ^3(x)}{3813964890624 x^3+916142488128 x^4+91662930072 x^5+4889659851 x^6+146670075 x^7+2345625 x^8+15625 x^9+\left (18308203200 x^3+2931843600 x^4+175965075 x^5+4691250 x^6+46875 x^7\right ) \log (x)+\left (29295000 x^3+2345625 x^4+46875 x^5\right ) \log ^2(x)+15625 x^3 \log ^3(x)} \, dx=\frac {25 \left ((25+x)^2+\log (x)\right )^2}{x^2 \left (15624+1251 x+25 x^2+25 \log (x)\right )^2} \] Input:

Integrate[(-305156281250 - 73279658750*x - 7328903800*x^2 - 390814950*x^3 
- 11721300*x^4 - 187500*x^5 - 1250*x^6 + (-1464781300 - 234497450*x - 1407 
0000*x^2 - 375100*x^3 - 3750*x^4)*Log[x] + (-2343700 - 187600*x - 3750*x^2 
)*Log[x]^2 - 1250*Log[x]^3)/(3813964890624*x^3 + 916142488128*x^4 + 916629 
30072*x^5 + 4889659851*x^6 + 146670075*x^7 + 2345625*x^8 + 15625*x^9 + (18 
308203200*x^3 + 2931843600*x^4 + 175965075*x^5 + 4691250*x^6 + 46875*x^7)* 
Log[x] + (29295000*x^3 + 2345625*x^4 + 46875*x^5)*Log[x]^2 + 15625*x^3*Log 
[x]^3),x]
 

Output:

(25*((25 + x)^2 + Log[x])^2)/(x^2*(15624 + 1251*x + 25*x^2 + 25*Log[x])^2)
 

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.

\(\displaystyle \int \frac {-1250 x^6-187500 x^5-11721300 x^4-390814950 x^3-7328903800 x^2+\left (-3750 x^2-187600 x-2343700\right ) \log ^2(x)+\left (-3750 x^4-375100 x^3-14070000 x^2-234497450 x-1464781300\right ) \log (x)-73279658750 x-1250 \log ^3(x)-305156281250}{15625 x^9+2345625 x^8+146670075 x^7+4889659851 x^6+91662930072 x^5+916142488128 x^4+3813964890624 x^3+15625 x^3 \log ^3(x)+\left (46875 x^5+2345625 x^4+29295000 x^3\right ) \log ^2(x)+\left (46875 x^7+4691250 x^6+175965075 x^5+2931843600 x^4+18308203200 x^3\right ) \log (x)} \, dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {50 \left (-\left (75 x^2+3752 x+46874\right ) \log ^2(x)-(x+25)^2 \left (25 x^4+2500 x^3+93801 x^2+1563749 x+9765001\right )-\left (75 x^4+7502 x^3+281400 x^2+4689949 x+29295626\right ) \log (x)-25 \log ^3(x)\right )}{x^3 \left (25 x^2+1251 x+25 \log (x)+15624\right )^3}dx\)

\(\Big \downarrow \) 27

\(\displaystyle 50 \int -\frac {25 \log ^3(x)+\left (75 x^2+3752 x+46874\right ) \log ^2(x)+\left (75 x^4+7502 x^3+281400 x^2+4689949 x+29295626\right ) \log (x)+(x+25)^2 \left (25 x^4+2500 x^3+93801 x^2+1563749 x+9765001\right )}{x^3 \left (25 x^2+1251 x+25 \log (x)+15624\right )^3}dx\)

\(\Big \downarrow \) 25

\(\displaystyle -50 \int \frac {25 \log ^3(x)+\left (75 x^2+3752 x+46874\right ) \log ^2(x)+\left (75 x^4+7502 x^3+281400 x^2+4689949 x+29295626\right ) \log (x)+(x+25)^2 \left (25 x^4+2500 x^3+93801 x^2+1563749 x+9765001\right )}{x^3 \left (25 x^2+1251 x+25 \log (x)+15624\right )^3}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -50 \int \left (\frac {\left (50 x^2+1251 x+25\right ) (x-1)^2}{625 x^3 \left (25 x^2+1251 x+25 \log (x)+15624\right )^3}+\frac {2-x}{625 x^3 \left (25 x^2+1251 x+25 \log (x)+15624\right )}+\frac {-50 x^3-1201 x^2+1225 x+26}{625 x^3 \left (25 x^2+1251 x+25 \log (x)+15624\right )^2}+\frac {1}{625 x^3}\right )dx\)

\(\Big \downarrow \) 2009

\(\displaystyle -50 \left (\frac {1151}{625} \int \frac {1}{\left (25 x^2+1251 x+25 \log (x)+15624\right )^3}dx+\frac {1201}{625} \int \frac {1}{x^2 \left (25 x^2+1251 x+25 \log (x)+15624\right )^3}dx-\frac {2427}{625} \int \frac {1}{x \left (25 x^2+1251 x+25 \log (x)+15624\right )^3}dx+\frac {2}{25} \int \frac {x}{\left (25 x^2+1251 x+25 \log (x)+15624\right )^3}dx-\frac {2}{25} \int \frac {1}{\left (25 x^2+1251 x+25 \log (x)+15624\right )^2}dx+\frac {49}{25} \int \frac {1}{x^2 \left (25 x^2+1251 x+25 \log (x)+15624\right )^2}dx-\frac {1201}{625} \int \frac {1}{x \left (25 x^2+1251 x+25 \log (x)+15624\right )^2}dx-\frac {1}{625} \int \frac {1}{x^2 \left (25 x^2+1251 x+25 \log (x)+15624\right )}dx+\frac {1}{25} \int \frac {1}{x^3 \left (25 x^2+1251 x+25 \log (x)+15624\right )^3}dx+\frac {26}{625} \int \frac {1}{x^3 \left (25 x^2+1251 x+25 \log (x)+15624\right )^2}dx+\frac {2}{625} \int \frac {1}{x^3 \left (25 x^2+1251 x+25 \log (x)+15624\right )}dx-\frac {1}{1250 x^2}\right )\)

Input:

Int[(-305156281250 - 73279658750*x - 7328903800*x^2 - 390814950*x^3 - 1172 
1300*x^4 - 187500*x^5 - 1250*x^6 + (-1464781300 - 234497450*x - 14070000*x 
^2 - 375100*x^3 - 3750*x^4)*Log[x] + (-2343700 - 187600*x - 3750*x^2)*Log[ 
x]^2 - 1250*Log[x]^3)/(3813964890624*x^3 + 916142488128*x^4 + 91662930072* 
x^5 + 4889659851*x^6 + 146670075*x^7 + 2345625*x^8 + 15625*x^9 + (18308203 
200*x^3 + 2931843600*x^4 + 175965075*x^5 + 4691250*x^6 + 46875*x^7)*Log[x] 
 + (29295000*x^3 + 2345625*x^4 + 46875*x^5)*Log[x]^2 + 15625*x^3*Log[x]^3) 
,x]
 

Output:

$Aborted
 

Maple [B] (verified)

Leaf count of result is larger than twice the leaf count of optimal. \(51\) vs. \(2(23)=46\).

Time = 3.84 (sec) , antiderivative size = 52, normalized size of antiderivative = 2.08

method	result	size
risch	\(\frac {1}{25 x^{2}}-\frac {50 x^{3}+2451 x^{2}+50 x \ln \left (x \right )+28748 x -50 \ln \left (x \right )-31249}{25 x^{2} \left (25 x^{2}+25 \ln \left (x \right )+1251 x +15624\right )^{2}}\)	\(52\)
parallelrisch	\(\frac {6103515625+976562500 x +31250 x^{2} \ln \left (x \right )+1562500 x \ln \left (x \right )[phone] \ln \left (x \right )+15625 \ln \left (x \right )^{2}[phone] x^{2}+1562500 x^{3}+15625 x^{4}}{625 x^{2} \left (625 x^{4}+62550 x^{3}+1250 x^{2} \ln \left (x \right )+2346201 x^{2}+62550 x \ln \left (x \right )+625 \ln \left (x \right )^{2}[phone] x +781200 \ln \left (x \right )[phone]\right )}\)	\(92\)
default	\(-\frac {50 \left (\ln \left (x \right )^{2}+1300 \ln \left (x \right )+421875\right )}{\left (15624+25 \ln \left (x \right )\right )^{3} x}+\frac {25 \ln \left (x \right )^{2}+31250 \ln \left (x \right )+9765625}{\left (15624+25 \ln \left (x \right )\right )^{2} x^{2}}+\frac {31250 x^{3} \ln \left (x \right )^{2}+31250 x \ln \left (x \right )^{3}+3096250 x^{2} \ln \left (x \right )^{2}[phone] x^{3} \ln \left (x \right )+1533125 \ln \left (x \right )^{3}[phone] x \ln \left (x \right )^{2}[phone] x^{2} \ln \left (x \right )[phone] x^{3}[phone] \ln \left (x \right )^{2}[phone] x \ln \left (x \right )[phone] x^{2}[phone] \ln \left (x \right )[phone] x [phone]}{\left (25 x^{2}+25 \ln \left (x \right )+1251 x +15624\right )^{2} \left (15624+25 \ln \left (x \right )\right ) \left (625 \ln \left (x \right )^{2}+781200 \ln \left (x \right )[phone]\right )}\)	\(170\)

Input:

int((-1250*ln(x)^3+(-3750*x^2-187600*x-2343700)*ln(x)^2+(-3750*x^4-375100* 
x^3-14070000*x^2-234497450*x-1464781300)*ln(x)-1250*x^6-187500*x^5-1172130 
0*x^4-390814950*x^3-7328903800*x^2-73279658750*x-305156281250)/(15625*x^3* 
ln(x)^3+(46875*x^5+2345625*x^4+29295000*x^3)*ln(x)^2+(46875*x^7+4691250*x^ 
6+175965075*x^5+2931843600*x^4+18308203200*x^3)*ln(x)+15625*x^9+2345625*x^ 
8+146670075*x^7+4889659851*x^6+91662930072*x^5+916142488128*x^4+3813964890 
624*x^3),x,method=_RETURNVERBOSE)
 

Output:

1/25/x^2-1/25*(50*x^3+2451*x^2+50*x*ln(x)+28748*x-50*ln(x)-31249)/x^2/(25* 
x^2+25*ln(x)+1251*x+15624)^2
 

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 93 vs. \(2 (23) = 46\).

Time = 0.10 (sec) , antiderivative size = 93, normalized size of antiderivative = 3.72 \[ \int \frac {-305156281250-73279658750 x-7328903800 x^2-390814950 x^3-11721300 x^4-187500 x^5-1250 x^6+\left (-1464781300-234497450 x-14070000 x^2-375100 x^3-3750 x^4\right ) \log (x)+\left (-2343700-187600 x-3750 x^2\right ) \log ^2(x)-1250 \log ^3(x)}{3813964890624 x^3+916142488128 x^4+91662930072 x^5+4889659851 x^6+146670075 x^7+2345625 x^8+15625 x^9+\left (18308203200 x^3+2931843600 x^4+175965075 x^5+4691250 x^6+46875 x^7\right ) \log (x)+\left (29295000 x^3+2345625 x^4+46875 x^5\right ) \log ^2(x)+15625 x^3 \log ^3(x)} \, dx=\frac {25 \, {\left (x^{4} + 100 \, x^{3} + 3750 \, x^{2} + 2 \, {\left (x^{2} + 50 \, x + 625\right )} \log \left (x\right ) + \log \left (x\right )^{2} + 62500 \, x + 390625\right )}}{625 \, x^{6} + 62550 \, x^{5} + 2346201 \, x^{4} + 625 \, x^{2} \log \left (x\right )^{2} + 39091248 \, x^{3} + 244109376 \, x^{2} + 50 \, {\left (25 \, x^{4} + 1251 \, x^{3} + 15624 \, x^{2}\right )} \log \left (x\right )} \] Input:

integrate((-1250*log(x)^3+(-3750*x^2-187600*x-2343700)*log(x)^2+(-3750*x^4 
-375100*x^3-14070000*x^2-234497450*x-1464781300)*log(x)-1250*x^6-187500*x^ 
5-11721300*x^4-390814950*x^3-7328903800*x^2-73279658750*x-305156281250)/(1 
5625*x^3*log(x)^3+(46875*x^5+2345625*x^4+29295000*x^3)*log(x)^2+(46875*x^7 
+4691250*x^6+175965075*x^5+2931843600*x^4+18308203200*x^3)*log(x)+15625*x^ 
9+2345625*x^8+146670075*x^7+4889659851*x^6+91662930072*x^5+916142488128*x^ 
4+3813964890624*x^3),x, algorithm="fricas")
 

Output:

25*(x^4 + 100*x^3 + 3750*x^2 + 2*(x^2 + 50*x + 625)*log(x) + log(x)^2 + 62 
500*x + 390625)/(625*x^6 + 62550*x^5 + 2346201*x^4 + 625*x^2*log(x)^2 + 39 
091248*x^3 + 244109376*x^2 + 50*(25*x^4 + 1251*x^3 + 15624*x^2)*log(x))
 

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 83 vs. \(2 (22) = 44\).

Time = 0.12 (sec) , antiderivative size = 83, normalized size of antiderivative = 3.32 \[ \int \frac {-305156281250-73279658750 x-7328903800 x^2-390814950 x^3-11721300 x^4-187500 x^5-1250 x^6+\left (-1464781300-234497450 x-14070000 x^2-375100 x^3-3750 x^4\right ) \log (x)+\left (-2343700-187600 x-3750 x^2\right ) \log ^2(x)-1250 \log ^3(x)}{3813964890624 x^3+916142488128 x^4+91662930072 x^5+4889659851 x^6+146670075 x^7+2345625 x^8+15625 x^9+\left (18308203200 x^3+2931843600 x^4+175965075 x^5+4691250 x^6+46875 x^7\right ) \log (x)+\left (29295000 x^3+2345625 x^4+46875 x^5\right ) \log ^2(x)+15625 x^3 \log ^3(x)} \, dx=\frac {- 50 x^{3} - 2451 x^{2} - 28748 x + \left (50 - 50 x\right ) \log {\left (x \right )} + 31249}{15625 x^{6} + 1563750 x^{5} + 58655025 x^{4} + 977281200 x^{3} + 15625 x^{2} \log {\left (x \right )}^{2} + 6102734400 x^{2} + \left (31250 x^{4} + 1563750 x^{3} + 19530000 x^{2}\right ) \log {\left (x \right )}} + \frac {1}{25 x^{2}} \] Input:

integrate((-1250*ln(x)**3+(-3750*x**2-187600*x-2343700)*ln(x)**2+(-3750*x* 
*4-375100*x**3-14070000*x**2-234497450*x-1464781300)*ln(x)-1250*x**6-18750 
0*x**5-11721300*x**4-390814950*x**3-7328903800*x**2-73279658750*x-30515628 
1250)/(15625*x**3*ln(x)**3+(46875*x**5+2345625*x**4+29295000*x**3)*ln(x)** 
2+(46875*x**7+4691250*x**6+175965075*x**5+2931843600*x**4+18308203200*x**3 
)*ln(x)+15625*x**9+2345625*x**8+146670075*x**7+4889659851*x**6+91662930072 
*x**5+916142488128*x**4+3813964890624*x**3),x)
 

Output:

(-50*x**3 - 2451*x**2 - 28748*x + (50 - 50*x)*log(x) + 31249)/(15625*x**6 
+ 1563750*x**5 + 58655025*x**4 + 977281200*x**3 + 15625*x**2*log(x)**2 + 6 
102734400*x**2 + (31250*x**4 + 1563750*x**3 + 19530000*x**2)*log(x)) + 1/( 
25*x**2)
 

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 93 vs. \(2 (23) = 46\).

Time = 0.07 (sec) , antiderivative size = 93, normalized size of antiderivative = 3.72 \[ \int \frac {-305156281250-73279658750 x-7328903800 x^2-390814950 x^3-11721300 x^4-187500 x^5-1250 x^6+\left (-1464781300-234497450 x-14070000 x^2-375100 x^3-3750 x^4\right ) \log (x)+\left (-2343700-187600 x-3750 x^2\right ) \log ^2(x)-1250 \log ^3(x)}{3813964890624 x^3+916142488128 x^4+91662930072 x^5+4889659851 x^6+146670075 x^7+2345625 x^8+15625 x^9+\left (18308203200 x^3+2931843600 x^4+175965075 x^5+4691250 x^6+46875 x^7\right ) \log (x)+\left (29295000 x^3+2345625 x^4+46875 x^5\right ) \log ^2(x)+15625 x^3 \log ^3(x)} \, dx=\frac {25 \, {\left (x^{4} + 100 \, x^{3} + 3750 \, x^{2} + 2 \, {\left (x^{2} + 50 \, x + 625\right )} \log \left (x\right ) + \log \left (x\right )^{2} + 62500 \, x + 390625\right )}}{625 \, x^{6} + 62550 \, x^{5} + 2346201 \, x^{4} + 625 \, x^{2} \log \left (x\right )^{2} + 39091248 \, x^{3} + 244109376 \, x^{2} + 50 \, {\left (25 \, x^{4} + 1251 \, x^{3} + 15624 \, x^{2}\right )} \log \left (x\right )} \] Input:

integrate((-1250*log(x)^3+(-3750*x^2-187600*x-2343700)*log(x)^2+(-3750*x^4 
-375100*x^3-14070000*x^2-234497450*x-1464781300)*log(x)-1250*x^6-187500*x^ 
5-11721300*x^4-390814950*x^3-7328903800*x^2-73279658750*x-305156281250)/(1 
5625*x^3*log(x)^3+(46875*x^5+2345625*x^4+29295000*x^3)*log(x)^2+(46875*x^7 
+4691250*x^6+175965075*x^5+2931843600*x^4+18308203200*x^3)*log(x)+15625*x^ 
9+2345625*x^8+146670075*x^7+4889659851*x^6+91662930072*x^5+916142488128*x^ 
4+3813964890624*x^3),x, algorithm="maxima")
 

Output:

25*(x^4 + 100*x^3 + 3750*x^2 + 2*(x^2 + 50*x + 625)*log(x) + log(x)^2 + 62 
500*x + 390625)/(625*x^6 + 62550*x^5 + 2346201*x^4 + 625*x^2*log(x)^2 + 39 
091248*x^3 + 244109376*x^2 + 50*(25*x^4 + 1251*x^3 + 15624*x^2)*log(x))
 

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 90 vs. \(2 (23) = 46\).

Time = 0.13 (sec) , antiderivative size = 90, normalized size of antiderivative = 3.60 \[ \int \frac {-305156281250-73279658750 x-7328903800 x^2-390814950 x^3-11721300 x^4-187500 x^5-1250 x^6+\left (-1464781300-234497450 x-14070000 x^2-375100 x^3-3750 x^4\right ) \log (x)+\left (-2343700-187600 x-3750 x^2\right ) \log ^2(x)-1250 \log ^3(x)}{3813964890624 x^3+916142488128 x^4+91662930072 x^5+4889659851 x^6+146670075 x^7+2345625 x^8+15625 x^9+\left (18308203200 x^3+2931843600 x^4+175965075 x^5+4691250 x^6+46875 x^7\right ) \log (x)+\left (29295000 x^3+2345625 x^4+46875 x^5\right ) \log ^2(x)+15625 x^3 \log ^3(x)} \, dx=-\frac {50 \, x^{3} + 2451 \, x^{2} + 50 \, x \log \left (x\right ) + 28748 \, x - 50 \, \log \left (x\right ) - 31249}{25 \, {\left (625 \, x^{6} + 62550 \, x^{5} + 1250 \, x^{4} \log \left (x\right ) + 2346201 \, x^{4} + 62550 \, x^{3} \log \left (x\right ) + 625 \, x^{2} \log \left (x\right )^{2} + 39091248 \, x^{3} + 781200 \, x^{2} \log \left (x\right ) + 244109376 \, x^{2}\right )}} + \frac {1}{25 \, x^{2}} \] Input:

integrate((-1250*log(x)^3+(-3750*x^2-187600*x-2343700)*log(x)^2+(-3750*x^4 
-375100*x^3-14070000*x^2-234497450*x-1464781300)*log(x)-1250*x^6-187500*x^ 
5-11721300*x^4-390814950*x^3-7328903800*x^2-73279658750*x-305156281250)/(1 
5625*x^3*log(x)^3+(46875*x^5+2345625*x^4+29295000*x^3)*log(x)^2+(46875*x^7 
+4691250*x^6+175965075*x^5+2931843600*x^4+18308203200*x^3)*log(x)+15625*x^ 
9+2345625*x^8+146670075*x^7+4889659851*x^6+91662930072*x^5+916142488128*x^ 
4+3813964890624*x^3),x, algorithm="giac")
 

Output:

-1/25*(50*x^3 + 2451*x^2 + 50*x*log(x) + 28748*x - 50*log(x) - 31249)/(625 
*x^6 + 62550*x^5 + 1250*x^4*log(x) + 2346201*x^4 + 62550*x^3*log(x) + 625* 
x^2*log(x)^2 + 39091248*x^3 + 781200*x^2*log(x) + 244109376*x^2) + 1/25/x^ 
2
 

Mupad [F(-1)]

Timed out. \[ \int \frac {-305156281250-73279658750 x-7328903800 x^2-390814950 x^3-11721300 x^4-187500 x^5-1250 x^6+\left (-1464781300-234497450 x-14070000 x^2-375100 x^3-3750 x^4\right ) \log (x)+\left (-2343700-187600 x-3750 x^2\right ) \log ^2(x)-1250 \log ^3(x)}{3813964890624 x^3+916142488128 x^4+91662930072 x^5+4889659851 x^6+146670075 x^7+2345625 x^8+15625 x^9+\left (18308203200 x^3+2931843600 x^4+175965075 x^5+4691250 x^6+46875 x^7\right ) \log (x)+\left (29295000 x^3+2345625 x^4+46875 x^5\right ) \log ^2(x)+15625 x^3 \log ^3(x)} \, dx=\int -\frac {73279658750\,x+{\ln \left (x\right )}^2\,\left (3750\,x^2+187600\,x+2343700\right )+1250\,{\ln \left (x\right )}^3+\ln \left (x\right )\,\left (3750\,x^4+375100\,x^3+14070000\,x^2+234497450\,x+1464781300\right )[phone]\,x^2+390814950\,x^3+11721300\,x^4+187500\,x^5+1250\,x^6+305156281250}{15625\,x^3\,{\ln \left (x\right )}^3+{\ln \left (x\right )}^2\,\left (46875\,x^5+2345625\,x^4+29295000\,x^3\right )+\ln \left (x\right )\,\left (46875\,x^7+4691250\,x^6+175965075\,x^5+2931843600\,x^4+18308203200\,x^3\right )[phone]\,x^3+916142488128\,x^4+91662930072\,x^5+4889659851\,x^6+146670075\,x^7+2345625\,x^8+15625\,x^9} \,d x \] Input:

int(-(73279658750*x + log(x)^2*(187600*x + 3750*x^2 + 2343700) + 1250*log( 
x)^3 + log(x)*(234497450*x + 14070000*x^2 + 375100*x^3 + 3750*x^4 + 146478 
1300) + 7328903800*x^2 + 390814950*x^3 + 11721300*x^4 + 187500*x^5 + 1250* 
x^6 + 305156281250)/(15625*x^3*log(x)^3 + log(x)^2*(29295000*x^3 + 2345625 
*x^4 + 46875*x^5) + log(x)*(18308203200*x^3 + 2931843600*x^4 + 175965075*x 
^5 + 4691250*x^6 + 46875*x^7) + 3813964890624*x^3 + 916142488128*x^4 + 916 
62930072*x^5 + 4889659851*x^6 + 146670075*x^7 + 2345625*x^8 + 15625*x^9),x 
)
 

Output:

int(-(73279658750*x + log(x)^2*(187600*x + 3750*x^2 + 2343700) + 1250*log( 
x)^3 + log(x)*(234497450*x + 14070000*x^2 + 375100*x^3 + 3750*x^4 + 146478 
1300) + 7328903800*x^2 + 390814950*x^3 + 11721300*x^4 + 187500*x^5 + 1250* 
x^6 + 305156281250)/(15625*x^3*log(x)^3 + log(x)^2*(29295000*x^3 + 2345625 
*x^4 + 46875*x^5) + log(x)*(18308203200*x^3 + 2931843600*x^4 + 175965075*x 
^5 + 4691250*x^6 + 46875*x^7) + 3813964890624*x^3 + 916142488128*x^4 + 916 
62930072*x^5 + 4889659851*x^6 + 146670075*x^7 + 2345625*x^8 + 15625*x^9), 
x)
 

Reduce [B] (verification not implemented)

Time = 0.17 (sec) , antiderivative size = 119, normalized size of antiderivative = 4.76 \[ \int \frac {-305156281250-73279658750 x-7328903800 x^2-390814950 x^3-11721300 x^4-187500 x^5-1250 x^6+\left (-1464781300-234497450 x-14070000 x^2-375100 x^3-3750 x^4\right ) \log (x)+\left (-2343700-187600 x-3750 x^2\right ) \log ^2(x)-1250 \log ^3(x)}{3813964890624 x^3+916142488128 x^4+91662930072 x^5+4889659851 x^6+146670075 x^7+2345625 x^8+15625 x^9+\left (18308203200 x^3+2931843600 x^4+175965075 x^5+4691250 x^6+46875 x^7\right ) \log (x)+\left (29295000 x^3+2345625 x^4+46875 x^5\right ) \log ^2(x)+15625 x^3 \log ^3(x)} \, dx=\frac {-\frac {15625 \mathrm {log}\left (x \right )^{2} x^{2}}{2346201}+25 \mathrm {log}\left (x \right )^{2}-\frac {31250 \,\mathrm {log}\left (x \right ) x^{4}}{2346201}-\frac {173750 \,\mathrm {log}\left (x \right ) x^{3}}{260689}+\frac {10864450 \,\mathrm {log}\left (x \right ) x^{2}}{260689}+2500 \,\mathrm {log}\left (x \right ) x +31250 \,\mathrm {log}\left (x \right )-\frac {15625 x^{6}}{2346201}-\frac {173750 x^{5}}{260689}+\frac {543135700 x^{3}}{260689}+\frac {23761512150 x^{2}}{260689}+1562500 x +9765625}{x^{2} \left (625 \mathrm {log}\left (x \right )^{2}+1250 \,\mathrm {log}\left (x \right ) x^{2}+62550 \,\mathrm {log}\left (x \right ) x +781200 \,\mathrm {log}\left (x \right )+625 x^{4}+62550 x^{3}+2346201 x^{2}[phone] x [phone]\right )} \] Input:

int((-1250*log(x)^3+(-3750*x^2-187600*x-2343700)*log(x)^2+(-3750*x^4-37510 
0*x^3-14070000*x^2-234497450*x-1464781300)*log(x)-1250*x^6-187500*x^5-1172 
1300*x^4-390814950*x^3-7328903800*x^2-73279658750*x-305156281250)/(15625*x 
^3*log(x)^3+(46875*x^5+2345625*x^4+29295000*x^3)*log(x)^2+(46875*x^7+46912 
50*x^6+175965075*x^5+2931843600*x^4+18308203200*x^3)*log(x)+15625*x^9+2345 
625*x^8+146670075*x^7+4889659851*x^6+91662930072*x^5+916142488128*x^4+3813 
964890624*x^3),x)
 

Output:

(25*( - 625*log(x)**2*x**2 + 2346201*log(x)**2 - 1250*log(x)*x**4 - 62550* 
log(x)*x**3 + 3911202*log(x)*x**2 + 234620100*log(x)*x + 2932751250*log(x) 
 - 625*x**6 - 62550*x**5 + 195528852*x**3 + 8554144374*x**2 + 146637562500 
*x + 916484765625))/(2346201*x**2*(625*log(x)**2 + 1250*log(x)*x**2 + 6255 
0*log(x)*x + 781200*log(x) + 625*x**4 + 62550*x**3 + 2346201*x**2 + 390912 
48*x + 244109376))