\(\int \frac {(-1+x^2) (\frac {-1+x^2}{x})^{e^{e^{15+x^2-2 x \log (2)+\log ^2(2)}}} (1+x^2+e^{e^{15+x^2-2 x \log (2)+\log ^2(2)}} (1+x^2+e^{15+x^2-2 x \log (2)+\log ^2(2)} (-2 x^2+2 x^4+(2 x-2 x^3) \log (2)) \log (\frac {-1+x^2}{x})))}{x (-x+x^3)} \, dx\) [2816]

Optimal result

Integrand size = 125, antiderivative size = 24 \[ \int \frac {\left (-1+x^2\right ) \left (\frac {-1+x^2}{x}\right )^{e^{e^{15+x^2-2 x \log (2)+\log ^2(2)}}} \left (1+x^2+e^{e^{15+x^2-2 x \log (2)+\log ^2(2)}} \left (1+x^2+e^{15+x^2-2 x \log (2)+\log ^2(2)} \left (-2 x^2+2 x^4+\left (2 x-2 x^3\right ) \log (2)\right ) \log \left (\frac {-1+x^2}{x}\right )\right )\right )}{x \left (-x+x^3\right )} \, dx=\left (-\frac {1}{x}+x\right )^{1+e^{e^{15+(x-\log (2))^2}}} \] Output:

exp((1+exp(exp((x-ln(2))^2+15)))*ln(x-1/x))
 

Mathematica [A] (verified)

Time = 0.42 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.17 \[ \int \frac {\left (-1+x^2\right ) \left (\frac {-1+x^2}{x}\right )^{e^{e^{15+x^2-2 x \log (2)+\log ^2(2)}}} \left (1+x^2+e^{e^{15+x^2-2 x \log (2)+\log ^2(2)}} \left (1+x^2+e^{15+x^2-2 x \log (2)+\log ^2(2)} \left (-2 x^2+2 x^4+\left (2 x-2 x^3\right ) \log (2)\right ) \log \left (\frac {-1+x^2}{x}\right )\right )\right )}{x \left (-x+x^3\right )} \, dx=\left (-\frac {1}{x}+x\right )^{1+e^{e^{15+x^2+\log ^2(2)-x \log (4)}}} \] Input:

Integrate[((-1 + x^2)*((-1 + x^2)/x)^E^E^(15 + x^2 - 2*x*Log[2] + Log[2]^2 
)*(1 + x^2 + E^E^(15 + x^2 - 2*x*Log[2] + Log[2]^2)*(1 + x^2 + E^(15 + x^2 
 - 2*x*Log[2] + Log[2]^2)*(-2*x^2 + 2*x^4 + (2*x - 2*x^3)*Log[2])*Log[(-1 
+ x^2)/x])))/(x*(-x + x^3)),x]
 

Output:

(-x^(-1) + x)^(1 + E^E^(15 + x^2 + Log[2]^2 - x*Log[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.

\(\displaystyle \int \frac {\left (x^2-1\right ) \left (\frac {x^2-1}{x}\right )^{e^{e^{x^2-2 x \log (2)+15+\log ^2(2)}}} \left (x^2+e^{e^{x^2-2 x \log (2)+15+\log ^2(2)}} \left (x^2+e^{x^2-2 x \log (2)+15+\log ^2(2)} \left (2 x^4+\left (2 x-2 x^3\right ) \log (2)-2 x^2\right ) \log \left (\frac {x^2-1}{x}\right )+1\right )+1\right )}{x \left (x^3-x\right )} \, dx\)

\(\Big \downarrow \) 9

\(\displaystyle \int \frac {\left (-\frac {1-x^2}{x}\right )^{e^{2^{-2 x} e^{x^2+15+\log ^2(2)}}} \left (x^2+e^{2^{-2 x} e^{x^2+15+\log ^2(2)}} \left (x^2-2^{1-2 x} e^{x^2+15+\log ^2(2)} \left (-x^4-\left (x-x^3\right ) \log (2)+x^2\right ) \log \left (-\frac {1-x^2}{x}\right )+1\right )+1\right )}{x^2}dx\)

\(\Big \downarrow \) 7292

\(\displaystyle \int \frac {\left (\frac {x^2-1}{x}\right )^{e^{2^{-2 x} e^{x^2+15+\log ^2(2)}}} \left (x^2+e^{2^{-2 x} e^{x^2+15+\log ^2(2)}} \left (x^2-2^{1-2 x} e^{x^2+15+\log ^2(2)} \left (-x^4-\left (x-x^3\right ) \log (2)+x^2\right ) \log \left (-\frac {1-x^2}{x}\right )+1\right )+1\right )}{x^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (\frac {2^{1-2 x} (1-x) (x+1) (\log (2)-x) \log \left (\frac {x^2-1}{x}\right ) \left (\frac {x^2-1}{x}\right )^{e^{2^{-2 x} e^{x^2+15+\log ^2(2)}}} \exp \left (x^2+2^{-2 x} e^{x^2+15+\log ^2(2)}+15 \left (1+\frac {\log ^2(2)}{15}\right )\right )}{x}+\frac {\left (x^2+1\right ) \left (e^{4^{-x} e^{x^2+15+\log ^2(2)}}+1\right ) \left (\frac {x^2-1}{x}\right )^{e^{2^{-2 x} e^{x^2+15+\log ^2(2)}}}}{x^2}\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (\frac {2^{1-2 x} (1-x) (x+1) (\log (2)-x) \log \left (\frac {x^2-1}{x}\right ) \left (\frac {x^2-1}{x}\right )^{e^{2^{-2 x} e^{x^2+15+\log ^2(2)}}} \exp \left (x^2+2^{-2 x} e^{x^2+15+\log ^2(2)}+15 \left (1+\frac {\log ^2(2)}{15}\right )\right )}{x}+\frac {\left (x^2+1\right ) \left (e^{4^{-x} e^{x^2+15+\log ^2(2)}}+1\right ) \left (\frac {x^2-1}{x}\right )^{e^{4^{-x} e^{x^2+15+\log ^2(2)}}}}{x^2}\right )dx\)

\(\Big \downarrow \) 2009

\(\displaystyle -\log \left (-\frac {1-x^2}{x}\right ) \int 2^{1-2 x} e^{x^2+2^{-2 x} e^{x^2+\log ^2(2)+15}+15 \left (1+\frac {\log ^2(2)}{15}\right )} \left (\frac {x^2-1}{x}\right )^{e^{2^{-2 x} e^{x^2+\log ^2(2)+15}}}dx+\log (2) \log \left (-\frac {1-x^2}{x}\right ) \int \frac {2^{1-2 x} e^{x^2+2^{-2 x} e^{x^2+\log ^2(2)+15}+15 \left (1+\frac {\log ^2(2)}{15}\right )} \left (\frac {x^2-1}{x}\right )^{e^{2^{-2 x} e^{x^2+\log ^2(2)+15}}}}{x}dx-\log (2) \log \left (-\frac {1-x^2}{x}\right ) \int 2^{1-2 x} e^{x^2+2^{-2 x} e^{x^2+\log ^2(2)+15}+15 \left (1+\frac {\log ^2(2)}{15}\right )} x \left (\frac {x^2-1}{x}\right )^{e^{2^{-2 x} e^{x^2+\log ^2(2)+15}}}dx+\log \left (-\frac {1-x^2}{x}\right ) \int 2^{1-2 x} e^{x^2+2^{-2 x} e^{x^2+\log ^2(2)+15}+15 \left (1+\frac {\log ^2(2)}{15}\right )} x^2 \left (\frac {x^2-1}{x}\right )^{e^{2^{-2 x} e^{x^2+\log ^2(2)+15}}}dx+\int \left (\frac {x^2-1}{x}\right )^{e^{4^{-x} e^{x^2+\log ^2(2)+15}}}dx+\int e^{4^{-x} e^{x^2+\log ^2(2)+15}} \left (\frac {x^2-1}{x}\right )^{e^{4^{-x} e^{x^2+\log ^2(2)+15}}}dx+\int \frac {\left (\frac {x^2-1}{x}\right )^{e^{4^{-x} e^{x^2+\log ^2(2)+15}}}}{x^2}dx+\int \frac {e^{4^{-x} e^{x^2+\log ^2(2)+15}} \left (\frac {x^2-1}{x}\right )^{e^{4^{-x} e^{x^2+\log ^2(2)+15}}}}{x^2}dx+\int \frac {\int 2^{1-2 x} e^{x^2+4^{-x} e^{x^2+\log ^2(2)+15}+15 \left (1+\frac {\log ^2(2)}{15}\right )} \left (\frac {x^2-1}{x}\right )^{e^{4^{-x} e^{x^2+\log ^2(2)+15}}}dx}{x-1}dx-\int \frac {\int 2^{1-2 x} e^{x^2+4^{-x} e^{x^2+\log ^2(2)+15}+15 \left (1+\frac {\log ^2(2)}{15}\right )} \left (\frac {x^2-1}{x}\right )^{e^{4^{-x} e^{x^2+\log ^2(2)+15}}}dx}{x}dx+\int \frac {\int 2^{1-2 x} e^{x^2+4^{-x} e^{x^2+\log ^2(2)+15}+15 \left (1+\frac {\log ^2(2)}{15}\right )} \left (\frac {x^2-1}{x}\right )^{e^{4^{-x} e^{x^2+\log ^2(2)+15}}}dx}{x+1}dx+\log (2) \int \frac {\int \frac {2^{1-2 x} e^{x^2+4^{-x} e^{x^2+\log ^2(2)+15}+15 \left (1+\frac {\log ^2(2)}{15}\right )} \left (\frac {x^2-1}{x}\right )^{e^{4^{-x} e^{x^2+\log ^2(2)+15}}}}{x}dx}{-x-1}dx+\log (2) \int \frac {\int \frac {2^{1-2 x} e^{x^2+4^{-x} e^{x^2+\log ^2(2)+15}+15 \left (1+\frac {\log ^2(2)}{15}\right )} \left (\frac {x^2-1}{x}\right )^{e^{4^{-x} e^{x^2+\log ^2(2)+15}}}}{x}dx}{1-x}dx+\log (2) \int \frac {\int \frac {2^{1-2 x} e^{x^2+4^{-x} e^{x^2+\log ^2(2)+15}+15 \left (1+\frac {\log ^2(2)}{15}\right )} \left (\frac {x^2-1}{x}\right )^{e^{4^{-x} e^{x^2+\log ^2(2)+15}}}}{x}dx}{x}dx+\log (2) \int \frac {\int 2^{1-2 x} e^{x^2+4^{-x} e^{x^2+\log ^2(2)+15}+15 \left (1+\frac {\log ^2(2)}{15}\right )} x \left (\frac {x^2-1}{x}\right )^{e^{4^{-x} e^{x^2+\log ^2(2)+15}}}dx}{x-1}dx-\log (2) \int \frac {\int 2^{1-2 x} e^{x^2+4^{-x} e^{x^2+\log ^2(2)+15}+15 \left (1+\frac {\log ^2(2)}{15}\right )} x \left (\frac {x^2-1}{x}\right )^{e^{4^{-x} e^{x^2+\log ^2(2)+15}}}dx}{x}dx+\log (2) \int \frac {\int 2^{1-2 x} e^{x^2+4^{-x} e^{x^2+\log ^2(2)+15}+15 \left (1+\frac {\log ^2(2)}{15}\right )} x \left (\frac {x^2-1}{x}\right )^{e^{4^{-x} e^{x^2+\log ^2(2)+15}}}dx}{x+1}dx-\int \frac {\int 2^{1-2 x} e^{x^2+4^{-x} e^{x^2+\log ^2(2)+15}+15 \left (1+\frac {\log ^2(2)}{15}\right )} x^2 \left (\frac {x^2-1}{x}\right )^{e^{4^{-x} e^{x^2+\log ^2(2)+15}}}dx}{x-1}dx+\int \frac {\int 2^{1-2 x} e^{x^2+4^{-x} e^{x^2+\log ^2(2)+15}+15 \left (1+\frac {\log ^2(2)}{15}\right )} x^2 \left (\frac {x^2-1}{x}\right )^{e^{4^{-x} e^{x^2+\log ^2(2)+15}}}dx}{x}dx-\int \frac {\int 2^{1-2 x} e^{x^2+4^{-x} e^{x^2+\log ^2(2)+15}+15 \left (1+\frac {\log ^2(2)}{15}\right )} x^2 \left (\frac {x^2-1}{x}\right )^{e^{4^{-x} e^{x^2+\log ^2(2)+15}}}dx}{x+1}dx\)

Input:

Int[((-1 + x^2)*((-1 + x^2)/x)^E^E^(15 + x^2 - 2*x*Log[2] + Log[2]^2)*(1 + 
 x^2 + E^E^(15 + x^2 - 2*x*Log[2] + Log[2]^2)*(1 + x^2 + E^(15 + x^2 - 2*x 
*Log[2] + Log[2]^2)*(-2*x^2 + 2*x^4 + (2*x - 2*x^3)*Log[2])*Log[(-1 + x^2) 
/x])))/(x*(-x + x^3)),x]
 

Output:

$Aborted
 

Maple [C] (warning: unable to verify)

Result contains higher order function than in optimal. Order 9 vs. order 3.

Time = 0.06 (sec) , antiderivative size = 134, normalized size of antiderivative = 5.58

\[\frac {\left (x^{2}-1\right ) x^{-{\mathrm e}^{4^{-x} {\mathrm e}^{\ln \left (2\right )^{2}+15+x^{2}}}} \left (x^{2}-1\right )^{{\mathrm e}^{4^{-x} {\mathrm e}^{\ln \left (2\right )^{2}+15+x^{2}}}} {\mathrm e}^{-\frac {i \pi \,\operatorname {csgn}\left (\frac {i \left (x^{2}-1\right )}{x}\right ) \left (-\operatorname {csgn}\left (\frac {i \left (x^{2}-1\right )}{x}\right )+\operatorname {csgn}\left (i \left (x^{2}-1\right )\right )\right ) \left (-\operatorname {csgn}\left (\frac {i \left (x^{2}-1\right )}{x}\right )+\operatorname {csgn}\left (\frac {i}{x}\right )\right ) \left ({\mathrm e}^{\left (\frac {1}{4}\right )^{x} {\mathrm e}^{\ln \left (2\right )^{2}+15+x^{2}}}+1\right )}{2}}}{x}\]

Input:

int(((((-2*x^3+2*x)*ln(2)+2*x^4-2*x^2)*exp(ln(2)^2-2*x*ln(2)+x^2+15)*ln((x 
^2-1)/x)+x^2+1)*exp(exp(ln(2)^2-2*x*ln(2)+x^2+15))+x^2+1)*exp(ln((x^2-1)/x 
)*exp(exp(ln(2)^2-2*x*ln(2)+x^2+15))+ln((x^2-1)/x))/(x^3-x),x)
 

Output:

(x^2-1)/x*x^(-exp(4^(-x)*exp(ln(2)^2+15+x^2)))*(x^2-1)^exp(4^(-x)*exp(ln(2 
)^2+15+x^2))*exp(-1/2*I*Pi*csgn(I/x*(x^2-1))*(-csgn(I/x*(x^2-1))+csgn(I*(x 
^2-1)))*(-csgn(I/x*(x^2-1))+csgn(I/x))*(exp((1/4)^x*exp(ln(2)^2+15+x^2))+1 
))
 

Fricas [A] (verification not implemented)

Time = 0.08 (sec) , antiderivative size = 39, normalized size of antiderivative = 1.62 \[ \int \frac {\left (-1+x^2\right ) \left (\frac {-1+x^2}{x}\right )^{e^{e^{15+x^2-2 x \log (2)+\log ^2(2)}}} \left (1+x^2+e^{e^{15+x^2-2 x \log (2)+\log ^2(2)}} \left (1+x^2+e^{15+x^2-2 x \log (2)+\log ^2(2)} \left (-2 x^2+2 x^4+\left (2 x-2 x^3\right ) \log (2)\right ) \log \left (\frac {-1+x^2}{x}\right )\right )\right )}{x \left (-x+x^3\right )} \, dx=e^{\left (e^{\left (e^{\left (x^{2} - 2 \, x \log \left (2\right ) + \log \left (2\right )^{2} + 15\right )}\right )} \log \left (\frac {x^{2} - 1}{x}\right ) + \log \left (\frac {x^{2} - 1}{x}\right )\right )} \] Input:

integrate(((((-2*x^3+2*x)*log(2)+2*x^4-2*x^2)*exp(log(2)^2-2*x*log(2)+x^2+ 
15)*log((x^2-1)/x)+x^2+1)*exp(exp(log(2)^2-2*x*log(2)+x^2+15))+x^2+1)*exp( 
log((x^2-1)/x)*exp(exp(log(2)^2-2*x*log(2)+x^2+15))+log((x^2-1)/x))/(x^3-x 
),x, algorithm="fricas")
 

Output:

e^(e^(e^(x^2 - 2*x*log(2) + log(2)^2 + 15))*log((x^2 - 1)/x) + log((x^2 - 
1)/x))
 

Sympy [A] (verification not implemented)

Time = 5.06 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.50 \[ \int \frac {\left (-1+x^2\right ) \left (\frac {-1+x^2}{x}\right )^{e^{e^{15+x^2-2 x \log (2)+\log ^2(2)}}} \left (1+x^2+e^{e^{15+x^2-2 x \log (2)+\log ^2(2)}} \left (1+x^2+e^{15+x^2-2 x \log (2)+\log ^2(2)} \left (-2 x^2+2 x^4+\left (2 x-2 x^3\right ) \log (2)\right ) \log \left (\frac {-1+x^2}{x}\right )\right )\right )}{x \left (-x+x^3\right )} \, dx=\frac {\left (x^{2} - 1\right ) e^{e^{e^{x^{2} - 2 x \log {\left (2 \right )} + \log {\left (2 \right )}^{2} + 15}} \log {\left (\frac {x^{2} - 1}{x} \right )}}}{x} \] Input:

integrate(((((-2*x**3+2*x)*ln(2)+2*x**4-2*x**2)*exp(ln(2)**2-2*x*ln(2)+x** 
2+15)*ln((x**2-1)/x)+x**2+1)*exp(exp(ln(2)**2-2*x*ln(2)+x**2+15))+x**2+1)* 
exp(ln((x**2-1)/x)*exp(exp(ln(2)**2-2*x*ln(2)+x**2+15))+ln((x**2-1)/x))/(x 
**3-x),x)
 

Output:

(x**2 - 1)*exp(exp(exp(x**2 - 2*x*log(2) + log(2)**2 + 15))*log((x**2 - 1) 
/x))/x
 

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 73 vs. \(2 (22) = 44\).

Time = 0.42 (sec) , antiderivative size = 73, normalized size of antiderivative = 3.04 \[ \int \frac {\left (-1+x^2\right ) \left (\frac {-1+x^2}{x}\right )^{e^{e^{15+x^2-2 x \log (2)+\log ^2(2)}}} \left (1+x^2+e^{e^{15+x^2-2 x \log (2)+\log ^2(2)}} \left (1+x^2+e^{15+x^2-2 x \log (2)+\log ^2(2)} \left (-2 x^2+2 x^4+\left (2 x-2 x^3\right ) \log (2)\right ) \log \left (\frac {-1+x^2}{x}\right )\right )\right )}{x \left (-x+x^3\right )} \, dx=\frac {{\left (x^{2} - 1\right )} e^{\left (e^{\left (e^{\left (x^{2} - 2 \, x \log \left (2\right ) + \log \left (2\right )^{2} + 15\right )}\right )} \log \left (x + 1\right ) + e^{\left (e^{\left (x^{2} - 2 \, x \log \left (2\right ) + \log \left (2\right )^{2} + 15\right )}\right )} \log \left (x - 1\right ) - e^{\left (e^{\left (x^{2} - 2 \, x \log \left (2\right ) + \log \left (2\right )^{2} + 15\right )}\right )} \log \left (x\right )\right )}}{x} \] Input:

integrate(((((-2*x^3+2*x)*log(2)+2*x^4-2*x^2)*exp(log(2)^2-2*x*log(2)+x^2+ 
15)*log((x^2-1)/x)+x^2+1)*exp(exp(log(2)^2-2*x*log(2)+x^2+15))+x^2+1)*exp( 
log((x^2-1)/x)*exp(exp(log(2)^2-2*x*log(2)+x^2+15))+log((x^2-1)/x))/(x^3-x 
),x, algorithm="maxima")
 

Output:

(x^2 - 1)*e^(e^(e^(x^2 - 2*x*log(2) + log(2)^2 + 15))*log(x + 1) + e^(e^(x 
^2 - 2*x*log(2) + log(2)^2 + 15))*log(x - 1) - e^(e^(x^2 - 2*x*log(2) + lo 
g(2)^2 + 15))*log(x))/x
 

Giac [A] (verification not implemented)

Time = 1.41 (sec) , antiderivative size = 35, normalized size of antiderivative = 1.46 \[ \int \frac {\left (-1+x^2\right ) \left (\frac {-1+x^2}{x}\right )^{e^{e^{15+x^2-2 x \log (2)+\log ^2(2)}}} \left (1+x^2+e^{e^{15+x^2-2 x \log (2)+\log ^2(2)}} \left (1+x^2+e^{15+x^2-2 x \log (2)+\log ^2(2)} \left (-2 x^2+2 x^4+\left (2 x-2 x^3\right ) \log (2)\right ) \log \left (\frac {-1+x^2}{x}\right )\right )\right )}{x \left (-x+x^3\right )} \, dx=e^{\left (e^{\left (e^{\left (x^{2} - 2 \, x \log \left (2\right ) + \log \left (2\right )^{2} + 15\right )}\right )} \log \left (x - \frac {1}{x}\right ) + \log \left (x - \frac {1}{x}\right )\right )} \] Input:

integrate(((((-2*x^3+2*x)*log(2)+2*x^4-2*x^2)*exp(log(2)^2-2*x*log(2)+x^2+ 
15)*log((x^2-1)/x)+x^2+1)*exp(exp(log(2)^2-2*x*log(2)+x^2+15))+x^2+1)*exp( 
log((x^2-1)/x)*exp(exp(log(2)^2-2*x*log(2)+x^2+15))+log((x^2-1)/x))/(x^3-x 
),x, algorithm="giac")
 

Output:

e^(e^(e^(x^2 - 2*x*log(2) + log(2)^2 + 15))*log(x - 1/x) + log(x - 1/x))
 

Mupad [B] (verification not implemented)

Time = 2.27 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.54 \[ \int \frac {\left (-1+x^2\right ) \left (\frac {-1+x^2}{x}\right )^{e^{e^{15+x^2-2 x \log (2)+\log ^2(2)}}} \left (1+x^2+e^{e^{15+x^2-2 x \log (2)+\log ^2(2)}} \left (1+x^2+e^{15+x^2-2 x \log (2)+\log ^2(2)} \left (-2 x^2+2 x^4+\left (2 x-2 x^3\right ) \log (2)\right ) \log \left (\frac {-1+x^2}{x}\right )\right )\right )}{x \left (-x+x^3\right )} \, dx=\frac {{\left (x-\frac {1}{x}\right )}^{{\mathrm {e}}^{\frac {{\mathrm {e}}^{{\ln \left (2\right )}^2}\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^{15}}{2^{2\,x}}}}\,\left (x^2-1\right )}{x} \] Input:

int(-(exp(log((x^2 - 1)/x) + exp(exp(log(2)^2 - 2*x*log(2) + x^2 + 15))*lo 
g((x^2 - 1)/x))*(exp(exp(log(2)^2 - 2*x*log(2) + x^2 + 15))*(x^2 + exp(log 
(2)^2 - 2*x*log(2) + x^2 + 15)*log((x^2 - 1)/x)*(log(2)*(2*x - 2*x^3) - 2* 
x^2 + 2*x^4) + 1) + x^2 + 1))/(x - x^3),x)
 

Output:

((x - 1/x)^exp((exp(log(2)^2)*exp(x^2)*exp(15))/2^(2*x))*(x^2 - 1))/x
 

Reduce [F]

\[ \int \frac {\left (-1+x^2\right ) \left (\frac {-1+x^2}{x}\right )^{e^{e^{15+x^2-2 x \log (2)+\log ^2(2)}}} \left (1+x^2+e^{e^{15+x^2-2 x \log (2)+\log ^2(2)}} \left (1+x^2+e^{15+x^2-2 x \log (2)+\log ^2(2)} \left (-2 x^2+2 x^4+\left (2 x-2 x^3\right ) \log (2)\right ) \log \left (\frac {-1+x^2}{x}\right )\right )\right )}{x \left (-x+x^3\right )} \, dx =\text {Too large to display} \] Input:

int(((((-2*x^3+2*x)*log(2)+2*x^4-2*x^2)*exp(log(2)^2-2*x*log(2)+x^2+15)*lo 
g((x^2-1)/x)+x^2+1)*exp(exp(log(2)^2-2*x*log(2)+x^2+15))+x^2+1)*exp(log((x 
^2-1)/x)*exp(exp(log(2)^2-2*x*log(2)+x^2+15))+log((x^2-1)/x))/(x^3-x),x)
 

Output:

2*e**(log(2)**2)*int((e**((e**(log(2)**2 + x**2)*e**15 + e**((e**(log(2)** 
2 + x**2)*e**15)/2**(2*x))*2**(2*x)*log((x**2 - 1)/x) + 2**(2*x)*x**2)/2** 
(2*x))*log((x**2 - 1)/x)*x**2)/2**(2*x),x)*e**15 - 2*e**(log(2)**2)*int((e 
**((e**(log(2)**2 + x**2)*e**15 + e**((e**(log(2)**2 + x**2)*e**15)/2**(2* 
x))*2**(2*x)*log((x**2 - 1)/x) + 2**(2*x)*x**2)/2**(2*x))*log((x**2 - 1)/x 
)*x)/2**(2*x),x)*log(2)*e**15 - 2*e**(log(2)**2)*int((e**((e**(log(2)**2 + 
 x**2)*e**15 + e**((e**(log(2)**2 + x**2)*e**15)/2**(2*x))*2**(2*x)*log((x 
**2 - 1)/x) + 2**(2*x)*x**2)/2**(2*x))*log((x**2 - 1)/x))/2**(2*x),x)*e**1 
5 + 2*e**(log(2)**2)*int((e**((e**(log(2)**2 + x**2)*e**15 + e**((e**(log( 
2)**2 + x**2)*e**15)/2**(2*x))*2**(2*x)*log((x**2 - 1)/x) + 2**(2*x)*x**2) 
/2**(2*x))*log((x**2 - 1)/x))/(2**(2*x)*x),x)*log(2)*e**15 + int(e**((e**( 
log(2)**2 + x**2)*e**15 + e**((e**(log(2)**2 + x**2)*e**15)/2**(2*x))*2**( 
2*x)*log((x**2 - 1)/x))/2**(2*x)),x) + int(e**(e**((e**(log(2)**2 + x**2)* 
e**15)/2**(2*x))*log((x**2 - 1)/x)),x) + int(e**((e**(log(2)**2 + x**2)*e* 
*15 + e**((e**(log(2)**2 + x**2)*e**15)/2**(2*x))*2**(2*x)*log((x**2 - 1)/ 
x))/2**(2*x))/x**2,x) + int(e**(e**((e**(log(2)**2 + x**2)*e**15)/2**(2*x) 
)*log((x**2 - 1)/x))/x**2,x)