Integrand size = 195, antiderivative size = 25 \[ \int \frac {-16 x-16 x^2 \log (2)+\left (-20+20 x-4 x^3\right ) \log ^2(2)+\left (16 x \log (2)+8 x^2 \log ^2(2)\right ) \log (-x)-4 x \log ^2(2) \log ^2(-x)}{64 x-32 x^2+4 x^3+\left (-80 x+84 x^2-32 x^3+4 x^4\right ) \log (2)+\left (25 x-40 x^2+26 x^3-8 x^4+x^5\right ) \log ^2(2)+\left (\left (-64 x+32 x^2-4 x^3\right ) \log (2)+\left (40 x-42 x^2+16 x^3-2 x^4\right ) \log ^2(2)\right ) \log (-x)+\left (16 x-8 x^2+x^3\right ) \log ^2(2) \log ^2(-x)} \, dx=\frac {4}{-4+x+\frac {5}{x+\frac {2}{\log (2)}-\log (-x)}} \] Output:
4/(5/(2/ln(2)+x-ln(-x))+x-4)
\[ \int \frac {-16 x-16 x^2 \log (2)+\left (-20+20 x-4 x^3\right ) \log ^2(2)+\left (16 x \log (2)+8 x^2 \log ^2(2)\right ) \log (-x)-4 x \log ^2(2) \log ^2(-x)}{64 x-32 x^2+4 x^3+\left (-80 x+84 x^2-32 x^3+4 x^4\right ) \log (2)+\left (25 x-40 x^2+26 x^3-8 x^4+x^5\right ) \log ^2(2)+\left (\left (-64 x+32 x^2-4 x^3\right ) \log (2)+\left (40 x-42 x^2+16 x^3-2 x^4\right ) \log ^2(2)\right ) \log (-x)+\left (16 x-8 x^2+x^3\right ) \log ^2(2) \log ^2(-x)} \, dx=\int \frac {-16 x-16 x^2 \log (2)+\left (-20+20 x-4 x^3\right ) \log ^2(2)+\left (16 x \log (2)+8 x^2 \log ^2(2)\right ) \log (-x)-4 x \log ^2(2) \log ^2(-x)}{64 x-32 x^2+4 x^3+\left (-80 x+84 x^2-32 x^3+4 x^4\right ) \log (2)+\left (25 x-40 x^2+26 x^3-8 x^4+x^5\right ) \log ^2(2)+\left (\left (-64 x+32 x^2-4 x^3\right ) \log (2)+\left (40 x-42 x^2+16 x^3-2 x^4\right ) \log ^2(2)\right ) \log (-x)+\left (16 x-8 x^2+x^3\right ) \log ^2(2) \log ^2(-x)} \, dx \] Input:
Integrate[(-16*x - 16*x^2*Log[2] + (-20 + 20*x - 4*x^3)*Log[2]^2 + (16*x*L og[2] + 8*x^2*Log[2]^2)*Log[-x] - 4*x*Log[2]^2*Log[-x]^2)/(64*x - 32*x^2 + 4*x^3 + (-80*x + 84*x^2 - 32*x^3 + 4*x^4)*Log[2] + (25*x - 40*x^2 + 26*x^ 3 - 8*x^4 + x^5)*Log[2]^2 + ((-64*x + 32*x^2 - 4*x^3)*Log[2] + (40*x - 42* x^2 + 16*x^3 - 2*x^4)*Log[2]^2)*Log[-x] + (16*x - 8*x^2 + x^3)*Log[2]^2*Lo g[-x]^2),x]
Output:
Integrate[(-16*x - 16*x^2*Log[2] + (-20 + 20*x - 4*x^3)*Log[2]^2 + (16*x*L og[2] + 8*x^2*Log[2]^2)*Log[-x] - 4*x*Log[2]^2*Log[-x]^2)/(64*x - 32*x^2 + 4*x^3 + (-80*x + 84*x^2 - 32*x^3 + 4*x^4)*Log[2] + (25*x - 40*x^2 + 26*x^ 3 - 8*x^4 + x^5)*Log[2]^2 + ((-64*x + 32*x^2 - 4*x^3)*Log[2] + (40*x - 42* x^2 + 16*x^3 - 2*x^4)*Log[2]^2)*Log[-x] + (16*x - 8*x^2 + x^3)*Log[2]^2*Lo g[-x]^2), x]
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.
| \(\displaystyle \int \frac {\left (-4 x^3+20 x-20\right ) \log ^2(2)+\left (8 x^2 \log ^2(2)+16 x \log (2)\right ) \log (-x)-16 x^2 \log (2)-16 x-4 x \log ^2(2) \log ^2(-x)}{4 x^3-32 x^2+\left (x^3-8 x^2+16 x\right ) \log ^2(2) \log ^2(-x)+\left (\left (-4 x^3+32 x^2-64 x\right ) \log (2)+\left (-2 x^4+16 x^3-42 x^2+40 x\right ) \log ^2(2)\right ) \log (-x)+\left (4 x^4-32 x^3+84 x^2-80 x\right ) \log (2)+\left (x^5-8 x^4+26 x^3-40 x^2+25 x\right ) \log ^2(2)+64 x} \, dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {4 \left (x^3 \left (-\log ^2(2)\right )-x^2 \log (16)-x \log ^2(2) \log ^2(-x)-x \left (4-5 \log ^2(2)\right )+2 x \log (2) (x \log (2)+2) \log (-x)-5 \log ^2(2)\right )}{x \left (x^2 \log (2)+x (2-4 \log (2))+(\log (16)-x \log (2)) \log (-x)-8 \left (1-\frac {5 \log (2)}{8}\right )\right )^2}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 4 \int -\frac {\log ^2(2) x^3+\log (16) x^2+\log ^2(2) \log ^2(-x) x-2 \log (2) (\log (2) x+2) \log (-x) x+\left (4-5 \log ^2(2)\right ) x+5 \log ^2(2)}{x \left (-\log (2) x^2-2 (1-\log (4)) x+(x \log (2)-\log (16)) \log (-x)-\log (32)+8\right )^2}dx\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle -4 \int \frac {\log ^2(2) x^3+\log (16) x^2+\log ^2(2) \log ^2(-x) x-2 \log (2) (\log (2) x+2) \log (-x) x+\left (4-5 \log ^2(2)\right ) x+5 \log ^2(2)}{x \left (-\log (2) x^2-2 (1-\log (4)) x+(x \log (2)-\log (16)) \log (-x)-\log (32)+8\right )^2}dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle -4 \int \frac {\log ^2(2) x^3+\log (16) x^2+\log ^2(2) \log ^2(-x) x-2 \log (2) (\log (2) x+2) \log (-x) x+\left (4-5 \log ^2(2)\right ) x+5 \log ^2(2)}{x \left (-\log (2) x^2-2 (1-\log (4)) x+(x \log (2)-\log (16)) \log (-x)+8 \left (1-\frac {5 \log (2)}{8}\right )\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -4 \int \left (\frac {2 \log (2) \left (5 \log ^2(2)-x \left (\log ^2(4)-\log (2) \log (16)\right )\right )}{(x \log (2)-\log (16))^2 \left (-\log (2) x^2+\log (2) \log (-x) x-2 (1-\log (4)) x-\log (16) \log (-x)+8 \left (1-\frac {5 \log (2)}{8}\right )\right )}+\frac {\log ^2(2)}{(x \log (2)-\log (16))^2}+\frac {-\log (2) \left (5 \log ^3(2)+2 \log ^2(16)-\log (2) \left (4 \log ^2(4)-4 \log (4) \log (16)+\log (16) (8+\log (16))\right )\right ) x^3+\left (5 \log ^4(2)+20 \log ^3(2) \log (4)-8 \log (2) \log (4) \log (16)+\log ^3(16)\right ) x^2+\left (25 \log ^4(2)-32 \log (2) \log (16)+4 \log ^2(16)-10 \log ^3(2) (8+\log (16))+\log ^2(2) \left (64+20 \log (16)-5 \log ^2(16)\right )\right ) x+5 \log ^2(2) \log ^2(16)}{x (x \log (2)-\log (16))^2 \left (-\log (2) x^2+\log (2) \log (-x) x-2 (1-\log (4)) x-\log (16) \log (-x)+8 \left (1-\frac {5 \log (2)}{8}\right )\right )^2}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle -4 \left (10 \log ^3(2) \int \frac {1}{(x \log (2)-\log (16))^2 \left (-\log (2) x^2+\log (2) \log (-x) x-2 (1-\log (4)) x-\log (16) \log (-x)+8 \left (1-\frac {5 \log (2)}{8}\right )\right )}dx+5 \log ^2(2) \int \frac {1}{x \left (-\log (2) x^2+\log (2) \log (-x) x-2 (1-\log (4)) x-\log (16) \log (-x)+8 \left (1-\frac {5 \log (2)}{8}\right )\right )^2}dx-\frac {\left (5 \log ^3(2)+(2+\log (4)) \log ^2(16)-\log (2) \left (4 \log ^2(4)+\log (16) (8+\log (16))\right )\right ) \int \frac {1}{\left (-\log (2) x^2+\log (2) \log (-x) x-2 (1-\log (4)) x-\log (16) \log (-x)+8 \left (1-\frac {5 \log (2)}{8}\right )\right )^2}dx}{\log (2)}-\frac {\left (-25 \log ^5(2)+80 \log ^4(2)+32 \log ^2(2) \log (16)-\log (2) \log ^2(16) \left (\log ^2(16)+\log (65536)\right )-\log ^3(16) \left (1+\log ^2(4)-\log (16)-\log (4) \log (16)\right )-\log ^3(2) \left (64-10 \log ^2(16)+20 (1+\log (4)) \log (16)\right )\right ) \int \frac {1}{(x \log (2)-\log (16))^2 \left (-\log (2) x^2+\log (2) \log (-x) x-2 (1-\log (4)) x-\log (16) \log (-x)+8 \left (1-\frac {5 \log (2)}{8}\right )\right )^2}dx}{\log (2)}-\frac {\log (2)}{x \log (2)-\log (16)}\right )\) |
Input:
Int[(-16*x - 16*x^2*Log[2] + (-20 + 20*x - 4*x^3)*Log[2]^2 + (16*x*Log[2] + 8*x^2*Log[2]^2)*Log[-x] - 4*x*Log[2]^2*Log[-x]^2)/(64*x - 32*x^2 + 4*x^3 + (-80*x + 84*x^2 - 32*x^3 + 4*x^4)*Log[2] + (25*x - 40*x^2 + 26*x^3 - 8* x^4 + x^5)*Log[2]^2 + ((-64*x + 32*x^2 - 4*x^3)*Log[2] + (40*x - 42*x^2 + 16*x^3 - 2*x^4)*Log[2]^2)*Log[-x] + (16*x - 8*x^2 + x^3)*Log[2]^2*Log[-x]^ 2),x]
Output:
$Aborted
Leaf count of result is larger than twice the leaf count of optimal. \(55\) vs. \(2(25)=50\).
Time = 2.96 (sec) , antiderivative size = 56, normalized size of antiderivative = 2.24
| method | result | size |
| derivativedivides | \(\frac {4 x \ln \left (2\right )-4 \ln \left (2\right ) \ln \left (-x \right )+8}{x^{2} \ln \left (2\right )-\ln \left (2\right ) \ln \left (-x \right ) x -4 x \ln \left (2\right )+4 \ln \left (2\right ) \ln \left (-x \right )+2 x +5 \ln \left (2\right )-8}\) | \(56\) |
| default | \(\frac {4 x \ln \left (2\right )-4 \ln \left (2\right ) \ln \left (-x \right )+8}{x^{2} \ln \left (2\right )-\ln \left (2\right ) \ln \left (-x \right ) x -4 x \ln \left (2\right )+4 \ln \left (2\right ) \ln \left (-x \right )+2 x +5 \ln \left (2\right )-8}\) | \(56\) |
| norman | \(\frac {4 x \ln \left (2\right )-4 \ln \left (2\right ) \ln \left (-x \right )+8}{x^{2} \ln \left (2\right )-\ln \left (2\right ) \ln \left (-x \right ) x -4 x \ln \left (2\right )+4 \ln \left (2\right ) \ln \left (-x \right )+2 x +5 \ln \left (2\right )-8}\) | \(56\) |
| risch | \(\frac {4}{x -4}-\frac {20 \ln \left (2\right )}{\left (x -4\right ) \left (x^{2} \ln \left (2\right )-\ln \left (2\right ) \ln \left (-x \right ) x -4 x \ln \left (2\right )+4 \ln \left (2\right ) \ln \left (-x \right )+2 x +5 \ln \left (2\right )-8\right )}\) | \(57\) |
| parallelrisch | \(\frac {-4 \ln \left (-x \right ) \ln \left (2\right )^{2}+4 x \ln \left (2\right )^{2}+8 \ln \left (2\right )}{\ln \left (2\right ) \left (x^{2} \ln \left (2\right )-\ln \left (2\right ) \ln \left (-x \right ) x -4 x \ln \left (2\right )+4 \ln \left (2\right ) \ln \left (-x \right )+2 x +5 \ln \left (2\right )-8\right )}\) | \(67\) |
Input:
int((-4*x*ln(2)^2*ln(-x)^2+(8*x^2*ln(2)^2+16*x*ln(2))*ln(-x)+(-4*x^3+20*x- 20)*ln(2)^2-16*x^2*ln(2)-16*x)/((x^3-8*x^2+16*x)*ln(2)^2*ln(-x)^2+((-2*x^4 +16*x^3-42*x^2+40*x)*ln(2)^2+(-4*x^3+32*x^2-64*x)*ln(2))*ln(-x)+(x^5-8*x^4 +26*x^3-40*x^2+25*x)*ln(2)^2+(4*x^4-32*x^3+84*x^2-80*x)*ln(2)+4*x^3-32*x^2 +64*x),x,method=_RETURNVERBOSE)
Output:
4*(-ln(2)*ln(-x)+x*ln(2)+2)/(x^2*ln(2)-ln(2)*ln(-x)*x-4*x*ln(2)+4*ln(2)*ln (-x)+2*x+5*ln(2)-8)
Time = 0.09 (sec) , antiderivative size = 45, normalized size of antiderivative = 1.80 \[ \int \frac {-16 x-16 x^2 \log (2)+\left (-20+20 x-4 x^3\right ) \log ^2(2)+\left (16 x \log (2)+8 x^2 \log ^2(2)\right ) \log (-x)-4 x \log ^2(2) \log ^2(-x)}{64 x-32 x^2+4 x^3+\left (-80 x+84 x^2-32 x^3+4 x^4\right ) \log (2)+\left (25 x-40 x^2+26 x^3-8 x^4+x^5\right ) \log ^2(2)+\left (\left (-64 x+32 x^2-4 x^3\right ) \log (2)+\left (40 x-42 x^2+16 x^3-2 x^4\right ) \log ^2(2)\right ) \log (-x)+\left (16 x-8 x^2+x^3\right ) \log ^2(2) \log ^2(-x)} \, dx=-\frac {4 \, {\left (x \log \left (2\right ) - \log \left (2\right ) \log \left (-x\right ) + 2\right )}}{{\left (x - 4\right )} \log \left (2\right ) \log \left (-x\right ) - {\left (x^{2} - 4 \, x + 5\right )} \log \left (2\right ) - 2 \, x + 8} \] Input:
integrate((-4*x*log(2)^2*log(-x)^2+(8*x^2*log(2)^2+16*x*log(2))*log(-x)+(- 4*x^3+20*x-20)*log(2)^2-16*x^2*log(2)-16*x)/((x^3-8*x^2+16*x)*log(2)^2*log (-x)^2+((-2*x^4+16*x^3-42*x^2+40*x)*log(2)^2+(-4*x^3+32*x^2-64*x)*log(2))* log(-x)+(x^5-8*x^4+26*x^3-40*x^2+25*x)*log(2)^2+(4*x^4-32*x^3+84*x^2-80*x) *log(2)+4*x^3-32*x^2+64*x),x, algorithm="fricas")
Output:
-4*(x*log(2) - log(2)*log(-x) + 2)/((x - 4)*log(2)*log(-x) - (x^2 - 4*x + 5)*log(2) - 2*x + 8)
Leaf count of result is larger than twice the leaf count of optimal. 70 vs. \(2 (17) = 34\).
Time = 0.21 (sec) , antiderivative size = 70, normalized size of antiderivative = 2.80 \[ \int \frac {-16 x-16 x^2 \log (2)+\left (-20+20 x-4 x^3\right ) \log ^2(2)+\left (16 x \log (2)+8 x^2 \log ^2(2)\right ) \log (-x)-4 x \log ^2(2) \log ^2(-x)}{64 x-32 x^2+4 x^3+\left (-80 x+84 x^2-32 x^3+4 x^4\right ) \log (2)+\left (25 x-40 x^2+26 x^3-8 x^4+x^5\right ) \log ^2(2)+\left (\left (-64 x+32 x^2-4 x^3\right ) \log (2)+\left (40 x-42 x^2+16 x^3-2 x^4\right ) \log ^2(2)\right ) \log (-x)+\left (16 x-8 x^2+x^3\right ) \log ^2(2) \log ^2(-x)} \, dx=\frac {20 \log {\left (2 \right )}}{- x^{3} \log {\left (2 \right )} - 2 x^{2} + 8 x^{2} \log {\left (2 \right )} - 21 x \log {\left (2 \right )} + 16 x + \left (x^{2} \log {\left (2 \right )} - 8 x \log {\left (2 \right )} + 16 \log {\left (2 \right )}\right ) \log {\left (- x \right )} - 32 + 20 \log {\left (2 \right )}} + \frac {4}{x - 4} \] Input:
integrate((-4*x*ln(2)**2*ln(-x)**2+(8*x**2*ln(2)**2+16*x*ln(2))*ln(-x)+(-4 *x**3+20*x-20)*ln(2)**2-16*x**2*ln(2)-16*x)/((x**3-8*x**2+16*x)*ln(2)**2*l n(-x)**2+((-2*x**4+16*x**3-42*x**2+40*x)*ln(2)**2+(-4*x**3+32*x**2-64*x)*l n(2))*ln(-x)+(x**5-8*x**4+26*x**3-40*x**2+25*x)*ln(2)**2+(4*x**4-32*x**3+8 4*x**2-80*x)*ln(2)+4*x**3-32*x**2+64*x),x)
Output:
20*log(2)/(-x**3*log(2) - 2*x**2 + 8*x**2*log(2) - 21*x*log(2) + 16*x + (x **2*log(2) - 8*x*log(2) + 16*log(2))*log(-x) - 32 + 20*log(2)) + 4/(x - 4)
Leaf count of result is larger than twice the leaf count of optimal. 54 vs. \(2 (25) = 50\).
Time = 0.16 (sec) , antiderivative size = 54, normalized size of antiderivative = 2.16 \[ \int \frac {-16 x-16 x^2 \log (2)+\left (-20+20 x-4 x^3\right ) \log ^2(2)+\left (16 x \log (2)+8 x^2 \log ^2(2)\right ) \log (-x)-4 x \log ^2(2) \log ^2(-x)}{64 x-32 x^2+4 x^3+\left (-80 x+84 x^2-32 x^3+4 x^4\right ) \log (2)+\left (25 x-40 x^2+26 x^3-8 x^4+x^5\right ) \log ^2(2)+\left (\left (-64 x+32 x^2-4 x^3\right ) \log (2)+\left (40 x-42 x^2+16 x^3-2 x^4\right ) \log ^2(2)\right ) \log (-x)+\left (16 x-8 x^2+x^3\right ) \log ^2(2) \log ^2(-x)} \, dx=\frac {4 \, {\left (x \log \left (2\right ) - \log \left (2\right ) \log \left (-x\right ) + 2\right )}}{x^{2} \log \left (2\right ) - 2 \, x {\left (2 \, \log \left (2\right ) - 1\right )} - {\left (x \log \left (2\right ) - 4 \, \log \left (2\right )\right )} \log \left (-x\right ) + 5 \, \log \left (2\right ) - 8} \] Input:
integrate((-4*x*log(2)^2*log(-x)^2+(8*x^2*log(2)^2+16*x*log(2))*log(-x)+(- 4*x^3+20*x-20)*log(2)^2-16*x^2*log(2)-16*x)/((x^3-8*x^2+16*x)*log(2)^2*log (-x)^2+((-2*x^4+16*x^3-42*x^2+40*x)*log(2)^2+(-4*x^3+32*x^2-64*x)*log(2))* log(-x)+(x^5-8*x^4+26*x^3-40*x^2+25*x)*log(2)^2+(4*x^4-32*x^3+84*x^2-80*x) *log(2)+4*x^3-32*x^2+64*x),x, algorithm="maxima")
Output:
4*(x*log(2) - log(2)*log(-x) + 2)/(x^2*log(2) - 2*x*(2*log(2) - 1) - (x*lo g(2) - 4*log(2))*log(-x) + 5*log(2) - 8)
Leaf count of result is larger than twice the leaf count of optimal. 74 vs. \(2 (25) = 50\).
Time = 0.14 (sec) , antiderivative size = 74, normalized size of antiderivative = 2.96 \[ \int \frac {-16 x-16 x^2 \log (2)+\left (-20+20 x-4 x^3\right ) \log ^2(2)+\left (16 x \log (2)+8 x^2 \log ^2(2)\right ) \log (-x)-4 x \log ^2(2) \log ^2(-x)}{64 x-32 x^2+4 x^3+\left (-80 x+84 x^2-32 x^3+4 x^4\right ) \log (2)+\left (25 x-40 x^2+26 x^3-8 x^4+x^5\right ) \log ^2(2)+\left (\left (-64 x+32 x^2-4 x^3\right ) \log (2)+\left (40 x-42 x^2+16 x^3-2 x^4\right ) \log ^2(2)\right ) \log (-x)+\left (16 x-8 x^2+x^3\right ) \log ^2(2) \log ^2(-x)} \, dx=-\frac {20 \, \log \left (2\right )}{x^{3} \log \left (2\right ) - x^{2} \log \left (2\right ) \log \left (-x\right ) - 8 \, x^{2} \log \left (2\right ) + 8 \, x \log \left (2\right ) \log \left (-x\right ) + 2 \, x^{2} + 21 \, x \log \left (2\right ) - 16 \, \log \left (2\right ) \log \left (-x\right ) - 16 \, x - 20 \, \log \left (2\right ) + 32} + \frac {4}{x - 4} \] Input:
integrate((-4*x*log(2)^2*log(-x)^2+(8*x^2*log(2)^2+16*x*log(2))*log(-x)+(- 4*x^3+20*x-20)*log(2)^2-16*x^2*log(2)-16*x)/((x^3-8*x^2+16*x)*log(2)^2*log (-x)^2+((-2*x^4+16*x^3-42*x^2+40*x)*log(2)^2+(-4*x^3+32*x^2-64*x)*log(2))* log(-x)+(x^5-8*x^4+26*x^3-40*x^2+25*x)*log(2)^2+(4*x^4-32*x^3+84*x^2-80*x) *log(2)+4*x^3-32*x^2+64*x),x, algorithm="giac")
Output:
-20*log(2)/(x^3*log(2) - x^2*log(2)*log(-x) - 8*x^2*log(2) + 8*x*log(2)*lo g(-x) + 2*x^2 + 21*x*log(2) - 16*log(2)*log(-x) - 16*x - 20*log(2) + 32) + 4/(x - 4)
Timed out. \[ \int \frac {-16 x-16 x^2 \log (2)+\left (-20+20 x-4 x^3\right ) \log ^2(2)+\left (16 x \log (2)+8 x^2 \log ^2(2)\right ) \log (-x)-4 x \log ^2(2) \log ^2(-x)}{64 x-32 x^2+4 x^3+\left (-80 x+84 x^2-32 x^3+4 x^4\right ) \log (2)+\left (25 x-40 x^2+26 x^3-8 x^4+x^5\right ) \log ^2(2)+\left (\left (-64 x+32 x^2-4 x^3\right ) \log (2)+\left (40 x-42 x^2+16 x^3-2 x^4\right ) \log ^2(2)\right ) \log (-x)+\left (16 x-8 x^2+x^3\right ) \log ^2(2) \log ^2(-x)} \, dx=\int -\frac {16\,x-\ln \left (-x\right )\,\left (8\,{\ln \left (2\right )}^2\,x^2+16\,\ln \left (2\right )\,x\right )+{\ln \left (2\right )}^2\,\left (4\,x^3-20\,x+20\right )+16\,x^2\,\ln \left (2\right )+4\,x\,{\ln \left (-x\right )}^2\,{\ln \left (2\right )}^2}{64\,x+\ln \left (-x\right )\,\left ({\ln \left (2\right )}^2\,\left (-2\,x^4+16\,x^3-42\,x^2+40\,x\right )-\ln \left (2\right )\,\left (4\,x^3-32\,x^2+64\,x\right )\right )-\ln \left (2\right )\,\left (-4\,x^4+32\,x^3-84\,x^2+80\,x\right )-32\,x^2+4\,x^3+{\ln \left (2\right )}^2\,\left (x^5-8\,x^4+26\,x^3-40\,x^2+25\,x\right )+{\ln \left (-x\right )}^2\,{\ln \left (2\right )}^2\,\left (x^3-8\,x^2+16\,x\right )} \,d x \] Input:
int(-(16*x - log(-x)*(8*x^2*log(2)^2 + 16*x*log(2)) + log(2)^2*(4*x^3 - 20 *x + 20) + 16*x^2*log(2) + 4*x*log(-x)^2*log(2)^2)/(64*x + log(-x)*(log(2) ^2*(40*x - 42*x^2 + 16*x^3 - 2*x^4) - log(2)*(64*x - 32*x^2 + 4*x^3)) - lo g(2)*(80*x - 84*x^2 + 32*x^3 - 4*x^4) - 32*x^2 + 4*x^3 + log(2)^2*(25*x - 40*x^2 + 26*x^3 - 8*x^4 + x^5) + log(-x)^2*log(2)^2*(16*x - 8*x^2 + x^3)), x)
Output:
int(-(16*x - log(-x)*(8*x^2*log(2)^2 + 16*x*log(2)) + log(2)^2*(4*x^3 - 20 *x + 20) + 16*x^2*log(2) + 4*x*log(-x)^2*log(2)^2)/(64*x + log(-x)*(log(2) ^2*(40*x - 42*x^2 + 16*x^3 - 2*x^4) - log(2)*(64*x - 32*x^2 + 4*x^3)) - lo g(2)*(80*x - 84*x^2 + 32*x^3 - 4*x^4) - 32*x^2 + 4*x^3 + log(2)^2*(25*x - 40*x^2 + 26*x^3 - 8*x^4 + x^5) + log(-x)^2*log(2)^2*(16*x - 8*x^2 + x^3)), x)
Time = 0.16 (sec) , antiderivative size = 306, normalized size of antiderivative = 12.24 \[ \int \frac {-16 x-16 x^2 \log (2)+\left (-20+20 x-4 x^3\right ) \log ^2(2)+\left (16 x \log (2)+8 x^2 \log ^2(2)\right ) \log (-x)-4 x \log ^2(2) \log ^2(-x)}{64 x-32 x^2+4 x^3+\left (-80 x+84 x^2-32 x^3+4 x^4\right ) \log (2)+\left (25 x-40 x^2+26 x^3-8 x^4+x^5\right ) \log ^2(2)+\left (\left (-64 x+32 x^2-4 x^3\right ) \log (2)+\left (40 x-42 x^2+16 x^3-2 x^4\right ) \log ^2(2)\right ) \log (-x)+\left (16 x-8 x^2+x^3\right ) \log ^2(2) \log ^2(-x)} \, dx=\frac {20 \mathrm {log}\left (-x \right )^{2} \mathrm {log}\left (2\right )^{3} x -80 \mathrm {log}\left (-x \right )^{2} \mathrm {log}\left (2\right )^{3}-20 \,\mathrm {log}\left (-x \right ) \mathrm {log}\left (x \right ) \mathrm {log}\left (2\right )^{3} x +80 \,\mathrm {log}\left (-x \right ) \mathrm {log}\left (x \right ) \mathrm {log}\left (2\right )^{3}-20 \,\mathrm {log}\left (-x \right ) \mathrm {log}\left (2\right )^{3} x^{2}+80 \,\mathrm {log}\left (-x \right ) \mathrm {log}\left (2\right )^{3} x -80 \,\mathrm {log}\left (-x \right ) \mathrm {log}\left (2\right )^{2} x +64 \,\mathrm {log}\left (-x \right ) \mathrm {log}\left (2\right ) x +20 \,\mathrm {log}\left (x \right ) \mathrm {log}\left (2\right )^{3} x^{2}-80 \,\mathrm {log}\left (x \right ) \mathrm {log}\left (2\right )^{3} x +100 \,\mathrm {log}\left (x \right ) \mathrm {log}\left (2\right )^{3}+40 \,\mathrm {log}\left (x \right ) \mathrm {log}\left (2\right )^{2} x -160 \,\mathrm {log}\left (x \right ) \mathrm {log}\left (2\right )^{2}-100 \mathrm {log}\left (2\right )^{3} x +40 \mathrm {log}\left (2\right )^{2} x^{2}+160 \mathrm {log}\left (2\right )^{2} x -64 \,\mathrm {log}\left (2\right ) x^{2}+80 \,\mathrm {log}\left (2\right ) x -128 x}{25 \,\mathrm {log}\left (-x \right ) \mathrm {log}\left (2\right )^{3} x -100 \,\mathrm {log}\left (-x \right ) \mathrm {log}\left (2\right )^{3}-80 \,\mathrm {log}\left (-x \right ) \mathrm {log}\left (2\right )^{2} x +320 \,\mathrm {log}\left (-x \right ) \mathrm {log}\left (2\right )^{2}+64 \,\mathrm {log}\left (-x \right ) \mathrm {log}\left (2\right ) x -256 \,\mathrm {log}\left (-x \right ) \mathrm {log}\left (2\right )-25 \mathrm {log}\left (2\right )^{3} x^{2}+100 \mathrm {log}\left (2\right )^{3} x -125 \mathrm {log}\left (2\right )^{3}+80 \mathrm {log}\left (2\right )^{2} x^{2}-370 \mathrm {log}\left (2\right )^{2} x +600 \mathrm {log}\left (2\right )^{2}-64 \,\mathrm {log}\left (2\right ) x^{2}+416 \,\mathrm {log}\left (2\right ) x -960 \,\mathrm {log}\left (2\right )-128 x +512} \] Input:
int((-4*x*log(2)^2*log(-x)^2+(8*x^2*log(2)^2+16*x*log(2))*log(-x)+(-4*x^3+ 20*x-20)*log(2)^2-16*x^2*log(2)-16*x)/((x^3-8*x^2+16*x)*log(2)^2*log(-x)^2 +((-2*x^4+16*x^3-42*x^2+40*x)*log(2)^2+(-4*x^3+32*x^2-64*x)*log(2))*log(-x )+(x^5-8*x^4+26*x^3-40*x^2+25*x)*log(2)^2+(4*x^4-32*x^3+84*x^2-80*x)*log(2 )+4*x^3-32*x^2+64*x),x)
Output:
(4*(5*log( - x)**2*log(2)**3*x - 20*log( - x)**2*log(2)**3 - 5*log( - x)*l og(x)*log(2)**3*x + 20*log( - x)*log(x)*log(2)**3 - 5*log( - x)*log(2)**3* x**2 + 20*log( - x)*log(2)**3*x - 20*log( - x)*log(2)**2*x + 16*log( - x)* log(2)*x + 5*log(x)*log(2)**3*x**2 - 20*log(x)*log(2)**3*x + 25*log(x)*log (2)**3 + 10*log(x)*log(2)**2*x - 40*log(x)*log(2)**2 - 25*log(2)**3*x + 10 *log(2)**2*x**2 + 40*log(2)**2*x - 16*log(2)*x**2 + 20*log(2)*x - 32*x))/( 25*log( - x)*log(2)**3*x - 100*log( - x)*log(2)**3 - 80*log( - x)*log(2)** 2*x + 320*log( - x)*log(2)**2 + 64*log( - x)*log(2)*x - 256*log( - x)*log( 2) - 25*log(2)**3*x**2 + 100*log(2)**3*x - 125*log(2)**3 + 80*log(2)**2*x* *2 - 370*log(2)**2*x + 600*log(2)**2 - 64*log(2)*x**2 + 416*log(2)*x - 960 *log(2) - 128*x + 512)