\(\int \frac {3 x^3-x^4+(3 x+x^2) \log (\frac {16}{5})+(2 x^4-2 x^2 \log (\frac {16}{5})+(-6 x^3+6 x \log (\frac {16}{5})) \log (\frac {x^2-\log (\frac {16}{5})}{x})) \log (\frac {1}{3} (x-3 \log (\frac {x^2-\log (\frac {16}{5})}{x})))}{(x^3-x \log (\frac {16}{5})+(-3 x^2+3 \log (\frac {16}{5})) \log (\frac {x^2-\log (\frac {16}{5})}{x})) \log ^2(\frac {1}{3} (x-3 \log (\frac {x^2-\log (\frac {16}{5})}{x})))} \, dx\) [2044]

Optimal result

Integrand size = 160, antiderivative size = 27 \[ \int \frac {3 x^3-x^4+\left (3 x+x^2\right ) \log \left (\frac {16}{5}\right )+\left (2 x^4-2 x^2 \log \left (\frac {16}{5}\right )+\left (-6 x^3+6 x \log \left (\frac {16}{5}\right )\right ) \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log \left (\frac {1}{3} \left (x-3 \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )}{\left (x^3-x \log \left (\frac {16}{5}\right )+\left (-3 x^2+3 \log \left (\frac {16}{5}\right )\right ) \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log ^2\left (\frac {1}{3} \left (x-3 \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )} \, dx=\frac {x^2}{\log \left (\frac {x}{3}-\log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right )} \] Output:

x^2/ln(1/3*x-ln(x-ln(16/5)/x))
 

Mathematica [A] (verified)

Time = 0.04 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.00 \[ \int \frac {3 x^3-x^4+\left (3 x+x^2\right ) \log \left (\frac {16}{5}\right )+\left (2 x^4-2 x^2 \log \left (\frac {16}{5}\right )+\left (-6 x^3+6 x \log \left (\frac {16}{5}\right )\right ) \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log \left (\frac {1}{3} \left (x-3 \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )}{\left (x^3-x \log \left (\frac {16}{5}\right )+\left (-3 x^2+3 \log \left (\frac {16}{5}\right )\right ) \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log ^2\left (\frac {1}{3} \left (x-3 \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )} \, dx=\frac {x^2}{\log \left (\frac {1}{3} \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )} \] Input:

Integrate[(3*x^3 - x^4 + (3*x + x^2)*Log[16/5] + (2*x^4 - 2*x^2*Log[16/5] 
+ (-6*x^3 + 6*x*Log[16/5])*Log[(x^2 - Log[16/5])/x])*Log[(x - 3*Log[(x^2 - 
 Log[16/5])/x])/3])/((x^3 - x*Log[16/5] + (-3*x^2 + 3*Log[16/5])*Log[(x^2 
- Log[16/5])/x])*Log[(x - 3*Log[(x^2 - Log[16/5])/x])/3]^2),x]
 

Output:

x^2/Log[(x - 3*Log[x - Log[16/5]/x])/3]
 

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.

\(\displaystyle \int \frac {-x^4+3 x^3+\left (x^2+3 x\right ) \log \left (\frac {16}{5}\right )+\left (2 x^4-2 x^2 \log \left (\frac {16}{5}\right )+\left (6 x \log \left (\frac {16}{5}\right )-6 x^3\right ) \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log \left (\frac {1}{3} \left (x-3 \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )}{\left (x^3+\left (3 \log \left (\frac {16}{5}\right )-3 x^2\right ) \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )-x \log \left (\frac {16}{5}\right )\right ) \log ^2\left (\frac {1}{3} \left (x-3 \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )} \, dx\)

\(\Big \downarrow \) 7292

\(\displaystyle \int \frac {-x^4+3 x^3+\left (x^2+3 x\right ) \log \left (\frac {16}{5}\right )+\left (2 x^4-2 x^2 \log \left (\frac {16}{5}\right )+\left (6 x \log \left (\frac {16}{5}\right )-6 x^3\right ) \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log \left (\frac {1}{3} \left (x-3 \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )}{\left (x^2-\log \left (\frac {16}{5}\right )\right ) \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log ^2\left (\frac {1}{3} \left (x-3 \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )}dx\)

\(\Big \downarrow \) 7276

\(\displaystyle \int \left (\frac {2 x}{\log \left (\frac {1}{3} \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )}-\frac {x \left (x^3-3 x^2-x \log \left (\frac {16}{5}\right )-3 \log \left (\frac {16}{5}\right )\right )}{\left (x^2-\log \left (\frac {16}{5}\right )\right ) \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log ^2\left (\frac {1}{3} \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )}\right )dx\)

\(\Big \downarrow \) 2009

\(\displaystyle -\int \frac {x^2}{\left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log ^2\left (\frac {1}{3} \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )}dx+3 \int \frac {x}{\left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log ^2\left (\frac {1}{3} \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )}dx-3 \log \left (\frac {16}{5}\right ) \int \frac {1}{\left (\sqrt {\log \left (\frac {16}{5}\right )}-x\right ) \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log ^2\left (\frac {1}{3} \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )}dx+3 \log \left (\frac {16}{5}\right ) \int \frac {1}{\left (x+\sqrt {\log \left (\frac {16}{5}\right )}\right ) \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log ^2\left (\frac {1}{3} \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )}dx+2 \int \frac {x}{\log \left (\frac {1}{3} \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )}dx\)

Input:

Int[(3*x^3 - x^4 + (3*x + x^2)*Log[16/5] + (2*x^4 - 2*x^2*Log[16/5] + (-6* 
x^3 + 6*x*Log[16/5])*Log[(x^2 - Log[16/5])/x])*Log[(x - 3*Log[(x^2 - Log[1 
6/5])/x])/3])/((x^3 - x*Log[16/5] + (-3*x^2 + 3*Log[16/5])*Log[(x^2 - Log[ 
16/5])/x])*Log[(x - 3*Log[(x^2 - Log[16/5])/x])/3]^2),x]
 

Output:

$Aborted
 

Maple [A] (verified)

Time = 3.06 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.04

method	result	size
parallelrisch	\(\frac {x^{2}}{\ln \left (-\ln \left (-\frac {-x^{2}+\ln \left (\frac {16}{5}\right )}{x}\right )+\frac {x}{3}\right )}\)	\(28\)

Input:

int((((6*x*ln(16/5)-6*x^3)*ln((-ln(16/5)+x^2)/x)-2*x^2*ln(16/5)+2*x^4)*ln( 
-ln((-ln(16/5)+x^2)/x)+1/3*x)+(x^2+3*x)*ln(16/5)-x^4+3*x^3)/((3*ln(16/5)-3 
*x^2)*ln((-ln(16/5)+x^2)/x)-x*ln(16/5)+x^3)/ln(-ln((-ln(16/5)+x^2)/x)+1/3* 
x)^2,x,method=_RETURNVERBOSE)
 

Output:

x^2/ln(-ln(-(-x^2+ln(16/5))/x)+1/3*x)
 

Fricas [A] (verification not implemented)

Time = 0.08 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.96 \[ \int \frac {3 x^3-x^4+\left (3 x+x^2\right ) \log \left (\frac {16}{5}\right )+\left (2 x^4-2 x^2 \log \left (\frac {16}{5}\right )+\left (-6 x^3+6 x \log \left (\frac {16}{5}\right )\right ) \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log \left (\frac {1}{3} \left (x-3 \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )}{\left (x^3-x \log \left (\frac {16}{5}\right )+\left (-3 x^2+3 \log \left (\frac {16}{5}\right )\right ) \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log ^2\left (\frac {1}{3} \left (x-3 \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )} \, dx=\frac {x^{2}}{\log \left (\frac {1}{3} \, x - \log \left (\frac {x^{2} - \log \left (\frac {16}{5}\right )}{x}\right )\right )} \] Input:

integrate((((6*x*log(16/5)-6*x^3)*log((-log(16/5)+x^2)/x)-2*x^2*log(16/5)+ 
2*x^4)*log(-log((-log(16/5)+x^2)/x)+1/3*x)+(x^2+3*x)*log(16/5)-x^4+3*x^3)/ 
((3*log(16/5)-3*x^2)*log((-log(16/5)+x^2)/x)-x*log(16/5)+x^3)/log(-log((-l 
og(16/5)+x^2)/x)+1/3*x)^2,x, algorithm="fricas")
 

Output:

x^2/log(1/3*x - log((x^2 - log(16/5))/x))
 

Sympy [A] (verification not implemented)

Time = 0.32 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.70 \[ \int \frac {3 x^3-x^4+\left (3 x+x^2\right ) \log \left (\frac {16}{5}\right )+\left (2 x^4-2 x^2 \log \left (\frac {16}{5}\right )+\left (-6 x^3+6 x \log \left (\frac {16}{5}\right )\right ) \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log \left (\frac {1}{3} \left (x-3 \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )}{\left (x^3-x \log \left (\frac {16}{5}\right )+\left (-3 x^2+3 \log \left (\frac {16}{5}\right )\right ) \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log ^2\left (\frac {1}{3} \left (x-3 \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )} \, dx=\frac {x^{2}}{\log {\left (\frac {x}{3} - \log {\left (\frac {x^{2} - \log {\left (\frac {16}{5} \right )}}{x} \right )} \right )}} \] Input:

integrate((((6*x*ln(16/5)-6*x**3)*ln((-ln(16/5)+x**2)/x)-2*x**2*ln(16/5)+2 
*x**4)*ln(-ln((-ln(16/5)+x**2)/x)+1/3*x)+(x**2+3*x)*ln(16/5)-x**4+3*x**3)/ 
((3*ln(16/5)-3*x**2)*ln((-ln(16/5)+x**2)/x)-x*ln(16/5)+x**3)/ln(-ln((-ln(1 
6/5)+x**2)/x)+1/3*x)**2,x)
 

Output:

x**2/log(x/3 - log((x**2 - log(16/5))/x))
 

Maxima [A] (verification not implemented)

Time = 0.18 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.19 \[ \int \frac {3 x^3-x^4+\left (3 x+x^2\right ) \log \left (\frac {16}{5}\right )+\left (2 x^4-2 x^2 \log \left (\frac {16}{5}\right )+\left (-6 x^3+6 x \log \left (\frac {16}{5}\right )\right ) \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log \left (\frac {1}{3} \left (x-3 \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )}{\left (x^3-x \log \left (\frac {16}{5}\right )+\left (-3 x^2+3 \log \left (\frac {16}{5}\right )\right ) \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log ^2\left (\frac {1}{3} \left (x-3 \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )} \, dx=-\frac {x^{2}}{\log \left (3\right ) - \log \left (x - 3 \, \log \left (x^{2} + \log \left (5\right ) - 4 \, \log \left (2\right )\right ) + 3 \, \log \left (x\right )\right )} \] Input:

integrate((((6*x*log(16/5)-6*x^3)*log((-log(16/5)+x^2)/x)-2*x^2*log(16/5)+ 
2*x^4)*log(-log((-log(16/5)+x^2)/x)+1/3*x)+(x^2+3*x)*log(16/5)-x^4+3*x^3)/ 
((3*log(16/5)-3*x^2)*log((-log(16/5)+x^2)/x)-x*log(16/5)+x^3)/log(-log((-l 
og(16/5)+x^2)/x)+1/3*x)^2,x, algorithm="maxima")
 

Output:

-x^2/(log(3) - log(x - 3*log(x^2 + log(5) - 4*log(2)) + 3*log(x)))
 

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 1559 vs. \(2 (23) = 46\).

Time = 0.82 (sec) , antiderivative size = 1559, normalized size of antiderivative = 57.74 \[ \int \frac {3 x^3-x^4+\left (3 x+x^2\right ) \log \left (\frac {16}{5}\right )+\left (2 x^4-2 x^2 \log \left (\frac {16}{5}\right )+\left (-6 x^3+6 x \log \left (\frac {16}{5}\right )\right ) \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log \left (\frac {1}{3} \left (x-3 \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )}{\left (x^3-x \log \left (\frac {16}{5}\right )+\left (-3 x^2+3 \log \left (\frac {16}{5}\right )\right ) \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log ^2\left (\frac {1}{3} \left (x-3 \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )} \, dx=\text {Too large to display} \] Input:

integrate((((6*x*log(16/5)-6*x^3)*log((-log(16/5)+x^2)/x)-2*x^2*log(16/5)+ 
2*x^4)*log(-log((-log(16/5)+x^2)/x)+1/3*x)+(x^2+3*x)*log(16/5)-x^4+3*x^3)/ 
((3*log(16/5)-3*x^2)*log((-log(16/5)+x^2)/x)-x*log(16/5)+x^3)/log(-log((-l 
og(16/5)+x^2)/x)+1/3*x)^2,x, algorithm="giac")
 

Output:

-(x^8 - 3*x^7*log(x^2 - log(16/5)) + 3*x^7*log(x) - 3*x^7 + x^6*log(5) - x 
^6*log(16/5) - 4*x^6*log(2) + 9*x^6*log(x^2 - log(16/5)) - 3*x^5*log(5)*lo 
g(x^2 - log(16/5)) + 3*x^5*log(16/5)*log(x^2 - log(16/5)) + 12*x^5*log(2)* 
log(x^2 - log(16/5)) - 9*x^6*log(x) + 3*x^5*log(5)*log(x) - 3*x^5*log(16/5 
)*log(x) - 12*x^5*log(2)*log(x) + 3*x^5*log(5) + 3*x^5*log(16/5) - x^4*log 
(5)*log(16/5) - 12*x^5*log(2) + 4*x^4*log(16/5)*log(2) - 9*x^4*log(5)*log( 
x^2 - log(16/5)) - 9*x^4*log(16/5)*log(x^2 - log(16/5)) + 3*x^3*log(5)*log 
(16/5)*log(x^2 - log(16/5)) + 36*x^4*log(2)*log(x^2 - log(16/5)) - 12*x^3* 
log(16/5)*log(2)*log(x^2 - log(16/5)) + 9*x^4*log(5)*log(x) + 9*x^4*log(16 
/5)*log(x) - 3*x^3*log(5)*log(16/5)*log(x) - 36*x^4*log(2)*log(x) + 12*x^3 
*log(16/5)*log(2)*log(x) - 3*x^3*log(5)*log(16/5) + 12*x^3*log(16/5)*log(2 
) + 9*x^2*log(5)*log(16/5)*log(x^2 - log(16/5)) - 36*x^2*log(16/5)*log(2)* 
log(x^2 - log(16/5)) - 9*x^2*log(5)*log(16/5)*log(x) + 36*x^2*log(16/5)*lo 
g(2)*log(x))/(x^6*log(3) - x^6*log(x - 3*log(x^2 - log(16/5)) + 3*log(x)) 
- 3*x^5*log(3)*log((x^2 + log(5) - 4*log(2))/x) + 3*x^5*log(x - 3*log(x^2 
- log(16/5)) + 3*log(x))*log((x^2 + log(5) - 4*log(2))/x) - 3*x^5*log(3) + 
 x^4*log(5)*log(3) - x^4*log(16/5)*log(3) - 4*x^4*log(3)*log(2) + 3*x^5*lo 
g(x - 3*log(x^2 - log(16/5)) + 3*log(x)) - x^4*log(5)*log(x - 3*log(x^2 - 
log(16/5)) + 3*log(x)) + x^4*log(16/5)*log(x - 3*log(x^2 - log(16/5)) + 3* 
log(x)) + 4*x^4*log(2)*log(x - 3*log(x^2 - log(16/5)) + 3*log(x)) + 9*x...
 

Mupad [F(-1)]

Timed out. \[ \int \frac {3 x^3-x^4+\left (3 x+x^2\right ) \log \left (\frac {16}{5}\right )+\left (2 x^4-2 x^2 \log \left (\frac {16}{5}\right )+\left (-6 x^3+6 x \log \left (\frac {16}{5}\right )\right ) \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log \left (\frac {1}{3} \left (x-3 \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )}{\left (x^3-x \log \left (\frac {16}{5}\right )+\left (-3 x^2+3 \log \left (\frac {16}{5}\right )\right ) \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log ^2\left (\frac {1}{3} \left (x-3 \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )} \, dx=\int \frac {\ln \left (\frac {x}{3}-\ln \left (-\frac {\ln \left (\frac {16}{5}\right )-x^2}{x}\right )\right )\,\left (2\,x^4-2\,x^2\,\ln \left (\frac {16}{5}\right )+\ln \left (-\frac {\ln \left (\frac {16}{5}\right )-x^2}{x}\right )\,\left (6\,x\,\ln \left (\frac {16}{5}\right )-6\,x^3\right )\right )+3\,x^3-x^4+\ln \left (\frac {16}{5}\right )\,\left (x^2+3\,x\right )}{{\ln \left (\frac {x}{3}-\ln \left (-\frac {\ln \left (\frac {16}{5}\right )-x^2}{x}\right )\right )}^2\,\left (\ln \left (-\frac {\ln \left (\frac {16}{5}\right )-x^2}{x}\right )\,\left (3\,\ln \left (\frac {16}{5}\right )-3\,x^2\right )-x\,\ln \left (\frac {16}{5}\right )+x^3\right )} \,d x \] Input:

int((log(x/3 - log(-(log(16/5) - x^2)/x))*(2*x^4 - 2*x^2*log(16/5) + log(- 
(log(16/5) - x^2)/x)*(6*x*log(16/5) - 6*x^3)) + 3*x^3 - x^4 + log(16/5)*(3 
*x + x^2))/(log(x/3 - log(-(log(16/5) - x^2)/x))^2*(log(-(log(16/5) - x^2) 
/x)*(3*log(16/5) - 3*x^2) - x*log(16/5) + x^3)),x)
 

Output:

int((log(x/3 - log(-(log(16/5) - x^2)/x))*(2*x^4 - 2*x^2*log(16/5) + log(- 
(log(16/5) - x^2)/x)*(6*x*log(16/5) - 6*x^3)) + 3*x^3 - x^4 + log(16/5)*(3 
*x + x^2))/(log(x/3 - log(-(log(16/5) - x^2)/x))^2*(log(-(log(16/5) - x^2) 
/x)*(3*log(16/5) - 3*x^2) - x*log(16/5) + x^3)), x)
 

Reduce [B] (verification not implemented)

Time = 0.21 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.96 \[ \int \frac {3 x^3-x^4+\left (3 x+x^2\right ) \log \left (\frac {16}{5}\right )+\left (2 x^4-2 x^2 \log \left (\frac {16}{5}\right )+\left (-6 x^3+6 x \log \left (\frac {16}{5}\right )\right ) \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log \left (\frac {1}{3} \left (x-3 \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )}{\left (x^3-x \log \left (\frac {16}{5}\right )+\left (-3 x^2+3 \log \left (\frac {16}{5}\right )\right ) \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log ^2\left (\frac {1}{3} \left (x-3 \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )} \, dx=\frac {x^{2}}{\mathrm {log}\left (-\mathrm {log}\left (\frac {-\mathrm {log}\left (\frac {16}{5}\right )+x^{2}}{x}\right )+\frac {x}{3}\right )} \] Input:

int((((6*x*log(16/5)-6*x^3)*log((-log(16/5)+x^2)/x)-2*x^2*log(16/5)+2*x^4) 
*log(-log((-log(16/5)+x^2)/x)+1/3*x)+(x^2+3*x)*log(16/5)-x^4+3*x^3)/((3*lo 
g(16/5)-3*x^2)*log((-log(16/5)+x^2)/x)-x*log(16/5)+x^3)/log(-log((-log(16/ 
5)+x^2)/x)+1/3*x)^2,x)
 

Output:

x**2/log(( - 3*log(( - log(16/5) + x**2)/x) + x)/3)