Integrand size = 162, antiderivative size = 32 \[ \int \frac {2 \log (x)+(3+x-x \log (x)) \log \left (x^2\right )+\left (-14 x-4 x^2\right ) \log ^2\left (x^2\right )-3 x \log ^3\left (x^2\right )+\left (-\log \left (x^2\right )+4 x \log ^2\left (x^2\right )+x \log ^3\left (x^2\right )\right ) \log \left (\log \left (x^2\right )\right )}{\left (\left (3 x+x^2\right ) \log (x)+5 x \log ^2(x)\right ) \log \left (x^2\right )+\left (-3 x^2-x^3-10 x^2 \log (x)\right ) \log ^3\left (x^2\right )+5 x^3 \log ^5\left (x^2\right )+\left (-x \log (x) \log \left (x^2\right )+x^2 \log ^3\left (x^2\right )\right ) \log \left (\log \left (x^2\right )\right )} \, dx=\log \left (\frac {1}{5-\frac {3+x-\log \left (\log \left (x^2\right )\right )}{-\log (x)+x \log ^2\left (x^2\right )}}\right ) \] Output:
ln(1/(5-(3-ln(ln(x^2))+x)/(x*ln(x^2)^2-ln(x))))
\[ \int \frac {2 \log (x)+(3+x-x \log (x)) \log \left (x^2\right )+\left (-14 x-4 x^2\right ) \log ^2\left (x^2\right )-3 x \log ^3\left (x^2\right )+\left (-\log \left (x^2\right )+4 x \log ^2\left (x^2\right )+x \log ^3\left (x^2\right )\right ) \log \left (\log \left (x^2\right )\right )}{\left (\left (3 x+x^2\right ) \log (x)+5 x \log ^2(x)\right ) \log \left (x^2\right )+\left (-3 x^2-x^3-10 x^2 \log (x)\right ) \log ^3\left (x^2\right )+5 x^3 \log ^5\left (x^2\right )+\left (-x \log (x) \log \left (x^2\right )+x^2 \log ^3\left (x^2\right )\right ) \log \left (\log \left (x^2\right )\right )} \, dx=\int \frac {2 \log (x)+(3+x-x \log (x)) \log \left (x^2\right )+\left (-14 x-4 x^2\right ) \log ^2\left (x^2\right )-3 x \log ^3\left (x^2\right )+\left (-\log \left (x^2\right )+4 x \log ^2\left (x^2\right )+x \log ^3\left (x^2\right )\right ) \log \left (\log \left (x^2\right )\right )}{\left (\left (3 x+x^2\right ) \log (x)+5 x \log ^2(x)\right ) \log \left (x^2\right )+\left (-3 x^2-x^3-10 x^2 \log (x)\right ) \log ^3\left (x^2\right )+5 x^3 \log ^5\left (x^2\right )+\left (-x \log (x) \log \left (x^2\right )+x^2 \log ^3\left (x^2\right )\right ) \log \left (\log \left (x^2\right )\right )} \, dx \] Input:
Integrate[(2*Log[x] + (3 + x - x*Log[x])*Log[x^2] + (-14*x - 4*x^2)*Log[x^ 2]^2 - 3*x*Log[x^2]^3 + (-Log[x^2] + 4*x*Log[x^2]^2 + x*Log[x^2]^3)*Log[Lo g[x^2]])/(((3*x + x^2)*Log[x] + 5*x*Log[x]^2)*Log[x^2] + (-3*x^2 - x^3 - 1 0*x^2*Log[x])*Log[x^2]^3 + 5*x^3*Log[x^2]^5 + (-(x*Log[x]*Log[x^2]) + x^2* Log[x^2]^3)*Log[Log[x^2]]),x]
Output:
Integrate[(2*Log[x] + (3 + x - x*Log[x])*Log[x^2] + (-14*x - 4*x^2)*Log[x^ 2]^2 - 3*x*Log[x^2]^3 + (-Log[x^2] + 4*x*Log[x^2]^2 + x*Log[x^2]^3)*Log[Lo g[x^2]])/(((3*x + x^2)*Log[x] + 5*x*Log[x]^2)*Log[x^2] + (-3*x^2 - x^3 - 1 0*x^2*Log[x])*Log[x^2]^3 + 5*x^3*Log[x^2]^5 + (-(x*Log[x]*Log[x^2]) + x^2* Log[x^2]^3)*Log[Log[x^2]]), x]
Time = 4.14 (sec) , antiderivative size = 40, normalized size of antiderivative = 1.25, number of steps used = 3, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.019, Rules used = {7292, 7293, 2009}
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.
| \(\displaystyle \int \frac {-3 x \log ^3\left (x^2\right )+\left (-4 x^2-14 x\right ) \log ^2\left (x^2\right )+\left (x \log ^3\left (x^2\right )+4 x \log ^2\left (x^2\right )-\log \left (x^2\right )\right ) \log \left (\log \left (x^2\right )\right )+(x+x (-\log (x))+3) \log \left (x^2\right )+2 \log (x)}{\left (x^2 \log ^3\left (x^2\right )-x \log (x) \log \left (x^2\right )\right ) \log \left (\log \left (x^2\right )\right )+\left (\left (x^2+3 x\right ) \log (x)+5 x \log ^2(x)\right ) \log \left (x^2\right )+5 x^3 \log ^5\left (x^2\right )+\left (-x^3-3 x^2-10 x^2 \log (x)\right ) \log ^3\left (x^2\right )} \, dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {-3 x \log ^3\left (x^2\right )+\left (-4 x^2-14 x\right ) \log ^2\left (x^2\right )+\left (x \log ^3\left (x^2\right )+4 x \log ^2\left (x^2\right )-\log \left (x^2\right )\right ) \log \left (\log \left (x^2\right )\right )+(x+x (-\log (x))+3) \log \left (x^2\right )+2 \log (x)}{x \log \left (x^2\right ) \left (\log (x)-x \log ^2\left (x^2\right )\right ) \left (-5 x \log ^2\left (x^2\right )-\log \left (\log \left (x^2\right )\right )+x+5 \log (x)+3\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {x \log ^2\left (x^2\right )+4 x \log \left (x^2\right )-1}{x \left (x \log ^2\left (x^2\right )-\log (x)\right )}+\frac {-5 x \log ^3\left (x^2\right )-20 x \log ^2\left (x^2\right )+x \log \left (x^2\right )+5 \log \left (x^2\right )-2}{x \log \left (x^2\right ) \left (5 x \log ^2\left (x^2\right )+\log \left (\log \left (x^2\right )\right )-x-5 \log (x)-3\right )}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle \log \left (\log (x)-x \log ^2\left (x^2\right )\right )-\log \left (-5 x \log ^2\left (x^2\right )-\log \left (\log \left (x^2\right )\right )+x+5 \log (x)+3\right )\) |
Input:
Int[(2*Log[x] + (3 + x - x*Log[x])*Log[x^2] + (-14*x - 4*x^2)*Log[x^2]^2 - 3*x*Log[x^2]^3 + (-Log[x^2] + 4*x*Log[x^2]^2 + x*Log[x^2]^3)*Log[Log[x^2] ])/(((3*x + x^2)*Log[x] + 5*x*Log[x]^2)*Log[x^2] + (-3*x^2 - x^3 - 10*x^2* Log[x])*Log[x^2]^3 + 5*x^3*Log[x^2]^5 + (-(x*Log[x]*Log[x^2]) + x^2*Log[x^ 2]^3)*Log[Log[x^2]]),x]
Output:
Log[Log[x] - x*Log[x^2]^2] - Log[3 + x + 5*Log[x] - 5*x*Log[x^2]^2 - Log[L og[x^2]]]
Time = 35.32 (sec) , antiderivative size = 43, normalized size of antiderivative = 1.34
| method | result | size |
| parallelrisch | \(\ln \left (x \ln \left (x^{2}\right )^{2}-\ln \left (x \right )\right )-\ln \left (x \ln \left (x^{2}\right )^{2}-\frac {x}{5}-\ln \left (x \right )+\frac {\ln \left (\ln \left (x^{2}\right )\right )}{5}-\frac {3}{5}\right )\) | \(43\) |
| default | \(\ln \left (x \right )+\ln \left (-\frac {x \,\pi ^{2} \operatorname {csgn}\left (i x \right )^{4} \operatorname {csgn}\left (i x^{2}\right )^{2}-4 x \,\pi ^{2} \operatorname {csgn}\left (i x \right )^{3} \operatorname {csgn}\left (i x^{2}\right )^{3}+6 x \,\pi ^{2} \operatorname {csgn}\left (i x \right )^{2} \operatorname {csgn}\left (i x^{2}\right )^{4}-4 x \,\pi ^{2} \operatorname {csgn}\left (i x \right ) \operatorname {csgn}\left (i x^{2}\right )^{5}+x \,\pi ^{2} \operatorname {csgn}\left (i x^{2}\right )^{6}+4 \ln \left (x \right )}{16 x}+\ln \left (x \right )^{2}-\frac {i \pi \,\operatorname {csgn}\left (i x^{2}\right ) \left (\operatorname {csgn}\left (i x \right )^{2}-2 \,\operatorname {csgn}\left (i x^{2}\right ) \operatorname {csgn}\left (i x \right )+\operatorname {csgn}\left (i x^{2}\right )^{2}\right ) \ln \left (x \right )}{2}\right )-\ln \left (\ln \left (2 \ln \left (x \right )-\frac {i \pi \,\operatorname {csgn}\left (i x^{2}\right ) {\left (-\operatorname {csgn}\left (i x^{2}\right )+\operatorname {csgn}\left (i x \right )\right )}^{2}}{2}\right )-\frac {5 x \,\pi ^{2} \operatorname {csgn}\left (i x \right )^{4} \operatorname {csgn}\left (i x^{2}\right )^{2}}{4}+5 x \,\pi ^{2} \operatorname {csgn}\left (i x \right )^{3} \operatorname {csgn}\left (i x^{2}\right )^{3}-\frac {15 x \,\pi ^{2} \operatorname {csgn}\left (i x \right )^{2} \operatorname {csgn}\left (i x^{2}\right )^{4}}{2}+5 x \,\pi ^{2} \operatorname {csgn}\left (i x \right ) \operatorname {csgn}\left (i x^{2}\right )^{5}-\frac {5 x \,\pi ^{2} \operatorname {csgn}\left (i x^{2}\right )^{6}}{4}-10 i x \ln \left (x \right ) \pi \operatorname {csgn}\left (i x \right )^{2} \operatorname {csgn}\left (i x^{2}\right )+20 i x \ln \left (x \right ) \pi \,\operatorname {csgn}\left (i x \right ) \operatorname {csgn}\left (i x^{2}\right )^{2}-10 i x \ln \left (x \right ) \pi \operatorname {csgn}\left (i x^{2}\right )^{3}+20 x \ln \left (x \right )^{2}-5 \ln \left (x \right )-x -3\right )\) | \(375\) |
| risch | \(\text {Expression too large to display}\) | \(740\) |
Input:
int(((x*ln(x^2)^3+4*x*ln(x^2)^2-ln(x^2))*ln(ln(x^2))-3*x*ln(x^2)^3+(-4*x^2 -14*x)*ln(x^2)^2+(-x*ln(x)+3+x)*ln(x^2)+2*ln(x))/((x^2*ln(x^2)^3-x*ln(x)*l n(x^2))*ln(ln(x^2))+5*x^3*ln(x^2)^5+(-10*x^2*ln(x)-x^3-3*x^2)*ln(x^2)^3+(5 *x*ln(x)^2+(x^2+3*x)*ln(x))*ln(x^2)),x,method=_RETURNVERBOSE)
Output:
ln(x*ln(x^2)^2-ln(x))-ln(x*ln(x^2)^2-1/5*x-ln(x)+1/5*ln(ln(x^2))-3/5)
Time = 0.12 (sec) , antiderivative size = 42, normalized size of antiderivative = 1.31 \[ \int \frac {2 \log (x)+(3+x-x \log (x)) \log \left (x^2\right )+\left (-14 x-4 x^2\right ) \log ^2\left (x^2\right )-3 x \log ^3\left (x^2\right )+\left (-\log \left (x^2\right )+4 x \log ^2\left (x^2\right )+x \log ^3\left (x^2\right )\right ) \log \left (\log \left (x^2\right )\right )}{\left (\left (3 x+x^2\right ) \log (x)+5 x \log ^2(x)\right ) \log \left (x^2\right )+\left (-3 x^2-x^3-10 x^2 \log (x)\right ) \log ^3\left (x^2\right )+5 x^3 \log ^5\left (x^2\right )+\left (-x \log (x) \log \left (x^2\right )+x^2 \log ^3\left (x^2\right )\right ) \log \left (\log \left (x^2\right )\right )} \, dx=-\log \left (20 \, x \log \left (x\right )^{2} - x - 5 \, \log \left (x\right ) + \log \left (2 \, \log \left (x\right )\right ) - 3\right ) + \log \left (x\right ) + \log \left (\frac {4 \, x \log \left (x\right ) - 1}{x}\right ) + \log \left (\log \left (x\right )\right ) \] Input:
integrate(((x*log(x^2)^3+4*x*log(x^2)^2-log(x^2))*log(log(x^2))-3*x*log(x^ 2)^3+(-4*x^2-14*x)*log(x^2)^2+(-x*log(x)+3+x)*log(x^2)+2*log(x))/((x^2*log (x^2)^3-x*log(x)*log(x^2))*log(log(x^2))+5*x^3*log(x^2)^5+(-10*x^2*log(x)- x^3-3*x^2)*log(x^2)^3+(5*x*log(x)^2+(x^2+3*x)*log(x))*log(x^2)),x, algorit hm="fricas")
Output:
-log(20*x*log(x)^2 - x - 5*log(x) + log(2*log(x)) - 3) + log(x) + log((4*x *log(x) - 1)/x) + log(log(x))
Time = 0.21 (sec) , antiderivative size = 41, normalized size of antiderivative = 1.28 \[ \int \frac {2 \log (x)+(3+x-x \log (x)) \log \left (x^2\right )+\left (-14 x-4 x^2\right ) \log ^2\left (x^2\right )-3 x \log ^3\left (x^2\right )+\left (-\log \left (x^2\right )+4 x \log ^2\left (x^2\right )+x \log ^3\left (x^2\right )\right ) \log \left (\log \left (x^2\right )\right )}{\left (\left (3 x+x^2\right ) \log (x)+5 x \log ^2(x)\right ) \log \left (x^2\right )+\left (-3 x^2-x^3-10 x^2 \log (x)\right ) \log ^3\left (x^2\right )+5 x^3 \log ^5\left (x^2\right )+\left (-x \log (x) \log \left (x^2\right )+x^2 \log ^3\left (x^2\right )\right ) \log \left (\log \left (x^2\right )\right )} \, dx=\log {\left (x \right )} + \log {\left (\log {\left (x \right )}^{2} - \frac {\log {\left (x \right )}}{4 x} \right )} - \log {\left (20 x \log {\left (x \right )}^{2} - x - 5 \log {\left (x \right )} + \log {\left (2 \log {\left (x \right )} \right )} - 3 \right )} \] Input:
integrate(((x*ln(x**2)**3+4*x*ln(x**2)**2-ln(x**2))*ln(ln(x**2))-3*x*ln(x* *2)**3+(-4*x**2-14*x)*ln(x**2)**2+(-x*ln(x)+3+x)*ln(x**2)+2*ln(x))/((x**2* ln(x**2)**3-x*ln(x)*ln(x**2))*ln(ln(x**2))+5*x**3*ln(x**2)**5+(-10*x**2*ln (x)-x**3-3*x**2)*ln(x**2)**3+(5*x*ln(x)**2+(x**2+3*x)*ln(x))*ln(x**2)),x)
Output:
log(x) + log(log(x)**2 - log(x)/(4*x)) - log(20*x*log(x)**2 - x - 5*log(x) + log(2*log(x)) - 3)
Time = 0.21 (sec) , antiderivative size = 43, normalized size of antiderivative = 1.34 \[ \int \frac {2 \log (x)+(3+x-x \log (x)) \log \left (x^2\right )+\left (-14 x-4 x^2\right ) \log ^2\left (x^2\right )-3 x \log ^3\left (x^2\right )+\left (-\log \left (x^2\right )+4 x \log ^2\left (x^2\right )+x \log ^3\left (x^2\right )\right ) \log \left (\log \left (x^2\right )\right )}{\left (\left (3 x+x^2\right ) \log (x)+5 x \log ^2(x)\right ) \log \left (x^2\right )+\left (-3 x^2-x^3-10 x^2 \log (x)\right ) \log ^3\left (x^2\right )+5 x^3 \log ^5\left (x^2\right )+\left (-x \log (x) \log \left (x^2\right )+x^2 \log ^3\left (x^2\right )\right ) \log \left (\log \left (x^2\right )\right )} \, dx=-\log \left (20 \, x \log \left (x\right )^{2} - x + \log \left (2\right ) - 5 \, \log \left (x\right ) + \log \left (\log \left (x\right )\right ) - 3\right ) + \log \left (x\right ) + \log \left (\frac {4 \, x \log \left (x\right ) - 1}{4 \, x}\right ) + \log \left (\log \left (x\right )\right ) \] Input:
integrate(((x*log(x^2)^3+4*x*log(x^2)^2-log(x^2))*log(log(x^2))-3*x*log(x^ 2)^3+(-4*x^2-14*x)*log(x^2)^2+(-x*log(x)+3+x)*log(x^2)+2*log(x))/((x^2*log (x^2)^3-x*log(x)*log(x^2))*log(log(x^2))+5*x^3*log(x^2)^5+(-10*x^2*log(x)- x^3-3*x^2)*log(x^2)^3+(5*x*log(x)^2+(x^2+3*x)*log(x))*log(x^2)),x, algorit hm="maxima")
Output:
-log(20*x*log(x)^2 - x + log(2) - 5*log(x) + log(log(x)) - 3) + log(x) + l og(1/4*(4*x*log(x) - 1)/x) + log(log(x))
\[ \int \frac {2 \log (x)+(3+x-x \log (x)) \log \left (x^2\right )+\left (-14 x-4 x^2\right ) \log ^2\left (x^2\right )-3 x \log ^3\left (x^2\right )+\left (-\log \left (x^2\right )+4 x \log ^2\left (x^2\right )+x \log ^3\left (x^2\right )\right ) \log \left (\log \left (x^2\right )\right )}{\left (\left (3 x+x^2\right ) \log (x)+5 x \log ^2(x)\right ) \log \left (x^2\right )+\left (-3 x^2-x^3-10 x^2 \log (x)\right ) \log ^3\left (x^2\right )+5 x^3 \log ^5\left (x^2\right )+\left (-x \log (x) \log \left (x^2\right )+x^2 \log ^3\left (x^2\right )\right ) \log \left (\log \left (x^2\right )\right )} \, dx=\int { -\frac {3 \, x \log \left (x^{2}\right )^{3} + 2 \, {\left (2 \, x^{2} + 7 \, x\right )} \log \left (x^{2}\right )^{2} + {\left (x \log \left (x\right ) - x - 3\right )} \log \left (x^{2}\right ) - {\left (x \log \left (x^{2}\right )^{3} + 4 \, x \log \left (x^{2}\right )^{2} - \log \left (x^{2}\right )\right )} \log \left (\log \left (x^{2}\right )\right ) - 2 \, \log \left (x\right )}{5 \, x^{3} \log \left (x^{2}\right )^{5} - {\left (x^{3} + 10 \, x^{2} \log \left (x\right ) + 3 \, x^{2}\right )} \log \left (x^{2}\right )^{3} + {\left (5 \, x \log \left (x\right )^{2} + {\left (x^{2} + 3 \, x\right )} \log \left (x\right )\right )} \log \left (x^{2}\right ) + {\left (x^{2} \log \left (x^{2}\right )^{3} - x \log \left (x^{2}\right ) \log \left (x\right )\right )} \log \left (\log \left (x^{2}\right )\right )} \,d x } \] Input:
integrate(((x*log(x^2)^3+4*x*log(x^2)^2-log(x^2))*log(log(x^2))-3*x*log(x^ 2)^3+(-4*x^2-14*x)*log(x^2)^2+(-x*log(x)+3+x)*log(x^2)+2*log(x))/((x^2*log (x^2)^3-x*log(x)*log(x^2))*log(log(x^2))+5*x^3*log(x^2)^5+(-10*x^2*log(x)- x^3-3*x^2)*log(x^2)^3+(5*x*log(x)^2+(x^2+3*x)*log(x))*log(x^2)),x, algorit hm="giac")
Output:
integrate(-(3*x*log(x^2)^3 + 2*(2*x^2 + 7*x)*log(x^2)^2 + (x*log(x) - x - 3)*log(x^2) - (x*log(x^2)^3 + 4*x*log(x^2)^2 - log(x^2))*log(log(x^2)) - 2 *log(x))/(5*x^3*log(x^2)^5 - (x^3 + 10*x^2*log(x) + 3*x^2)*log(x^2)^3 + (5 *x*log(x)^2 + (x^2 + 3*x)*log(x))*log(x^2) + (x^2*log(x^2)^3 - x*log(x^2)* log(x))*log(log(x^2))), x)
Time = 3.33 (sec) , antiderivative size = 46, normalized size of antiderivative = 1.44 \[ \int \frac {2 \log (x)+(3+x-x \log (x)) \log \left (x^2\right )+\left (-14 x-4 x^2\right ) \log ^2\left (x^2\right )-3 x \log ^3\left (x^2\right )+\left (-\log \left (x^2\right )+4 x \log ^2\left (x^2\right )+x \log ^3\left (x^2\right )\right ) \log \left (\log \left (x^2\right )\right )}{\left (\left (3 x+x^2\right ) \log (x)+5 x \log ^2(x)\right ) \log \left (x^2\right )+\left (-3 x^2-x^3-10 x^2 \log (x)\right ) \log ^3\left (x^2\right )+5 x^3 \log ^5\left (x^2\right )+\left (-x \log (x) \log \left (x^2\right )+x^2 \log ^3\left (x^2\right )\right ) \log \left (\log \left (x^2\right )\right )} \, dx=\ln \left (\frac {\ln \left (x\right )-x\,{\ln \left (x^2\right )}^2}{x}\right )-\ln \left (\ln \left (\ln \left (x^2\right )\right )-x-5\,\ln \left (x\right )+5\,x\,{\ln \left (x^2\right )}^2-3\right )+\ln \left (x\right ) \] Input:
int((2*log(x) + log(log(x^2))*(4*x*log(x^2)^2 - log(x^2) + x*log(x^2)^3) + log(x^2)*(x - x*log(x) + 3) - log(x^2)^2*(14*x + 4*x^2) - 3*x*log(x^2)^3) /(log(log(x^2))*(x^2*log(x^2)^3 - x*log(x^2)*log(x)) + log(x^2)*(5*x*log(x )^2 + log(x)*(3*x + x^2)) - log(x^2)^3*(10*x^2*log(x) + 3*x^2 + x^3) + 5*x ^3*log(x^2)^5),x)
Output:
log((log(x) - x*log(x^2)^2)/x) - log(log(log(x^2)) - x - 5*log(x) + 5*x*lo g(x^2)^2 - 3) + log(x)
\[ \int \frac {2 \log (x)+(3+x-x \log (x)) \log \left (x^2\right )+\left (-14 x-4 x^2\right ) \log ^2\left (x^2\right )-3 x \log ^3\left (x^2\right )+\left (-\log \left (x^2\right )+4 x \log ^2\left (x^2\right )+x \log ^3\left (x^2\right )\right ) \log \left (\log \left (x^2\right )\right )}{\left (\left (3 x+x^2\right ) \log (x)+5 x \log ^2(x)\right ) \log \left (x^2\right )+\left (-3 x^2-x^3-10 x^2 \log (x)\right ) \log ^3\left (x^2\right )+5 x^3 \log ^5\left (x^2\right )+\left (-x \log (x) \log \left (x^2\right )+x^2 \log ^3\left (x^2\right )\right ) \log \left (\log \left (x^2\right )\right )} \, dx=\int \frac {\left (x \mathrm {log}\left (x^{2}\right )^{3}+4 \mathrm {log}\left (x^{2}\right )^{2} x -\mathrm {log}\left (x^{2}\right )\right ) \mathrm {log}\left (\mathrm {log}\left (x^{2}\right )\right )-3 x \mathrm {log}\left (x^{2}\right )^{3}+\left (-4 x^{2}-14 x \right ) \mathrm {log}\left (x^{2}\right )^{2}+\left (-\mathrm {log}\left (x \right ) x +3+x \right ) \mathrm {log}\left (x^{2}\right )+2 \,\mathrm {log}\left (x \right )}{\left (x^{2} \mathrm {log}\left (x^{2}\right )^{3}-x \,\mathrm {log}\left (x \right ) \mathrm {log}\left (x^{2}\right )\right ) \mathrm {log}\left (\mathrm {log}\left (x^{2}\right )\right )+5 x^{3} \mathrm {log}\left (x^{2}\right )^{5}+\left (-10 \,\mathrm {log}\left (x \right ) x^{2}-x^{3}-3 x^{2}\right ) \mathrm {log}\left (x^{2}\right )^{3}+\left (5 \mathrm {log}\left (x \right )^{2} x +\left (x^{2}+3 x \right ) \mathrm {log}\left (x \right )\right ) \mathrm {log}\left (x^{2}\right )}d x \] Input:
int(((x*log(x^2)^3+4*x*log(x^2)^2-log(x^2))*log(log(x^2))-3*x*log(x^2)^3+( -4*x^2-14*x)*log(x^2)^2+(-x*log(x)+3+x)*log(x^2)+2*log(x))/((x^2*log(x^2)^ 3-x*log(x)*log(x^2))*log(log(x^2))+5*x^3*log(x^2)^5+(-10*x^2*log(x)-x^3-3* x^2)*log(x^2)^3+(5*x*log(x)^2+(x^2+3*x)*log(x))*log(x^2)),x)
Output:
int(((x*log(x^2)^3+4*x*log(x^2)^2-log(x^2))*log(log(x^2))-3*x*log(x^2)^3+( -4*x^2-14*x)*log(x^2)^2+(-x*log(x)+3+x)*log(x^2)+2*log(x))/((x^2*log(x^2)^ 3-x*log(x)*log(x^2))*log(log(x^2))+5*x^3*log(x^2)^5+(-10*x^2*log(x)-x^3-3* x^2)*log(x^2)^3+(5*x*log(x)^2+(x^2+3*x)*log(x))*log(x^2)),x)