Integrand size = 257, antiderivative size = 32 \[ \int \frac {-6+27 x-28 x^2+8 x^3+4 x^2 \log \left (\frac {1}{4} (-2+x)\right )+\left (-24 x+44 x^2-16 x^3\right ) \log ^2\left (\frac {1}{4} (-2+x)\right )+\left (-16 x^2+8 x^3\right ) \log ^4\left (\frac {1}{4} (-2+x)\right )+\left (12-46 x+52 x^2-16 x^3+\left (40 x-84 x^2+32 x^3\right ) \log ^2\left (\frac {1}{4} (-2+x)\right )+\left (32 x^2-16 x^3\right ) \log ^4\left (\frac {1}{4} (-2+x)\right )\right ) \log \left (\frac {-2 x+4 x^2-4 x^2 \log ^2\left (\frac {1}{4} (-2+x)\right )}{3-4 x+4 x \log ^2\left (\frac {1}{4} (-2+x)\right )}\right )}{-6 x^3+23 x^4-26 x^5+8 x^6+\left (-20 x^4+42 x^5-16 x^6\right ) \log ^2\left (\frac {1}{4} (-2+x)\right )+\left (-16 x^5+8 x^6\right ) \log ^4\left (\frac {1}{4} (-2+x)\right )} \, dx=\frac {\log \left (-x+\frac {x}{3-x \left (4-4 \log ^2\left (\frac {1}{4} (-2+x)\right )\right )}\right )}{x^2} \] Output:
ln(x/(3-(4-4*ln(1/4*x-1/2)^2)*x)-x)/x^2
Time = 1.80 (sec) , antiderivative size = 46, normalized size of antiderivative = 1.44 \[ \int \frac {-6+27 x-28 x^2+8 x^3+4 x^2 \log \left (\frac {1}{4} (-2+x)\right )+\left (-24 x+44 x^2-16 x^3\right ) \log ^2\left (\frac {1}{4} (-2+x)\right )+\left (-16 x^2+8 x^3\right ) \log ^4\left (\frac {1}{4} (-2+x)\right )+\left (12-46 x+52 x^2-16 x^3+\left (40 x-84 x^2+32 x^3\right ) \log ^2\left (\frac {1}{4} (-2+x)\right )+\left (32 x^2-16 x^3\right ) \log ^4\left (\frac {1}{4} (-2+x)\right )\right ) \log \left (\frac {-2 x+4 x^2-4 x^2 \log ^2\left (\frac {1}{4} (-2+x)\right )}{3-4 x+4 x \log ^2\left (\frac {1}{4} (-2+x)\right )}\right )}{-6 x^3+23 x^4-26 x^5+8 x^6+\left (-20 x^4+42 x^5-16 x^6\right ) \log ^2\left (\frac {1}{4} (-2+x)\right )+\left (-16 x^5+8 x^6\right ) \log ^4\left (\frac {1}{4} (-2+x)\right )} \, dx=\frac {\log \left (-\frac {2 x \left (1-2 x+2 x \log ^2\left (\frac {1}{4} (-2+x)\right )\right )}{3-4 x+4 x \log ^2\left (\frac {1}{4} (-2+x)\right )}\right )}{x^2} \] Input:
Integrate[(-6 + 27*x - 28*x^2 + 8*x^3 + 4*x^2*Log[(-2 + x)/4] + (-24*x + 4 4*x^2 - 16*x^3)*Log[(-2 + x)/4]^2 + (-16*x^2 + 8*x^3)*Log[(-2 + x)/4]^4 + (12 - 46*x + 52*x^2 - 16*x^3 + (40*x - 84*x^2 + 32*x^3)*Log[(-2 + x)/4]^2 + (32*x^2 - 16*x^3)*Log[(-2 + x)/4]^4)*Log[(-2*x + 4*x^2 - 4*x^2*Log[(-2 + x)/4]^2)/(3 - 4*x + 4*x*Log[(-2 + x)/4]^2)])/(-6*x^3 + 23*x^4 - 26*x^5 + 8*x^6 + (-20*x^4 + 42*x^5 - 16*x^6)*Log[(-2 + x)/4]^2 + (-16*x^5 + 8*x^6)* Log[(-2 + x)/4]^4),x]
Output:
Log[(-2*x*(1 - 2*x + 2*x*Log[(-2 + x)/4]^2))/(3 - 4*x + 4*x*Log[(-2 + x)/4 ]^2)]/x^2
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.
| \(\displaystyle \int \frac {8 x^3-28 x^2+4 x^2 \log \left (\frac {x-2}{4}\right )+\left (8 x^3-16 x^2\right ) \log ^4\left (\frac {x-2}{4}\right )+\left (-16 x^3+44 x^2-24 x\right ) \log ^2\left (\frac {x-2}{4}\right )+\left (-16 x^3+52 x^2+\left (32 x^2-16 x^3\right ) \log ^4\left (\frac {x-2}{4}\right )+\left (32 x^3-84 x^2+40 x\right ) \log ^2\left (\frac {x-2}{4}\right )-46 x+12\right ) \log \left (\frac {4 x^2-4 x^2 \log ^2\left (\frac {x-2}{4}\right )-2 x}{-4 x+4 x \log ^2\left (\frac {x-2}{4}\right )+3}\right )+27 x-6}{8 x^6-26 x^5+23 x^4-6 x^3+\left (8 x^6-16 x^5\right ) \log ^4\left (\frac {x-2}{4}\right )+\left (-16 x^6+42 x^5-20 x^4\right ) \log ^2\left (\frac {x-2}{4}\right )} \, dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {-8 x^3+28 x^2-4 x^2 \log \left (\frac {x-2}{4}\right )-\left (\left (8 x^3-16 x^2\right ) \log ^4\left (\frac {x-2}{4}\right )\right )-\left (-16 x^3+44 x^2-24 x\right ) \log ^2\left (\frac {x-2}{4}\right )-\left (-16 x^3+52 x^2+\left (32 x^2-16 x^3\right ) \log ^4\left (\frac {x-2}{4}\right )+\left (32 x^3-84 x^2+40 x\right ) \log ^2\left (\frac {x-2}{4}\right )-46 x+12\right ) \log \left (\frac {4 x^2-4 x^2 \log ^2\left (\frac {x-2}{4}\right )-2 x}{-4 x+4 x \log ^2\left (\frac {x-2}{4}\right )+3}\right )-27 x+6}{(2-x) x^3 \left (8 x^2+8 x^2 \log ^4\left (\frac {x-2}{4}\right )-16 x^2 \log ^2\left (\frac {x-2}{4}\right )-10 x+10 x \log ^2\left (\frac {x-2}{4}\right )+3\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {2 \log \left (-\frac {2 x \left (-2 x+2 x \log ^2\left (\frac {x-2}{4}\right )+1\right )}{-4 x+4 x \log ^2\left (\frac {x-2}{4}\right )+3}\right )}{x^3}-\frac {6}{(x-2) x^3 \left (-2 x+2 x \log ^2\left (\frac {x-2}{4}\right )+1\right ) \left (-4 x+4 x \log ^2\left (\frac {x-2}{4}\right )+3\right )}+\frac {4 (3-4 x) \log ^2\left (\frac {x}{4}-\frac {1}{2}\right )}{x^2 \left (-2 x+2 x \log ^2\left (\frac {x-2}{4}\right )+1\right ) \left (-4 x+4 x \log ^2\left (\frac {x-2}{4}\right )+3\right )}+\frac {27}{(x-2) x^2 \left (-2 x+2 x \log ^2\left (\frac {x-2}{4}\right )+1\right ) \left (-4 x+4 x \log ^2\left (\frac {x-2}{4}\right )+3\right )}+\frac {4 \log \left (\frac {x}{4}-\frac {1}{2}\right )}{(x-2) x \left (-2 x+2 x \log ^2\left (\frac {x-2}{4}\right )+1\right ) \left (-4 x+4 x \log ^2\left (\frac {x-2}{4}\right )+3\right )}+\frac {8}{(x-2) \left (-2 x+2 x \log ^2\left (\frac {x-2}{4}\right )+1\right ) \left (-4 x+4 x \log ^2\left (\frac {x-2}{4}\right )+3\right )}-\frac {28}{(x-2) x \left (-2 x+2 x \log ^2\left (\frac {x-2}{4}\right )+1\right ) \left (-4 x+4 x \log ^2\left (\frac {x-2}{4}\right )+3\right )}+\frac {8 \log ^4\left (\frac {x}{4}-\frac {1}{2}\right )}{x \left (-2 x+2 x \log ^2\left (\frac {x-2}{4}\right )+1\right ) \left (-4 x+4 x \log ^2\left (\frac {x-2}{4}\right )+3\right )}\right )dx\) |
| \(\Big \downarrow \) 7299 |
| \(\displaystyle \int \left (-\frac {2 \log \left (-\frac {2 x \left (-2 x+2 x \log ^2\left (\frac {x-2}{4}\right )+1\right )}{-4 x+4 x \log ^2\left (\frac {x-2}{4}\right )+3}\right )}{x^3}-\frac {6}{(x-2) x^3 \left (-2 x+2 x \log ^2\left (\frac {x-2}{4}\right )+1\right ) \left (-4 x+4 x \log ^2\left (\frac {x-2}{4}\right )+3\right )}+\frac {4 (3-4 x) \log ^2\left (\frac {x}{4}-\frac {1}{2}\right )}{x^2 \left (-2 x+2 x \log ^2\left (\frac {x-2}{4}\right )+1\right ) \left (-4 x+4 x \log ^2\left (\frac {x-2}{4}\right )+3\right )}+\frac {27}{(x-2) x^2 \left (-2 x+2 x \log ^2\left (\frac {x-2}{4}\right )+1\right ) \left (-4 x+4 x \log ^2\left (\frac {x-2}{4}\right )+3\right )}+\frac {4 \log \left (\frac {x}{4}-\frac {1}{2}\right )}{(x-2) x \left (-2 x+2 x \log ^2\left (\frac {x-2}{4}\right )+1\right ) \left (-4 x+4 x \log ^2\left (\frac {x-2}{4}\right )+3\right )}+\frac {8}{(x-2) \left (-2 x+2 x \log ^2\left (\frac {x-2}{4}\right )+1\right ) \left (-4 x+4 x \log ^2\left (\frac {x-2}{4}\right )+3\right )}-\frac {28}{(x-2) x \left (-2 x+2 x \log ^2\left (\frac {x-2}{4}\right )+1\right ) \left (-4 x+4 x \log ^2\left (\frac {x-2}{4}\right )+3\right )}+\frac {8 \log ^4\left (\frac {x}{4}-\frac {1}{2}\right )}{x \left (-2 x+2 x \log ^2\left (\frac {x-2}{4}\right )+1\right ) \left (-4 x+4 x \log ^2\left (\frac {x-2}{4}\right )+3\right )}\right )dx\) |
Input:
Int[(-6 + 27*x - 28*x^2 + 8*x^3 + 4*x^2*Log[(-2 + x)/4] + (-24*x + 44*x^2 - 16*x^3)*Log[(-2 + x)/4]^2 + (-16*x^2 + 8*x^3)*Log[(-2 + x)/4]^4 + (12 - 46*x + 52*x^2 - 16*x^3 + (40*x - 84*x^2 + 32*x^3)*Log[(-2 + x)/4]^2 + (32* x^2 - 16*x^3)*Log[(-2 + x)/4]^4)*Log[(-2*x + 4*x^2 - 4*x^2*Log[(-2 + x)/4] ^2)/(3 - 4*x + 4*x*Log[(-2 + x)/4]^2)])/(-6*x^3 + 23*x^4 - 26*x^5 + 8*x^6 + (-20*x^4 + 42*x^5 - 16*x^6)*Log[(-2 + x)/4]^2 + (-16*x^5 + 8*x^6)*Log[(- 2 + x)/4]^4),x]
Output:
$Aborted
Time = 68.22 (sec) , antiderivative size = 47, normalized size of antiderivative = 1.47
| method | result | size |
| parallelrisch | \(\frac {\ln \left (\frac {-4 x^{2} \ln \left (\frac {x}{4}-\frac {1}{2}\right )^{2}+4 x^{2}-2 x}{4 x \ln \left (\frac {x}{4}-\frac {1}{2}\right )^{2}+3-4 x}\right )}{x^{2}}\) | \(47\) |
| risch | \(\text {Expression too large to display}\) | \(568\) |
Input:
int((((-16*x^3+32*x^2)*ln(1/4*x-1/2)^4+(32*x^3-84*x^2+40*x)*ln(1/4*x-1/2)^ 2-16*x^3+52*x^2-46*x+12)*ln((-4*x^2*ln(1/4*x-1/2)^2+4*x^2-2*x)/(4*x*ln(1/4 *x-1/2)^2+3-4*x))+(8*x^3-16*x^2)*ln(1/4*x-1/2)^4+(-16*x^3+44*x^2-24*x)*ln( 1/4*x-1/2)^2+4*x^2*ln(1/4*x-1/2)+8*x^3-28*x^2+27*x-6)/((8*x^6-16*x^5)*ln(1 /4*x-1/2)^4+(-16*x^6+42*x^5-20*x^4)*ln(1/4*x-1/2)^2+8*x^6-26*x^5+23*x^4-6* x^3),x,method=_RETURNVERBOSE)
Output:
ln((-4*x^2*ln(1/4*x-1/2)^2+4*x^2-2*x)/(4*x*ln(1/4*x-1/2)^2+3-4*x))/x^2
Time = 0.09 (sec) , antiderivative size = 45, normalized size of antiderivative = 1.41 \[ \int \frac {-6+27 x-28 x^2+8 x^3+4 x^2 \log \left (\frac {1}{4} (-2+x)\right )+\left (-24 x+44 x^2-16 x^3\right ) \log ^2\left (\frac {1}{4} (-2+x)\right )+\left (-16 x^2+8 x^3\right ) \log ^4\left (\frac {1}{4} (-2+x)\right )+\left (12-46 x+52 x^2-16 x^3+\left (40 x-84 x^2+32 x^3\right ) \log ^2\left (\frac {1}{4} (-2+x)\right )+\left (32 x^2-16 x^3\right ) \log ^4\left (\frac {1}{4} (-2+x)\right )\right ) \log \left (\frac {-2 x+4 x^2-4 x^2 \log ^2\left (\frac {1}{4} (-2+x)\right )}{3-4 x+4 x \log ^2\left (\frac {1}{4} (-2+x)\right )}\right )}{-6 x^3+23 x^4-26 x^5+8 x^6+\left (-20 x^4+42 x^5-16 x^6\right ) \log ^2\left (\frac {1}{4} (-2+x)\right )+\left (-16 x^5+8 x^6\right ) \log ^4\left (\frac {1}{4} (-2+x)\right )} \, dx=\frac {\log \left (-\frac {2 \, {\left (2 \, x^{2} \log \left (\frac {1}{4} \, x - \frac {1}{2}\right )^{2} - 2 \, x^{2} + x\right )}}{4 \, x \log \left (\frac {1}{4} \, x - \frac {1}{2}\right )^{2} - 4 \, x + 3}\right )}{x^{2}} \] Input:
integrate((((-16*x^3+32*x^2)*log(1/4*x-1/2)^4+(32*x^3-84*x^2+40*x)*log(1/4 *x-1/2)^2-16*x^3+52*x^2-46*x+12)*log((-4*x^2*log(1/4*x-1/2)^2+4*x^2-2*x)/( 4*x*log(1/4*x-1/2)^2+3-4*x))+(8*x^3-16*x^2)*log(1/4*x-1/2)^4+(-16*x^3+44*x ^2-24*x)*log(1/4*x-1/2)^2+4*x^2*log(1/4*x-1/2)+8*x^3-28*x^2+27*x-6)/((8*x^ 6-16*x^5)*log(1/4*x-1/2)^4+(-16*x^6+42*x^5-20*x^4)*log(1/4*x-1/2)^2+8*x^6- 26*x^5+23*x^4-6*x^3),x, algorithm="fricas")
Output:
log(-2*(2*x^2*log(1/4*x - 1/2)^2 - 2*x^2 + x)/(4*x*log(1/4*x - 1/2)^2 - 4* x + 3))/x^2
Time = 0.41 (sec) , antiderivative size = 46, normalized size of antiderivative = 1.44 \[ \int \frac {-6+27 x-28 x^2+8 x^3+4 x^2 \log \left (\frac {1}{4} (-2+x)\right )+\left (-24 x+44 x^2-16 x^3\right ) \log ^2\left (\frac {1}{4} (-2+x)\right )+\left (-16 x^2+8 x^3\right ) \log ^4\left (\frac {1}{4} (-2+x)\right )+\left (12-46 x+52 x^2-16 x^3+\left (40 x-84 x^2+32 x^3\right ) \log ^2\left (\frac {1}{4} (-2+x)\right )+\left (32 x^2-16 x^3\right ) \log ^4\left (\frac {1}{4} (-2+x)\right )\right ) \log \left (\frac {-2 x+4 x^2-4 x^2 \log ^2\left (\frac {1}{4} (-2+x)\right )}{3-4 x+4 x \log ^2\left (\frac {1}{4} (-2+x)\right )}\right )}{-6 x^3+23 x^4-26 x^5+8 x^6+\left (-20 x^4+42 x^5-16 x^6\right ) \log ^2\left (\frac {1}{4} (-2+x)\right )+\left (-16 x^5+8 x^6\right ) \log ^4\left (\frac {1}{4} (-2+x)\right )} \, dx=\frac {\log {\left (\frac {- 4 x^{2} \log {\left (\frac {x}{4} - \frac {1}{2} \right )}^{2} + 4 x^{2} - 2 x}{4 x \log {\left (\frac {x}{4} - \frac {1}{2} \right )}^{2} - 4 x + 3} \right )}}{x^{2}} \] Input:
integrate((((-16*x**3+32*x**2)*ln(1/4*x-1/2)**4+(32*x**3-84*x**2+40*x)*ln( 1/4*x-1/2)**2-16*x**3+52*x**2-46*x+12)*ln((-4*x**2*ln(1/4*x-1/2)**2+4*x**2 -2*x)/(4*x*ln(1/4*x-1/2)**2+3-4*x))+(8*x**3-16*x**2)*ln(1/4*x-1/2)**4+(-16 *x**3+44*x**2-24*x)*ln(1/4*x-1/2)**2+4*x**2*ln(1/4*x-1/2)+8*x**3-28*x**2+2 7*x-6)/((8*x**6-16*x**5)*ln(1/4*x-1/2)**4+(-16*x**6+42*x**5-20*x**4)*ln(1/ 4*x-1/2)**2+8*x**6-26*x**5+23*x**4-6*x**3),x)
Output:
log((-4*x**2*log(x/4 - 1/2)**2 + 4*x**2 - 2*x)/(4*x*log(x/4 - 1/2)**2 - 4* x + 3))/x**2
Result contains complex when optimal does not.
Time = 0.18 (sec) , antiderivative size = 75, normalized size of antiderivative = 2.34 \[ \int \frac {-6+27 x-28 x^2+8 x^3+4 x^2 \log \left (\frac {1}{4} (-2+x)\right )+\left (-24 x+44 x^2-16 x^3\right ) \log ^2\left (\frac {1}{4} (-2+x)\right )+\left (-16 x^2+8 x^3\right ) \log ^4\left (\frac {1}{4} (-2+x)\right )+\left (12-46 x+52 x^2-16 x^3+\left (40 x-84 x^2+32 x^3\right ) \log ^2\left (\frac {1}{4} (-2+x)\right )+\left (32 x^2-16 x^3\right ) \log ^4\left (\frac {1}{4} (-2+x)\right )\right ) \log \left (\frac {-2 x+4 x^2-4 x^2 \log ^2\left (\frac {1}{4} (-2+x)\right )}{3-4 x+4 x \log ^2\left (\frac {1}{4} (-2+x)\right )}\right )}{-6 x^3+23 x^4-26 x^5+8 x^6+\left (-20 x^4+42 x^5-16 x^6\right ) \log ^2\left (\frac {1}{4} (-2+x)\right )+\left (-16 x^5+8 x^6\right ) \log ^4\left (\frac {1}{4} (-2+x)\right )} \, dx=-\frac {-i \, \pi - \log \left (2\right ) + \log \left (4 \, {\left (4 \, \log \left (2\right )^{2} - 4 \, \log \left (2\right ) \log \left (x - 2\right ) + \log \left (x - 2\right )^{2} - 1\right )} x + 3\right ) - \log \left (2 \, {\left (4 \, \log \left (2\right )^{2} - 4 \, \log \left (2\right ) \log \left (x - 2\right ) + \log \left (x - 2\right )^{2} - 1\right )} x + 1\right ) - \log \left (x\right )}{x^{2}} \] Input:
integrate((((-16*x^3+32*x^2)*log(1/4*x-1/2)^4+(32*x^3-84*x^2+40*x)*log(1/4 *x-1/2)^2-16*x^3+52*x^2-46*x+12)*log((-4*x^2*log(1/4*x-1/2)^2+4*x^2-2*x)/( 4*x*log(1/4*x-1/2)^2+3-4*x))+(8*x^3-16*x^2)*log(1/4*x-1/2)^4+(-16*x^3+44*x ^2-24*x)*log(1/4*x-1/2)^2+4*x^2*log(1/4*x-1/2)+8*x^3-28*x^2+27*x-6)/((8*x^ 6-16*x^5)*log(1/4*x-1/2)^4+(-16*x^6+42*x^5-20*x^4)*log(1/4*x-1/2)^2+8*x^6- 26*x^5+23*x^4-6*x^3),x, algorithm="maxima")
Output:
-(-I*pi - log(2) + log(4*(4*log(2)^2 - 4*log(2)*log(x - 2) + log(x - 2)^2 - 1)*x + 3) - log(2*(4*log(2)^2 - 4*log(2)*log(x - 2) + log(x - 2)^2 - 1)* x + 1) - log(x))/x^2
Timed out. \[ \int \frac {-6+27 x-28 x^2+8 x^3+4 x^2 \log \left (\frac {1}{4} (-2+x)\right )+\left (-24 x+44 x^2-16 x^3\right ) \log ^2\left (\frac {1}{4} (-2+x)\right )+\left (-16 x^2+8 x^3\right ) \log ^4\left (\frac {1}{4} (-2+x)\right )+\left (12-46 x+52 x^2-16 x^3+\left (40 x-84 x^2+32 x^3\right ) \log ^2\left (\frac {1}{4} (-2+x)\right )+\left (32 x^2-16 x^3\right ) \log ^4\left (\frac {1}{4} (-2+x)\right )\right ) \log \left (\frac {-2 x+4 x^2-4 x^2 \log ^2\left (\frac {1}{4} (-2+x)\right )}{3-4 x+4 x \log ^2\left (\frac {1}{4} (-2+x)\right )}\right )}{-6 x^3+23 x^4-26 x^5+8 x^6+\left (-20 x^4+42 x^5-16 x^6\right ) \log ^2\left (\frac {1}{4} (-2+x)\right )+\left (-16 x^5+8 x^6\right ) \log ^4\left (\frac {1}{4} (-2+x)\right )} \, dx=\text {Timed out} \] Input:
integrate((((-16*x^3+32*x^2)*log(1/4*x-1/2)^4+(32*x^3-84*x^2+40*x)*log(1/4 *x-1/2)^2-16*x^3+52*x^2-46*x+12)*log((-4*x^2*log(1/4*x-1/2)^2+4*x^2-2*x)/( 4*x*log(1/4*x-1/2)^2+3-4*x))+(8*x^3-16*x^2)*log(1/4*x-1/2)^4+(-16*x^3+44*x ^2-24*x)*log(1/4*x-1/2)^2+4*x^2*log(1/4*x-1/2)+8*x^3-28*x^2+27*x-6)/((8*x^ 6-16*x^5)*log(1/4*x-1/2)^4+(-16*x^6+42*x^5-20*x^4)*log(1/4*x-1/2)^2+8*x^6- 26*x^5+23*x^4-6*x^3),x, algorithm="giac")
Output:
Timed out
Time = 4.27 (sec) , antiderivative size = 45, normalized size of antiderivative = 1.41 \[ \int \frac {-6+27 x-28 x^2+8 x^3+4 x^2 \log \left (\frac {1}{4} (-2+x)\right )+\left (-24 x+44 x^2-16 x^3\right ) \log ^2\left (\frac {1}{4} (-2+x)\right )+\left (-16 x^2+8 x^3\right ) \log ^4\left (\frac {1}{4} (-2+x)\right )+\left (12-46 x+52 x^2-16 x^3+\left (40 x-84 x^2+32 x^3\right ) \log ^2\left (\frac {1}{4} (-2+x)\right )+\left (32 x^2-16 x^3\right ) \log ^4\left (\frac {1}{4} (-2+x)\right )\right ) \log \left (\frac {-2 x+4 x^2-4 x^2 \log ^2\left (\frac {1}{4} (-2+x)\right )}{3-4 x+4 x \log ^2\left (\frac {1}{4} (-2+x)\right )}\right )}{-6 x^3+23 x^4-26 x^5+8 x^6+\left (-20 x^4+42 x^5-16 x^6\right ) \log ^2\left (\frac {1}{4} (-2+x)\right )+\left (-16 x^5+8 x^6\right ) \log ^4\left (\frac {1}{4} (-2+x)\right )} \, dx=\frac {\ln \left (-\frac {2\,\left (2\,x^2\,{\ln \left (\frac {x}{4}-\frac {1}{2}\right )}^2-2\,x^2+x\right )}{4\,x\,{\ln \left (\frac {x}{4}-\frac {1}{2}\right )}^2-4\,x+3}\right )}{x^2} \] Input:
int(-(27*x - log(x/4 - 1/2)^2*(24*x - 44*x^2 + 16*x^3) + log(-(2*x + 4*x^2 *log(x/4 - 1/2)^2 - 4*x^2)/(4*x*log(x/4 - 1/2)^2 - 4*x + 3))*(log(x/4 - 1/ 2)^2*(40*x - 84*x^2 + 32*x^3) - 46*x + log(x/4 - 1/2)^4*(32*x^2 - 16*x^3) + 52*x^2 - 16*x^3 + 12) - log(x/4 - 1/2)^4*(16*x^2 - 8*x^3) - 28*x^2 + 8*x ^3 + 4*x^2*log(x/4 - 1/2) - 6)/(log(x/4 - 1/2)^4*(16*x^5 - 8*x^6) + log(x/ 4 - 1/2)^2*(20*x^4 - 42*x^5 + 16*x^6) + 6*x^3 - 23*x^4 + 26*x^5 - 8*x^6),x )
Output:
log(-(2*(x + 2*x^2*log(x/4 - 1/2)^2 - 2*x^2))/(4*x*log(x/4 - 1/2)^2 - 4*x + 3))/x^2
\[ \int \frac {-6+27 x-28 x^2+8 x^3+4 x^2 \log \left (\frac {1}{4} (-2+x)\right )+\left (-24 x+44 x^2-16 x^3\right ) \log ^2\left (\frac {1}{4} (-2+x)\right )+\left (-16 x^2+8 x^3\right ) \log ^4\left (\frac {1}{4} (-2+x)\right )+\left (12-46 x+52 x^2-16 x^3+\left (40 x-84 x^2+32 x^3\right ) \log ^2\left (\frac {1}{4} (-2+x)\right )+\left (32 x^2-16 x^3\right ) \log ^4\left (\frac {1}{4} (-2+x)\right )\right ) \log \left (\frac {-2 x+4 x^2-4 x^2 \log ^2\left (\frac {1}{4} (-2+x)\right )}{3-4 x+4 x \log ^2\left (\frac {1}{4} (-2+x)\right )}\right )}{-6 x^3+23 x^4-26 x^5+8 x^6+\left (-20 x^4+42 x^5-16 x^6\right ) \log ^2\left (\frac {1}{4} (-2+x)\right )+\left (-16 x^5+8 x^6\right ) \log ^4\left (\frac {1}{4} (-2+x)\right )} \, dx=\text {too large to display} \] Input:
int((((-16*x^3+32*x^2)*log(1/4*x-1/2)^4+(32*x^3-84*x^2+40*x)*log(1/4*x-1/2 )^2-16*x^3+52*x^2-46*x+12)*log((-4*x^2*log(1/4*x-1/2)^2+4*x^2-2*x)/(4*x*lo g(1/4*x-1/2)^2+3-4*x))+(8*x^3-16*x^2)*log(1/4*x-1/2)^4+(-16*x^3+44*x^2-24* x)*log(1/4*x-1/2)^2+4*x^2*log(1/4*x-1/2)+8*x^3-28*x^2+27*x-6)/((8*x^6-16*x ^5)*log(1/4*x-1/2)^4+(-16*x^6+42*x^5-20*x^4)*log(1/4*x-1/2)^2+8*x^6-26*x^5 +23*x^4-6*x^3),x)
Output:
- 16*int(log((x - 2)/4)**4/(8*log((x - 2)/4)**4*x**4 - 16*log((x - 2)/4)* *4*x**3 - 16*log((x - 2)/4)**2*x**4 + 42*log((x - 2)/4)**2*x**3 - 20*log(( x - 2)/4)**2*x**2 + 8*x**4 - 26*x**3 + 23*x**2 - 6*x),x) + 8*int(log((x - 2)/4)**4/(8*log((x - 2)/4)**4*x**3 - 16*log((x - 2)/4)**4*x**2 - 16*log((x - 2)/4)**2*x**3 + 42*log((x - 2)/4)**2*x**2 - 20*log((x - 2)/4)**2*x + 8* x**3 - 26*x**2 + 23*x - 6),x) - 24*int(log((x - 2)/4)**2/(8*log((x - 2)/4) **4*x**5 - 16*log((x - 2)/4)**4*x**4 - 16*log((x - 2)/4)**2*x**5 + 42*log( (x - 2)/4)**2*x**4 - 20*log((x - 2)/4)**2*x**3 + 8*x**5 - 26*x**4 + 23*x** 3 - 6*x**2),x) + 44*int(log((x - 2)/4)**2/(8*log((x - 2)/4)**4*x**4 - 16*l og((x - 2)/4)**4*x**3 - 16*log((x - 2)/4)**2*x**4 + 42*log((x - 2)/4)**2*x **3 - 20*log((x - 2)/4)**2*x**2 + 8*x**4 - 26*x**3 + 23*x**2 - 6*x),x) - 1 6*int(log((x - 2)/4)**2/(8*log((x - 2)/4)**4*x**3 - 16*log((x - 2)/4)**4*x **2 - 16*log((x - 2)/4)**2*x**3 + 42*log((x - 2)/4)**2*x**2 - 20*log((x - 2)/4)**2*x + 8*x**3 - 26*x**2 + 23*x - 6),x) + 12*int(log(( - 4*log((x - 2 )/4)**2*x**2 + 4*x**2 - 2*x)/(4*log((x - 2)/4)**2*x - 4*x + 3))/(8*log((x - 2)/4)**4*x**6 - 16*log((x - 2)/4)**4*x**5 - 16*log((x - 2)/4)**2*x**6 + 42*log((x - 2)/4)**2*x**5 - 20*log((x - 2)/4)**2*x**4 + 8*x**6 - 26*x**5 + 23*x**4 - 6*x**3),x) - 46*int(log(( - 4*log((x - 2)/4)**2*x**2 + 4*x**2 - 2*x)/(4*log((x - 2)/4)**2*x - 4*x + 3))/(8*log((x - 2)/4)**4*x**5 - 16*lo g((x - 2)/4)**4*x**4 - 16*log((x - 2)/4)**2*x**5 + 42*log((x - 2)/4)**2...