Integrand size = 238, antiderivative size = 29 \[ \int \frac {\left (4 x^6+8 x^3 \log (4)\right ) \log \left (\frac {121 x^4-110 x^5+25 x^6+\left (110 x^2-50 x^3\right ) \log (4)+25 \log ^2(4)}{4 x^4-4 x^5+x^6+\left (4 x^2-2 x^3\right ) \log (4)+\log ^2(4)}\right )+\left (44 x^5-42 x^6+10 x^7+\left (42 x^3-20 x^4\right ) \log (4)+10 x \log ^2(4)\right ) \log ^2\left (\frac {121 x^4-110 x^5+25 x^6+\left (110 x^2-50 x^3\right ) \log (4)+25 \log ^2(4)}{4 x^4-4 x^5+x^6+\left (4 x^2-2 x^3\right ) \log (4)+\log ^2(4)}\right )}{22 x^4-21 x^5+5 x^6+\left (21 x^2-10 x^3\right ) \log (4)+5 \log ^2(4)} \, dx=x^2 \log ^2\left (\left (-5+\frac {x}{-2 x+x^2-\frac {\log (4)}{x}}\right )^2\right ) \] Output:
ln((-5+x/(x^2-2*x-2*ln(2)/x))^2)^2*x^2
Result contains higher order function than in optimal. Order 9 vs. order 3 in optimal.
Time = 13.99 (sec) , antiderivative size = 57407, normalized size of antiderivative = 1979.55 \[ \int \frac {\left (4 x^6+8 x^3 \log (4)\right ) \log \left (\frac {121 x^4-110 x^5+25 x^6+\left (110 x^2-50 x^3\right ) \log (4)+25 \log ^2(4)}{4 x^4-4 x^5+x^6+\left (4 x^2-2 x^3\right ) \log (4)+\log ^2(4)}\right )+\left (44 x^5-42 x^6+10 x^7+\left (42 x^3-20 x^4\right ) \log (4)+10 x \log ^2(4)\right ) \log ^2\left (\frac {121 x^4-110 x^5+25 x^6+\left (110 x^2-50 x^3\right ) \log (4)+25 \log ^2(4)}{4 x^4-4 x^5+x^6+\left (4 x^2-2 x^3\right ) \log (4)+\log ^2(4)}\right )}{22 x^4-21 x^5+5 x^6+\left (21 x^2-10 x^3\right ) \log (4)+5 \log ^2(4)} \, dx=\text {Result too large to show} \] Input:
Integrate[((4*x^6 + 8*x^3*Log[4])*Log[(121*x^4 - 110*x^5 + 25*x^6 + (110*x ^2 - 50*x^3)*Log[4] + 25*Log[4]^2)/(4*x^4 - 4*x^5 + x^6 + (4*x^2 - 2*x^3)* Log[4] + Log[4]^2)] + (44*x^5 - 42*x^6 + 10*x^7 + (42*x^3 - 20*x^4)*Log[4] + 10*x*Log[4]^2)*Log[(121*x^4 - 110*x^5 + 25*x^6 + (110*x^2 - 50*x^3)*Log [4] + 25*Log[4]^2)/(4*x^4 - 4*x^5 + x^6 + (4*x^2 - 2*x^3)*Log[4] + Log[4]^ 2)]^2)/(22*x^4 - 21*x^5 + 5*x^6 + (21*x^2 - 10*x^3)*Log[4] + 5*Log[4]^2),x ]
Output:
Result too large to show
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.
| \(\displaystyle \int \frac {\left (4 x^6+8 x^3 \log (4)\right ) \log \left (\frac {25 x^6-110 x^5+121 x^4+\left (110 x^2-50 x^3\right ) \log (4)+25 \log ^2(4)}{x^6-4 x^5+4 x^4+\left (4 x^2-2 x^3\right ) \log (4)+\log ^2(4)}\right )+\left (10 x^7-42 x^6+44 x^5+\left (42 x^3-20 x^4\right ) \log (4)+10 x \log ^2(4)\right ) \log ^2\left (\frac {25 x^6-110 x^5+121 x^4+\left (110 x^2-50 x^3\right ) \log (4)+25 \log ^2(4)}{x^6-4 x^5+4 x^4+\left (4 x^2-2 x^3\right ) \log (4)+\log ^2(4)}\right )}{5 x^6-21 x^5+22 x^4+\left (21 x^2-10 x^3\right ) \log (4)+5 \log ^2(4)} \, dx\) |
| \(\Big \downarrow \) 2463 |
| \(\displaystyle \int \left (\frac {(5 x-11) \left (\left (4 x^6+8 x^3 \log (4)\right ) \log \left (\frac {25 x^6-110 x^5+121 x^4+\left (110 x^2-50 x^3\right ) \log (4)+25 \log ^2(4)}{x^6-4 x^5+4 x^4+\left (4 x^2-2 x^3\right ) \log (4)+\log ^2(4)}\right )+\left (10 x^7-42 x^6+44 x^5+\left (42 x^3-20 x^4\right ) \log (4)+10 x \log ^2(4)\right ) \log ^2\left (\frac {25 x^6-110 x^5+121 x^4+\left (110 x^2-50 x^3\right ) \log (4)+25 \log ^2(4)}{x^6-4 x^5+4 x^4+\left (4 x^2-2 x^3\right ) \log (4)+\log ^2(4)}\right )\right )}{\log (4) \left (5 x^3-11 x^2-5 \log (4)\right )}+\frac {(2-x) \left (\left (4 x^6+8 x^3 \log (4)\right ) \log \left (\frac {25 x^6-110 x^5+121 x^4+\left (110 x^2-50 x^3\right ) \log (4)+25 \log ^2(4)}{x^6-4 x^5+4 x^4+\left (4 x^2-2 x^3\right ) \log (4)+\log ^2(4)}\right )+\left (10 x^7-42 x^6+44 x^5+\left (42 x^3-20 x^4\right ) \log (4)+10 x \log ^2(4)\right ) \log ^2\left (\frac {25 x^6-110 x^5+121 x^4+\left (110 x^2-50 x^3\right ) \log (4)+25 \log ^2(4)}{x^6-4 x^5+4 x^4+\left (4 x^2-2 x^3\right ) \log (4)+\log ^2(4)}\right )\right )}{\log (4) \left (x^3-2 x^2-\log (4)\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2 x \log \left (\frac {\left (-5 x^3+11 x^2+5 \log (4)\right )^2}{\left (-x^3+2 x^2+\log (4)\right )^2}\right ) \left (2 x^2 \left (x^3+\log (16)\right )+\left (5 x^6-21 x^5+22 x^4-10 x^3 \log (4)+21 x^2 \log (4)+5 \log ^2(4)\right ) \log \left (\frac {\left (-5 x^3+11 x^2+5 \log (4)\right )^2}{\left (-x^3+2 x^2+\log (4)\right )^2}\right )\right )}{\left (-x^3+2 x^2+\log (4)\right ) \left (-5 x^3+11 x^2+5 \log (4)\right )}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 2 \int \frac {x \log \left (\frac {\left (-5 x^3+11 x^2+5 \log (4)\right )^2}{\left (-x^3+2 x^2+\log (4)\right )^2}\right ) \left (2 \left (x^3+\log (16)\right ) x^2+\left (5 x^6-21 x^5+22 x^4-10 \log (4) x^3+21 \log (4) x^2+5 \log ^2(4)\right ) \log \left (\frac {\left (-5 x^3+11 x^2+5 \log (4)\right )^2}{\left (-x^3+2 x^2+\log (4)\right )^2}\right )\right )}{\left (-x^3+2 x^2+\log (4)\right ) \left (-5 x^3+11 x^2+5 \log (4)\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (\frac {2 \left (x^3+\log (16)\right ) \log \left (\frac {\left (-5 x^3+11 x^2+5 \log (4)\right )^2}{\left (-x^3+2 x^2+\log (4)\right )^2}\right ) x^3}{\left (5 x^3-11 x^2-5 \log (4)\right ) \left (x^3-2 x^2-\log (4)\right )}+\log ^2\left (\frac {\left (-5 x^3+11 x^2+5 \log (4)\right )^2}{\left (-x^3+2 x^2+\log (4)\right )^2}\right ) x\right )dx\) |
| \(\Big \downarrow \) 7299 |
| \(\displaystyle 2 \int \left (\frac {2 \left (x^3+\log (16)\right ) \log \left (\frac {\left (-5 x^3+11 x^2+5 \log (4)\right )^2}{\left (-x^3+2 x^2+\log (4)\right )^2}\right ) x^3}{\left (5 x^3-11 x^2-5 \log (4)\right ) \left (x^3-2 x^2-\log (4)\right )}+\log ^2\left (\frac {\left (-5 x^3+11 x^2+5 \log (4)\right )^2}{\left (-x^3+2 x^2+\log (4)\right )^2}\right ) x\right )dx\) |
Input:
Int[((4*x^6 + 8*x^3*Log[4])*Log[(121*x^4 - 110*x^5 + 25*x^6 + (110*x^2 - 5 0*x^3)*Log[4] + 25*Log[4]^2)/(4*x^4 - 4*x^5 + x^6 + (4*x^2 - 2*x^3)*Log[4] + Log[4]^2)] + (44*x^5 - 42*x^6 + 10*x^7 + (42*x^3 - 20*x^4)*Log[4] + 10* x*Log[4]^2)*Log[(121*x^4 - 110*x^5 + 25*x^6 + (110*x^2 - 50*x^3)*Log[4] + 25*Log[4]^2)/(4*x^4 - 4*x^5 + x^6 + (4*x^2 - 2*x^3)*Log[4] + Log[4]^2)]^2) /(22*x^4 - 21*x^5 + 5*x^6 + (21*x^2 - 10*x^3)*Log[4] + 5*Log[4]^2),x]
Output:
$Aborted
Leaf count of result is larger than twice the leaf count of optimal. \(81\) vs. \(2(29)=58\).
Time = 7.85 (sec) , antiderivative size = 82, normalized size of antiderivative = 2.83
| method | result | size |
| parallelrisch | \(\ln \left (\frac {100 \ln \left (2\right )^{2}+2 \left (-50 x^{3}+110 x^{2}\right ) \ln \left (2\right )+25 x^{6}-110 x^{5}+121 x^{4}}{x^{6}-4 x^{5}-4 x^{3} \ln \left (2\right )+4 x^{4}+8 x^{2} \ln \left (2\right )+4 \ln \left (2\right )^{2}}\right )^{2} x^{2}\) | \(82\) |
| norman | \(x^{2} \ln \left (\frac {100 \ln \left (2\right )^{2}+2 \left (-50 x^{3}+110 x^{2}\right ) \ln \left (2\right )+25 x^{6}-110 x^{5}+121 x^{4}}{4 \ln \left (2\right )^{2}+2 \left (-2 x^{3}+4 x^{2}\right ) \ln \left (2\right )+x^{6}-4 x^{5}+4 x^{4}}\right )^{2}\) | \(83\) |
| risch | \(x^{2} \ln \left (\frac {100 \ln \left (2\right )^{2}+2 \left (-50 x^{3}+110 x^{2}\right ) \ln \left (2\right )+25 x^{6}-110 x^{5}+121 x^{4}}{4 \ln \left (2\right )^{2}+2 \left (-2 x^{3}+4 x^{2}\right ) \ln \left (2\right )+x^{6}-4 x^{5}+4 x^{4}}\right )^{2}\) | \(83\) |
Input:
int(((40*x*ln(2)^2+2*(-20*x^4+42*x^3)*ln(2)+10*x^7-42*x^6+44*x^5)*ln((100* ln(2)^2+2*(-50*x^3+110*x^2)*ln(2)+25*x^6-110*x^5+121*x^4)/(4*ln(2)^2+2*(-2 *x^3+4*x^2)*ln(2)+x^6-4*x^5+4*x^4))^2+(16*x^3*ln(2)+4*x^6)*ln((100*ln(2)^2 +2*(-50*x^3+110*x^2)*ln(2)+25*x^6-110*x^5+121*x^4)/(4*ln(2)^2+2*(-2*x^3+4* x^2)*ln(2)+x^6-4*x^5+4*x^4)))/(20*ln(2)^2+2*(-10*x^3+21*x^2)*ln(2)+5*x^6-2 1*x^5+22*x^4),x,method=_RETURNVERBOSE)
Output:
ln((100*ln(2)^2+2*(-50*x^3+110*x^2)*ln(2)+25*x^6-110*x^5+121*x^4)/(x^6-4*x ^5-4*x^3*ln(2)+4*x^4+8*x^2*ln(2)+4*ln(2)^2))^2*x^2
Leaf count of result is larger than twice the leaf count of optimal. 80 vs. \(2 (29) = 58\).
Time = 0.07 (sec) , antiderivative size = 80, normalized size of antiderivative = 2.76 \[ \int \frac {\left (4 x^6+8 x^3 \log (4)\right ) \log \left (\frac {121 x^4-110 x^5+25 x^6+\left (110 x^2-50 x^3\right ) \log (4)+25 \log ^2(4)}{4 x^4-4 x^5+x^6+\left (4 x^2-2 x^3\right ) \log (4)+\log ^2(4)}\right )+\left (44 x^5-42 x^6+10 x^7+\left (42 x^3-20 x^4\right ) \log (4)+10 x \log ^2(4)\right ) \log ^2\left (\frac {121 x^4-110 x^5+25 x^6+\left (110 x^2-50 x^3\right ) \log (4)+25 \log ^2(4)}{4 x^4-4 x^5+x^6+\left (4 x^2-2 x^3\right ) \log (4)+\log ^2(4)}\right )}{22 x^4-21 x^5+5 x^6+\left (21 x^2-10 x^3\right ) \log (4)+5 \log ^2(4)} \, dx=x^{2} \log \left (\frac {25 \, x^{6} - 110 \, x^{5} + 121 \, x^{4} - 20 \, {\left (5 \, x^{3} - 11 \, x^{2}\right )} \log \left (2\right ) + 100 \, \log \left (2\right )^{2}}{x^{6} - 4 \, x^{5} + 4 \, x^{4} - 4 \, {\left (x^{3} - 2 \, x^{2}\right )} \log \left (2\right ) + 4 \, \log \left (2\right )^{2}}\right )^{2} \] Input:
integrate(((40*x*log(2)^2+2*(-20*x^4+42*x^3)*log(2)+10*x^7-42*x^6+44*x^5)* log((100*log(2)^2+2*(-50*x^3+110*x^2)*log(2)+25*x^6-110*x^5+121*x^4)/(4*lo g(2)^2+2*(-2*x^3+4*x^2)*log(2)+x^6-4*x^5+4*x^4))^2+(16*x^3*log(2)+4*x^6)*l og((100*log(2)^2+2*(-50*x^3+110*x^2)*log(2)+25*x^6-110*x^5+121*x^4)/(4*log (2)^2+2*(-2*x^3+4*x^2)*log(2)+x^6-4*x^5+4*x^4)))/(20*log(2)^2+2*(-10*x^3+2 1*x^2)*log(2)+5*x^6-21*x^5+22*x^4),x, algorithm="fricas")
Output:
x^2*log((25*x^6 - 110*x^5 + 121*x^4 - 20*(5*x^3 - 11*x^2)*log(2) + 100*log (2)^2)/(x^6 - 4*x^5 + 4*x^4 - 4*(x^3 - 2*x^2)*log(2) + 4*log(2)^2))^2
Leaf count of result is larger than twice the leaf count of optimal. 75 vs. \(2 (24) = 48\).
Time = 0.21 (sec) , antiderivative size = 75, normalized size of antiderivative = 2.59 \[ \int \frac {\left (4 x^6+8 x^3 \log (4)\right ) \log \left (\frac {121 x^4-110 x^5+25 x^6+\left (110 x^2-50 x^3\right ) \log (4)+25 \log ^2(4)}{4 x^4-4 x^5+x^6+\left (4 x^2-2 x^3\right ) \log (4)+\log ^2(4)}\right )+\left (44 x^5-42 x^6+10 x^7+\left (42 x^3-20 x^4\right ) \log (4)+10 x \log ^2(4)\right ) \log ^2\left (\frac {121 x^4-110 x^5+25 x^6+\left (110 x^2-50 x^3\right ) \log (4)+25 \log ^2(4)}{4 x^4-4 x^5+x^6+\left (4 x^2-2 x^3\right ) \log (4)+\log ^2(4)}\right )}{22 x^4-21 x^5+5 x^6+\left (21 x^2-10 x^3\right ) \log (4)+5 \log ^2(4)} \, dx=x^{2} \log {\left (\frac {25 x^{6} - 110 x^{5} + 121 x^{4} + \left (- 100 x^{3} + 220 x^{2}\right ) \log {\left (2 \right )} + 100 \log {\left (2 \right )}^{2}}{x^{6} - 4 x^{5} + 4 x^{4} + \left (- 4 x^{3} + 8 x^{2}\right ) \log {\left (2 \right )} + 4 \log {\left (2 \right )}^{2}} \right )}^{2} \] Input:
integrate(((40*x*ln(2)**2+2*(-20*x**4+42*x**3)*ln(2)+10*x**7-42*x**6+44*x* *5)*ln((100*ln(2)**2+2*(-50*x**3+110*x**2)*ln(2)+25*x**6-110*x**5+121*x**4 )/(4*ln(2)**2+2*(-2*x**3+4*x**2)*ln(2)+x**6-4*x**5+4*x**4))**2+(16*x**3*ln (2)+4*x**6)*ln((100*ln(2)**2+2*(-50*x**3+110*x**2)*ln(2)+25*x**6-110*x**5+ 121*x**4)/(4*ln(2)**2+2*(-2*x**3+4*x**2)*ln(2)+x**6-4*x**5+4*x**4)))/(20*l n(2)**2+2*(-10*x**3+21*x**2)*ln(2)+5*x**6-21*x**5+22*x**4),x)
Output:
x**2*log((25*x**6 - 110*x**5 + 121*x**4 + (-100*x**3 + 220*x**2)*log(2) + 100*log(2)**2)/(x**6 - 4*x**5 + 4*x**4 + (-4*x**3 + 8*x**2)*log(2) + 4*log (2)**2))**2
Leaf count of result is larger than twice the leaf count of optimal. 80 vs. \(2 (29) = 58\).
Time = 0.16 (sec) , antiderivative size = 80, normalized size of antiderivative = 2.76 \[ \int \frac {\left (4 x^6+8 x^3 \log (4)\right ) \log \left (\frac {121 x^4-110 x^5+25 x^6+\left (110 x^2-50 x^3\right ) \log (4)+25 \log ^2(4)}{4 x^4-4 x^5+x^6+\left (4 x^2-2 x^3\right ) \log (4)+\log ^2(4)}\right )+\left (44 x^5-42 x^6+10 x^7+\left (42 x^3-20 x^4\right ) \log (4)+10 x \log ^2(4)\right ) \log ^2\left (\frac {121 x^4-110 x^5+25 x^6+\left (110 x^2-50 x^3\right ) \log (4)+25 \log ^2(4)}{4 x^4-4 x^5+x^6+\left (4 x^2-2 x^3\right ) \log (4)+\log ^2(4)}\right )}{22 x^4-21 x^5+5 x^6+\left (21 x^2-10 x^3\right ) \log (4)+5 \log ^2(4)} \, dx=4 \, x^{2} \log \left (5 \, x^{3} - 11 \, x^{2} - 10 \, \log \left (2\right )\right )^{2} - 8 \, x^{2} \log \left (5 \, x^{3} - 11 \, x^{2} - 10 \, \log \left (2\right )\right ) \log \left (x^{3} - 2 \, x^{2} - 2 \, \log \left (2\right )\right ) + 4 \, x^{2} \log \left (x^{3} - 2 \, x^{2} - 2 \, \log \left (2\right )\right )^{2} \] Input:
integrate(((40*x*log(2)^2+2*(-20*x^4+42*x^3)*log(2)+10*x^7-42*x^6+44*x^5)* log((100*log(2)^2+2*(-50*x^3+110*x^2)*log(2)+25*x^6-110*x^5+121*x^4)/(4*lo g(2)^2+2*(-2*x^3+4*x^2)*log(2)+x^6-4*x^5+4*x^4))^2+(16*x^3*log(2)+4*x^6)*l og((100*log(2)^2+2*(-50*x^3+110*x^2)*log(2)+25*x^6-110*x^5+121*x^4)/(4*log (2)^2+2*(-2*x^3+4*x^2)*log(2)+x^6-4*x^5+4*x^4)))/(20*log(2)^2+2*(-10*x^3+2 1*x^2)*log(2)+5*x^6-21*x^5+22*x^4),x, algorithm="maxima")
Output:
4*x^2*log(5*x^3 - 11*x^2 - 10*log(2))^2 - 8*x^2*log(5*x^3 - 11*x^2 - 10*lo g(2))*log(x^3 - 2*x^2 - 2*log(2)) + 4*x^2*log(x^3 - 2*x^2 - 2*log(2))^2
Leaf count of result is larger than twice the leaf count of optimal. 162 vs. \(2 (29) = 58\).
Time = 3.93 (sec) , antiderivative size = 162, normalized size of antiderivative = 5.59 \[ \int \frac {\left (4 x^6+8 x^3 \log (4)\right ) \log \left (\frac {121 x^4-110 x^5+25 x^6+\left (110 x^2-50 x^3\right ) \log (4)+25 \log ^2(4)}{4 x^4-4 x^5+x^6+\left (4 x^2-2 x^3\right ) \log (4)+\log ^2(4)}\right )+\left (44 x^5-42 x^6+10 x^7+\left (42 x^3-20 x^4\right ) \log (4)+10 x \log ^2(4)\right ) \log ^2\left (\frac {121 x^4-110 x^5+25 x^6+\left (110 x^2-50 x^3\right ) \log (4)+25 \log ^2(4)}{4 x^4-4 x^5+x^6+\left (4 x^2-2 x^3\right ) \log (4)+\log ^2(4)}\right )}{22 x^4-21 x^5+5 x^6+\left (21 x^2-10 x^3\right ) \log (4)+5 \log ^2(4)} \, dx=x^{2} \log \left (25 \, x^{6} - 110 \, x^{5} + 121 \, x^{4} - 100 \, x^{3} \log \left (2\right ) + 220 \, x^{2} \log \left (2\right ) + 100 \, \log \left (2\right )^{2}\right )^{2} - 2 \, x^{2} \log \left (25 \, x^{6} - 110 \, x^{5} + 121 \, x^{4} - 100 \, x^{3} \log \left (2\right ) + 220 \, x^{2} \log \left (2\right ) + 100 \, \log \left (2\right )^{2}\right ) \log \left (x^{6} - 4 \, x^{5} + 4 \, x^{4} - 4 \, x^{3} \log \left (2\right ) + 8 \, x^{2} \log \left (2\right ) + 4 \, \log \left (2\right )^{2}\right ) + x^{2} \log \left (x^{6} - 4 \, x^{5} + 4 \, x^{4} - 4 \, x^{3} \log \left (2\right ) + 8 \, x^{2} \log \left (2\right ) + 4 \, \log \left (2\right )^{2}\right )^{2} \] Input:
integrate(((40*x*log(2)^2+2*(-20*x^4+42*x^3)*log(2)+10*x^7-42*x^6+44*x^5)* log((100*log(2)^2+2*(-50*x^3+110*x^2)*log(2)+25*x^6-110*x^5+121*x^4)/(4*lo g(2)^2+2*(-2*x^3+4*x^2)*log(2)+x^6-4*x^5+4*x^4))^2+(16*x^3*log(2)+4*x^6)*l og((100*log(2)^2+2*(-50*x^3+110*x^2)*log(2)+25*x^6-110*x^5+121*x^4)/(4*log (2)^2+2*(-2*x^3+4*x^2)*log(2)+x^6-4*x^5+4*x^4)))/(20*log(2)^2+2*(-10*x^3+2 1*x^2)*log(2)+5*x^6-21*x^5+22*x^4),x, algorithm="giac")
Output:
x^2*log(25*x^6 - 110*x^5 + 121*x^4 - 100*x^3*log(2) + 220*x^2*log(2) + 100 *log(2)^2)^2 - 2*x^2*log(25*x^6 - 110*x^5 + 121*x^4 - 100*x^3*log(2) + 220 *x^2*log(2) + 100*log(2)^2)*log(x^6 - 4*x^5 + 4*x^4 - 4*x^3*log(2) + 8*x^2 *log(2) + 4*log(2)^2) + x^2*log(x^6 - 4*x^5 + 4*x^4 - 4*x^3*log(2) + 8*x^2 *log(2) + 4*log(2)^2)^2
Timed out. \[ \int \frac {\left (4 x^6+8 x^3 \log (4)\right ) \log \left (\frac {121 x^4-110 x^5+25 x^6+\left (110 x^2-50 x^3\right ) \log (4)+25 \log ^2(4)}{4 x^4-4 x^5+x^6+\left (4 x^2-2 x^3\right ) \log (4)+\log ^2(4)}\right )+\left (44 x^5-42 x^6+10 x^7+\left (42 x^3-20 x^4\right ) \log (4)+10 x \log ^2(4)\right ) \log ^2\left (\frac {121 x^4-110 x^5+25 x^6+\left (110 x^2-50 x^3\right ) \log (4)+25 \log ^2(4)}{4 x^4-4 x^5+x^6+\left (4 x^2-2 x^3\right ) \log (4)+\log ^2(4)}\right )}{22 x^4-21 x^5+5 x^6+\left (21 x^2-10 x^3\right ) \log (4)+5 \log ^2(4)} \, dx=\int \frac {\left (2\,\ln \left (2\right )\,\left (42\,x^3-20\,x^4\right )+40\,x\,{\ln \left (2\right )}^2+44\,x^5-42\,x^6+10\,x^7\right )\,{\ln \left (\frac {2\,\ln \left (2\right )\,\left (110\,x^2-50\,x^3\right )+100\,{\ln \left (2\right )}^2+121\,x^4-110\,x^5+25\,x^6}{2\,\ln \left (2\right )\,\left (4\,x^2-2\,x^3\right )+4\,{\ln \left (2\right )}^2+4\,x^4-4\,x^5+x^6}\right )}^2+\left (4\,x^6+16\,\ln \left (2\right )\,x^3\right )\,\ln \left (\frac {2\,\ln \left (2\right )\,\left (110\,x^2-50\,x^3\right )+100\,{\ln \left (2\right )}^2+121\,x^4-110\,x^5+25\,x^6}{2\,\ln \left (2\right )\,\left (4\,x^2-2\,x^3\right )+4\,{\ln \left (2\right )}^2+4\,x^4-4\,x^5+x^6}\right )}{2\,\ln \left (2\right )\,\left (21\,x^2-10\,x^3\right )+20\,{\ln \left (2\right )}^2+22\,x^4-21\,x^5+5\,x^6} \,d x \] Input:
int((log((2*log(2)*(110*x^2 - 50*x^3) + 100*log(2)^2 + 121*x^4 - 110*x^5 + 25*x^6)/(2*log(2)*(4*x^2 - 2*x^3) + 4*log(2)^2 + 4*x^4 - 4*x^5 + x^6))^2* (2*log(2)*(42*x^3 - 20*x^4) + 40*x*log(2)^2 + 44*x^5 - 42*x^6 + 10*x^7) + log((2*log(2)*(110*x^2 - 50*x^3) + 100*log(2)^2 + 121*x^4 - 110*x^5 + 25*x ^6)/(2*log(2)*(4*x^2 - 2*x^3) + 4*log(2)^2 + 4*x^4 - 4*x^5 + x^6))*(16*x^3 *log(2) + 4*x^6))/(2*log(2)*(21*x^2 - 10*x^3) + 20*log(2)^2 + 22*x^4 - 21* x^5 + 5*x^6),x)
Output:
int((log((2*log(2)*(110*x^2 - 50*x^3) + 100*log(2)^2 + 121*x^4 - 110*x^5 + 25*x^6)/(2*log(2)*(4*x^2 - 2*x^3) + 4*log(2)^2 + 4*x^4 - 4*x^5 + x^6))^2* (2*log(2)*(42*x^3 - 20*x^4) + 40*x*log(2)^2 + 44*x^5 - 42*x^6 + 10*x^7) + log((2*log(2)*(110*x^2 - 50*x^3) + 100*log(2)^2 + 121*x^4 - 110*x^5 + 25*x ^6)/(2*log(2)*(4*x^2 - 2*x^3) + 4*log(2)^2 + 4*x^4 - 4*x^5 + x^6))*(16*x^3 *log(2) + 4*x^6))/(2*log(2)*(21*x^2 - 10*x^3) + 20*log(2)^2 + 22*x^4 - 21* x^5 + 5*x^6), x)
Time = 0.21 (sec) , antiderivative size = 80, normalized size of antiderivative = 2.76 \[ \int \frac {\left (4 x^6+8 x^3 \log (4)\right ) \log \left (\frac {121 x^4-110 x^5+25 x^6+\left (110 x^2-50 x^3\right ) \log (4)+25 \log ^2(4)}{4 x^4-4 x^5+x^6+\left (4 x^2-2 x^3\right ) \log (4)+\log ^2(4)}\right )+\left (44 x^5-42 x^6+10 x^7+\left (42 x^3-20 x^4\right ) \log (4)+10 x \log ^2(4)\right ) \log ^2\left (\frac {121 x^4-110 x^5+25 x^6+\left (110 x^2-50 x^3\right ) \log (4)+25 \log ^2(4)}{4 x^4-4 x^5+x^6+\left (4 x^2-2 x^3\right ) \log (4)+\log ^2(4)}\right )}{22 x^4-21 x^5+5 x^6+\left (21 x^2-10 x^3\right ) \log (4)+5 \log ^2(4)} \, dx=\mathrm {log}\left (\frac {100 \mathrm {log}\left (2\right )^{2}-100 \,\mathrm {log}\left (2\right ) x^{3}+220 \,\mathrm {log}\left (2\right ) x^{2}+25 x^{6}-110 x^{5}+121 x^{4}}{4 \mathrm {log}\left (2\right )^{2}-4 \,\mathrm {log}\left (2\right ) x^{3}+8 \,\mathrm {log}\left (2\right ) x^{2}+x^{6}-4 x^{5}+4 x^{4}}\right )^{2} x^{2} \] Input:
int(((40*x*log(2)^2+2*(-20*x^4+42*x^3)*log(2)+10*x^7-42*x^6+44*x^5)*log((1 00*log(2)^2+2*(-50*x^3+110*x^2)*log(2)+25*x^6-110*x^5+121*x^4)/(4*log(2)^2 +2*(-2*x^3+4*x^2)*log(2)+x^6-4*x^5+4*x^4))^2+(16*x^3*log(2)+4*x^6)*log((10 0*log(2)^2+2*(-50*x^3+110*x^2)*log(2)+25*x^6-110*x^5+121*x^4)/(4*log(2)^2+ 2*(-2*x^3+4*x^2)*log(2)+x^6-4*x^5+4*x^4)))/(20*log(2)^2+2*(-10*x^3+21*x^2) *log(2)+5*x^6-21*x^5+22*x^4),x)
Output:
log((100*log(2)**2 - 100*log(2)*x**3 + 220*log(2)*x**2 + 25*x**6 - 110*x** 5 + 121*x**4)/(4*log(2)**2 - 4*log(2)*x**3 + 8*log(2)*x**2 + x**6 - 4*x**5 + 4*x**4))**2*x**2