Integrand size = 160, antiderivative size = 31 \[ \int \frac {20 x+4 x^2+e^4 \left (-60 x^2-144 x^3-24 x^4\right )+72 x^2 \log (4)+\left (44 x^2+8 x^3\right ) \log (x)+\left (10+2 x+e^4 \left (-30 x-72 x^2-12 x^3\right )+36 x \log (4)+\left (22 x+4 x^2\right ) \log (x)\right ) \log \left (\frac {e^4 \left (15 x+3 x^2\right )-9 \log (4)+(-5-x) \log (x)}{3 \log (4)}\right )}{e^4 \left (-15 x^2-3 x^3\right )+9 x \log (4)+\left (5 x+x^2\right ) \log (x)} \, dx=\left (2 x+\log \left (-3+\frac {(5+x) \left (3 e^4 x-\log (x)\right )}{3 \log (4)}\right )\right )^2 \] Output:
(2*x+ln(1/2*(5+x)/ln(2)*(x*exp(4)-1/3*ln(x))-3))^2
Leaf count is larger than twice the leaf count of optimal. \(71\) vs. \(2(31)=62\).
Time = 0.05 (sec) , antiderivative size = 71, normalized size of antiderivative = 2.29 \[ \int \frac {20 x+4 x^2+e^4 \left (-60 x^2-144 x^3-24 x^4\right )+72 x^2 \log (4)+\left (44 x^2+8 x^3\right ) \log (x)+\left (10+2 x+e^4 \left (-30 x-72 x^2-12 x^3\right )+36 x \log (4)+\left (22 x+4 x^2\right ) \log (x)\right ) \log \left (\frac {e^4 \left (15 x+3 x^2\right )-9 \log (4)+(-5-x) \log (x)}{3 \log (4)}\right )}{e^4 \left (-15 x^2-3 x^3\right )+9 x \log (4)+\left (5 x+x^2\right ) \log (x)} \, dx=-2 \left (-2 x^2-2 x \log \left (\frac {3 e^4 x (5+x)-9 \log (4)-(5+x) \log (x)}{\log (64)}\right )-\frac {1}{2} \log ^2\left (\frac {3 e^4 x (5+x)-9 \log (4)-(5+x) \log (x)}{\log (64)}\right )\right ) \] Input:
Integrate[(20*x + 4*x^2 + E^4*(-60*x^2 - 144*x^3 - 24*x^4) + 72*x^2*Log[4] + (44*x^2 + 8*x^3)*Log[x] + (10 + 2*x + E^4*(-30*x - 72*x^2 - 12*x^3) + 3 6*x*Log[4] + (22*x + 4*x^2)*Log[x])*Log[(E^4*(15*x + 3*x^2) - 9*Log[4] + ( -5 - x)*Log[x])/(3*Log[4])])/(E^4*(-15*x^2 - 3*x^3) + 9*x*Log[4] + (5*x + x^2)*Log[x]),x]
Output:
-2*(-2*x^2 - 2*x*Log[(3*E^4*x*(5 + x) - 9*Log[4] - (5 + x)*Log[x])/Log[64] ] - Log[(3*E^4*x*(5 + x) - 9*Log[4] - (5 + x)*Log[x])/Log[64]]^2/2)
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.
| \(\displaystyle \int \frac {4 x^2+72 x^2 \log (4)+\left (8 x^3+44 x^2\right ) \log (x)+\left (\left (4 x^2+22 x\right ) \log (x)+e^4 \left (-12 x^3-72 x^2-30 x\right )+2 x+36 x \log (4)+10\right ) \log \left (\frac {e^4 \left (3 x^2+15 x\right )+(-x-5) \log (x)-9 \log (4)}{3 \log (4)}\right )+e^4 \left (-24 x^4-144 x^3-60 x^2\right )+20 x}{\left (x^2+5 x\right ) \log (x)+e^4 \left (-3 x^3-15 x^2\right )+9 x \log (4)} \, dx\) |
| \(\Big \downarrow \) 6 |
| \(\displaystyle \int \frac {x^2 (4+72 \log (4))+\left (8 x^3+44 x^2\right ) \log (x)+\left (\left (4 x^2+22 x\right ) \log (x)+e^4 \left (-12 x^3-72 x^2-30 x\right )+2 x+36 x \log (4)+10\right ) \log \left (\frac {e^4 \left (3 x^2+15 x\right )+(-x-5) \log (x)-9 \log (4)}{3 \log (4)}\right )+e^4 \left (-24 x^4-144 x^3-60 x^2\right )+20 x}{\left (x^2+5 x\right ) \log (x)+e^4 \left (-3 x^3-15 x^2\right )+9 x \log (4)}dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {2 \left (-6 e^4 x^3-36 e^4 x^2+2 x^2 \log (x)+11 x \log (x)+x \left (1-15 e^4+18 \log (4)\right )+5\right ) \left (-2 x-\log \left (\frac {3 e^4 x (x+5)-(x+5) \log (x)-9 \log (4)}{\log (64)}\right )\right )}{-\left (x^2+5 x\right ) \log (x)-e^4 \left (-3 x^3-15 x^2\right )-9 x \log (4)}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 2 \int -\frac {\left (-6 e^4 x^3+2 \log (x) x^2-36 e^4 x^2+11 \log (x) x+\left (1-15 e^4+18 \log (4)\right ) x+5\right ) \left (2 x+\log \left (\frac {3 e^4 x (x+5)-\log (x) (x+5)-9 \log (4)}{\log (64)}\right )\right )}{-9 \log (4) x+3 e^4 \left (x^3+5 x^2\right )-\left (x^2+5 x\right ) \log (x)}dx\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle -2 \int \frac {\left (-6 e^4 x^3+2 \log (x) x^2-36 e^4 x^2+11 \log (x) x+\left (1-15 e^4+18 \log (4)\right ) x+5\right ) \left (2 x+\log \left (\frac {3 e^4 x (x+5)-\log (x) (x+5)-9 \log (4)}{\log (64)}\right )\right )}{-9 \log (4) x+3 e^4 \left (x^3+5 x^2\right )-\left (x^2+5 x\right ) \log (x)}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {\log \left (\frac {3 e^4 x (x+5)-\log (x) (x+5)-9 \log (4)}{\log (64)}\right ) \left (-6 e^4 x^3+2 \log (x) x^2-36 e^4 x^2+11 \log (x) x+\left (1-15 e^4+18 \log (4)\right ) x+5\right )}{x \left (3 e^4 x^2-\log (x) x+15 e^4 x-5 \log (x)-9 \log (4)\right )}+\frac {2 \left (-6 e^4 x^3+2 \log (x) x^2-36 e^4 x^2+11 \log (x) x+\left (1-15 e^4+18 \log (4)\right ) x+5\right )}{3 e^4 x^2-\log (x) x+15 e^4 x-5 \log (x)-9 \log (4)}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle -2 \left (2 (5-9 \log (4)) \int \frac {1}{3 e^4 x^2-\log (x) x+15 e^4 x-5 \log (x)-9 \log (4)}dx+2 \left (1-15 e^4\right ) \int \frac {x}{3 e^4 x^2-\log (x) x+15 e^4 x-5 \log (x)-9 \log (4)}dx-6 e^4 \int \frac {x^2}{3 e^4 x^2-\log (x) x+15 e^4 x-5 \log (x)-9 \log (4)}dx+90 \log (4) \int \frac {1}{(x+5) \left (3 e^4 x^2-\log (x) x+15 e^4 x-5 \log (x)-9 \log (4)\right )}dx+\left (1-15 e^4+18 \log (4)\right ) \int \frac {\log \left (\frac {3 e^4 x (x+5)-\log (x) (x+5)-9 \log (4)}{\log (64)}\right )}{3 e^4 x^2-\log (x) x+15 e^4 x-5 \log (x)-9 \log (4)}dx+5 \int \frac {\log \left (\frac {3 e^4 x (x+5)-\log (x) (x+5)-9 \log (4)}{\log (64)}\right )}{x \left (3 e^4 x^2-\log (x) x+15 e^4 x-5 \log (x)-9 \log (4)\right )}dx-36 e^4 \int \frac {x \log \left (\frac {3 e^4 x (x+5)-\log (x) (x+5)-9 \log (4)}{\log (64)}\right )}{3 e^4 x^2-\log (x) x+15 e^4 x-5 \log (x)-9 \log (4)}dx-6 e^4 \int \frac {x^2 \log \left (\frac {3 e^4 x (x+5)-\log (x) (x+5)-9 \log (4)}{\log (64)}\right )}{3 e^4 x^2-\log (x) x+15 e^4 x-5 \log (x)-9 \log (4)}dx+2 \int \frac {x \log (x) \log \left (\frac {3 e^4 x (x+5)-\log (x) (x+5)-9 \log (4)}{\log (64)}\right )}{3 e^4 x^2-\log (x) x+15 e^4 x-5 \log (x)-9 \log (4)}dx-11 \int \frac {\log (x) \log \left (\frac {3 e^4 x (x+5)-\log (x) (x+5)-9 \log (4)}{\log (64)}\right )}{-3 e^4 x^2+\log (x) x-15 e^4 x+5 \log (x)+9 \log (4)}dx-2 x^2-2 x+10 \log (x+5)\right )\) |
Input:
Int[(20*x + 4*x^2 + E^4*(-60*x^2 - 144*x^3 - 24*x^4) + 72*x^2*Log[4] + (44 *x^2 + 8*x^3)*Log[x] + (10 + 2*x + E^4*(-30*x - 72*x^2 - 12*x^3) + 36*x*Lo g[4] + (22*x + 4*x^2)*Log[x])*Log[(E^4*(15*x + 3*x^2) - 9*Log[4] + (-5 - x )*Log[x])/(3*Log[4])])/(E^4*(-15*x^2 - 3*x^3) + 9*x*Log[4] + (5*x + x^2)*L og[x]),x]
Output:
$Aborted
Leaf count of result is larger than twice the leaf count of optimal. \(76\) vs. \(2(27)=54\).
Time = 3.28 (sec) , antiderivative size = 77, normalized size of antiderivative = 2.48
| method | result | size |
| parallelrisch | \(-100+4 x^{2}+4 \ln \left (\frac {\left (-x -5\right ) \ln \left (x \right )-18 \ln \left (2\right )+\left (3 x^{2}+15 x \right ) {\mathrm e}^{4}}{6 \ln \left (2\right )}\right ) x +{\ln \left (\frac {\left (-x -5\right ) \ln \left (x \right )-18 \ln \left (2\right )+\left (3 x^{2}+15 x \right ) {\mathrm e}^{4}}{6 \ln \left (2\right )}\right )}^{2}\) | \(77\) |
Input:
int((((4*x^2+22*x)*ln(x)+72*x*ln(2)+(-12*x^3-72*x^2-30*x)*exp(4)+2*x+10)*l n(1/6*((-x-5)*ln(x)-18*ln(2)+(3*x^2+15*x)*exp(4))/ln(2))+(8*x^3+44*x^2)*ln (x)+144*x^2*ln(2)+(-24*x^4-144*x^3-60*x^2)*exp(4)+4*x^2+20*x)/((x^2+5*x)*l n(x)+18*x*ln(2)+(-3*x^3-15*x^2)*exp(4)),x,method=_RETURNVERBOSE)
Output:
-100+4*x^2+4*ln(1/6*((-x-5)*ln(x)-18*ln(2)+(3*x^2+15*x)*exp(4))/ln(2))*x+l n(1/6*((-x-5)*ln(x)-18*ln(2)+(3*x^2+15*x)*exp(4))/ln(2))^2
Leaf count of result is larger than twice the leaf count of optimal. 71 vs. \(2 (28) = 56\).
Time = 0.10 (sec) , antiderivative size = 71, normalized size of antiderivative = 2.29 \[ \int \frac {20 x+4 x^2+e^4 \left (-60 x^2-144 x^3-24 x^4\right )+72 x^2 \log (4)+\left (44 x^2+8 x^3\right ) \log (x)+\left (10+2 x+e^4 \left (-30 x-72 x^2-12 x^3\right )+36 x \log (4)+\left (22 x+4 x^2\right ) \log (x)\right ) \log \left (\frac {e^4 \left (15 x+3 x^2\right )-9 \log (4)+(-5-x) \log (x)}{3 \log (4)}\right )}{e^4 \left (-15 x^2-3 x^3\right )+9 x \log (4)+\left (5 x+x^2\right ) \log (x)} \, dx=4 \, x^{2} + 4 \, x \log \left (\frac {3 \, {\left (x^{2} + 5 \, x\right )} e^{4} - {\left (x + 5\right )} \log \left (x\right ) - 18 \, \log \left (2\right )}{6 \, \log \left (2\right )}\right ) + \log \left (\frac {3 \, {\left (x^{2} + 5 \, x\right )} e^{4} - {\left (x + 5\right )} \log \left (x\right ) - 18 \, \log \left (2\right )}{6 \, \log \left (2\right )}\right )^{2} \] Input:
integrate((((4*x^2+22*x)*log(x)+72*x*log(2)+(-12*x^3-72*x^2-30*x)*exp(4)+2 *x+10)*log(1/6*((-x-5)*log(x)-18*log(2)+(3*x^2+15*x)*exp(4))/log(2))+(8*x^ 3+44*x^2)*log(x)+144*x^2*log(2)+(-24*x^4-144*x^3-60*x^2)*exp(4)+4*x^2+20*x )/((x^2+5*x)*log(x)+18*x*log(2)+(-3*x^3-15*x^2)*exp(4)),x, algorithm="fric as")
Output:
4*x^2 + 4*x*log(1/6*(3*(x^2 + 5*x)*e^4 - (x + 5)*log(x) - 18*log(2))/log(2 )) + log(1/6*(3*(x^2 + 5*x)*e^4 - (x + 5)*log(x) - 18*log(2))/log(2))^2
Leaf count of result is larger than twice the leaf count of optimal. 76 vs. \(2 (27) = 54\).
Time = 0.32 (sec) , antiderivative size = 76, normalized size of antiderivative = 2.45 \[ \int \frac {20 x+4 x^2+e^4 \left (-60 x^2-144 x^3-24 x^4\right )+72 x^2 \log (4)+\left (44 x^2+8 x^3\right ) \log (x)+\left (10+2 x+e^4 \left (-30 x-72 x^2-12 x^3\right )+36 x \log (4)+\left (22 x+4 x^2\right ) \log (x)\right ) \log \left (\frac {e^4 \left (15 x+3 x^2\right )-9 \log (4)+(-5-x) \log (x)}{3 \log (4)}\right )}{e^4 \left (-15 x^2-3 x^3\right )+9 x \log (4)+\left (5 x+x^2\right ) \log (x)} \, dx=4 x^{2} + 4 x \log {\left (\frac {\frac {\left (- x - 5\right ) \log {\left (x \right )}}{6} + \frac {\left (3 x^{2} + 15 x\right ) e^{4}}{6} - 3 \log {\left (2 \right )}}{\log {\left (2 \right )}} \right )} + \log {\left (\frac {\frac {\left (- x - 5\right ) \log {\left (x \right )}}{6} + \frac {\left (3 x^{2} + 15 x\right ) e^{4}}{6} - 3 \log {\left (2 \right )}}{\log {\left (2 \right )}} \right )}^{2} \] Input:
integrate((((4*x**2+22*x)*ln(x)+72*x*ln(2)+(-12*x**3-72*x**2-30*x)*exp(4)+ 2*x+10)*ln(1/6*((-x-5)*ln(x)-18*ln(2)+(3*x**2+15*x)*exp(4))/ln(2))+(8*x**3 +44*x**2)*ln(x)+144*x**2*ln(2)+(-24*x**4-144*x**3-60*x**2)*exp(4)+4*x**2+2 0*x)/((x**2+5*x)*ln(x)+18*x*ln(2)+(-3*x**3-15*x**2)*exp(4)),x)
Output:
4*x**2 + 4*x*log(((-x - 5)*log(x)/6 + (3*x**2 + 15*x)*exp(4)/6 - 3*log(2)) /log(2)) + log(((-x - 5)*log(x)/6 + (3*x**2 + 15*x)*exp(4)/6 - 3*log(2))/l og(2))**2
\[ \int \frac {20 x+4 x^2+e^4 \left (-60 x^2-144 x^3-24 x^4\right )+72 x^2 \log (4)+\left (44 x^2+8 x^3\right ) \log (x)+\left (10+2 x+e^4 \left (-30 x-72 x^2-12 x^3\right )+36 x \log (4)+\left (22 x+4 x^2\right ) \log (x)\right ) \log \left (\frac {e^4 \left (15 x+3 x^2\right )-9 \log (4)+(-5-x) \log (x)}{3 \log (4)}\right )}{e^4 \left (-15 x^2-3 x^3\right )+9 x \log (4)+\left (5 x+x^2\right ) \log (x)} \, dx=\int { -\frac {2 \, {\left (72 \, x^{2} \log \left (2\right ) + 2 \, x^{2} - 6 \, {\left (2 \, x^{4} + 12 \, x^{3} + 5 \, x^{2}\right )} e^{4} + 2 \, {\left (2 \, x^{3} + 11 \, x^{2}\right )} \log \left (x\right ) - {\left (3 \, {\left (2 \, x^{3} + 12 \, x^{2} + 5 \, x\right )} e^{4} - 36 \, x \log \left (2\right ) - {\left (2 \, x^{2} + 11 \, x\right )} \log \left (x\right ) - x - 5\right )} \log \left (\frac {3 \, {\left (x^{2} + 5 \, x\right )} e^{4} - {\left (x + 5\right )} \log \left (x\right ) - 18 \, \log \left (2\right )}{6 \, \log \left (2\right )}\right ) + 10 \, x\right )}}{3 \, {\left (x^{3} + 5 \, x^{2}\right )} e^{4} - 18 \, x \log \left (2\right ) - {\left (x^{2} + 5 \, x\right )} \log \left (x\right )} \,d x } \] Input:
integrate((((4*x^2+22*x)*log(x)+72*x*log(2)+(-12*x^3-72*x^2-30*x)*exp(4)+2 *x+10)*log(1/6*((-x-5)*log(x)-18*log(2)+(3*x^2+15*x)*exp(4))/log(2))+(8*x^ 3+44*x^2)*log(x)+144*x^2*log(2)+(-24*x^4-144*x^3-60*x^2)*exp(4)+4*x^2+20*x )/((x^2+5*x)*log(x)+18*x*log(2)+(-3*x^3-15*x^2)*exp(4)),x, algorithm="maxi ma")
Output:
-2*integrate((72*x^2*log(2) + 2*x^2 - 6*(2*x^4 + 12*x^3 + 5*x^2)*e^4 + 2*( 2*x^3 + 11*x^2)*log(x) - (3*(2*x^3 + 12*x^2 + 5*x)*e^4 - 36*x*log(2) - (2* x^2 + 11*x)*log(x) - x - 5)*log(1/6*(3*(x^2 + 5*x)*e^4 - (x + 5)*log(x) - 18*log(2))/log(2)) + 10*x)/(3*(x^3 + 5*x^2)*e^4 - 18*x*log(2) - (x^2 + 5*x )*log(x)), x)
\[ \int \frac {20 x+4 x^2+e^4 \left (-60 x^2-144 x^3-24 x^4\right )+72 x^2 \log (4)+\left (44 x^2+8 x^3\right ) \log (x)+\left (10+2 x+e^4 \left (-30 x-72 x^2-12 x^3\right )+36 x \log (4)+\left (22 x+4 x^2\right ) \log (x)\right ) \log \left (\frac {e^4 \left (15 x+3 x^2\right )-9 \log (4)+(-5-x) \log (x)}{3 \log (4)}\right )}{e^4 \left (-15 x^2-3 x^3\right )+9 x \log (4)+\left (5 x+x^2\right ) \log (x)} \, dx=\int { -\frac {2 \, {\left (72 \, x^{2} \log \left (2\right ) + 2 \, x^{2} - 6 \, {\left (2 \, x^{4} + 12 \, x^{3} + 5 \, x^{2}\right )} e^{4} + 2 \, {\left (2 \, x^{3} + 11 \, x^{2}\right )} \log \left (x\right ) - {\left (3 \, {\left (2 \, x^{3} + 12 \, x^{2} + 5 \, x\right )} e^{4} - 36 \, x \log \left (2\right ) - {\left (2 \, x^{2} + 11 \, x\right )} \log \left (x\right ) - x - 5\right )} \log \left (\frac {3 \, {\left (x^{2} + 5 \, x\right )} e^{4} - {\left (x + 5\right )} \log \left (x\right ) - 18 \, \log \left (2\right )}{6 \, \log \left (2\right )}\right ) + 10 \, x\right )}}{3 \, {\left (x^{3} + 5 \, x^{2}\right )} e^{4} - 18 \, x \log \left (2\right ) - {\left (x^{2} + 5 \, x\right )} \log \left (x\right )} \,d x } \] Input:
integrate((((4*x^2+22*x)*log(x)+72*x*log(2)+(-12*x^3-72*x^2-30*x)*exp(4)+2 *x+10)*log(1/6*((-x-5)*log(x)-18*log(2)+(3*x^2+15*x)*exp(4))/log(2))+(8*x^ 3+44*x^2)*log(x)+144*x^2*log(2)+(-24*x^4-144*x^3-60*x^2)*exp(4)+4*x^2+20*x )/((x^2+5*x)*log(x)+18*x*log(2)+(-3*x^3-15*x^2)*exp(4)),x, algorithm="giac ")
Output:
integrate(-2*(72*x^2*log(2) + 2*x^2 - 6*(2*x^4 + 12*x^3 + 5*x^2)*e^4 + 2*( 2*x^3 + 11*x^2)*log(x) - (3*(2*x^3 + 12*x^2 + 5*x)*e^4 - 36*x*log(2) - (2* x^2 + 11*x)*log(x) - x - 5)*log(1/6*(3*(x^2 + 5*x)*e^4 - (x + 5)*log(x) - 18*log(2))/log(2)) + 10*x)/(3*(x^3 + 5*x^2)*e^4 - 18*x*log(2) - (x^2 + 5*x )*log(x)), x)
Time = 4.51 (sec) , antiderivative size = 38, normalized size of antiderivative = 1.23 \[ \int \frac {20 x+4 x^2+e^4 \left (-60 x^2-144 x^3-24 x^4\right )+72 x^2 \log (4)+\left (44 x^2+8 x^3\right ) \log (x)+\left (10+2 x+e^4 \left (-30 x-72 x^2-12 x^3\right )+36 x \log (4)+\left (22 x+4 x^2\right ) \log (x)\right ) \log \left (\frac {e^4 \left (15 x+3 x^2\right )-9 \log (4)+(-5-x) \log (x)}{3 \log (4)}\right )}{e^4 \left (-15 x^2-3 x^3\right )+9 x \log (4)+\left (5 x+x^2\right ) \log (x)} \, dx={\left (2\,x+\ln \left (-\frac {3\,\ln \left (2\right )+\frac {\ln \left (x\right )\,\left (x+5\right )}{6}-\frac {{\mathrm {e}}^4\,\left (3\,x^2+15\,x\right )}{6}}{\ln \left (2\right )}\right )\right )}^2 \] Input:
int((20*x + log(-(3*log(2) + (log(x)*(x + 5))/6 - (exp(4)*(15*x + 3*x^2))/ 6)/log(2))*(2*x + 72*x*log(2) - exp(4)*(30*x + 72*x^2 + 12*x^3) + log(x)*( 22*x + 4*x^2) + 10) + log(x)*(44*x^2 + 8*x^3) + 144*x^2*log(2) - exp(4)*(6 0*x^2 + 144*x^3 + 24*x^4) + 4*x^2)/(18*x*log(2) + log(x)*(5*x + x^2) - exp (4)*(15*x^2 + 3*x^3)),x)
Output:
(2*x + log(-(3*log(2) + (log(x)*(x + 5))/6 - (exp(4)*(15*x + 3*x^2))/6)/lo g(2)))^2
Time = 0.16 (sec) , antiderivative size = 148, normalized size of antiderivative = 4.77 \[ \int \frac {20 x+4 x^2+e^4 \left (-60 x^2-144 x^3-24 x^4\right )+72 x^2 \log (4)+\left (44 x^2+8 x^3\right ) \log (x)+\left (10+2 x+e^4 \left (-30 x-72 x^2-12 x^3\right )+36 x \log (4)+\left (22 x+4 x^2\right ) \log (x)\right ) \log \left (\frac {e^4 \left (15 x+3 x^2\right )-9 \log (4)+(-5-x) \log (x)}{3 \log (4)}\right )}{e^4 \left (-15 x^2-3 x^3\right )+9 x \log (4)+\left (5 x+x^2\right ) \log (x)} \, dx=-20 \,\mathrm {log}\left (\mathrm {log}\left (x \right ) x +5 \,\mathrm {log}\left (x \right )+18 \,\mathrm {log}\left (2\right )-3 e^{4} x^{2}-15 e^{4} x \right )+\mathrm {log}\left (\frac {-\mathrm {log}\left (x \right ) x -5 \,\mathrm {log}\left (x \right )-18 \,\mathrm {log}\left (2\right )+3 e^{4} x^{2}+15 e^{4} x}{6 \,\mathrm {log}\left (2\right )}\right )^{2}+4 \,\mathrm {log}\left (\frac {-\mathrm {log}\left (x \right ) x -5 \,\mathrm {log}\left (x \right )-18 \,\mathrm {log}\left (2\right )+3 e^{4} x^{2}+15 e^{4} x}{6 \,\mathrm {log}\left (2\right )}\right ) x +20 \,\mathrm {log}\left (\frac {-\mathrm {log}\left (x \right ) x -5 \,\mathrm {log}\left (x \right )-18 \,\mathrm {log}\left (2\right )+3 e^{4} x^{2}+15 e^{4} x}{6 \,\mathrm {log}\left (2\right )}\right )+4 x^{2} \] Input:
int((((4*x^2+22*x)*log(x)+72*x*log(2)+(-12*x^3-72*x^2-30*x)*exp(4)+2*x+10) *log(1/6*((-x-5)*log(x)-18*log(2)+(3*x^2+15*x)*exp(4))/log(2))+(8*x^3+44*x ^2)*log(x)+144*x^2*log(2)+(-24*x^4-144*x^3-60*x^2)*exp(4)+4*x^2+20*x)/((x^ 2+5*x)*log(x)+18*x*log(2)+(-3*x^3-15*x^2)*exp(4)),x)
Output:
- 20*log(log(x)*x + 5*log(x) + 18*log(2) - 3*e**4*x**2 - 15*e**4*x) + log (( - log(x)*x - 5*log(x) - 18*log(2) + 3*e**4*x**2 + 15*e**4*x)/(6*log(2)) )**2 + 4*log(( - log(x)*x - 5*log(x) - 18*log(2) + 3*e**4*x**2 + 15*e**4*x )/(6*log(2)))*x + 20*log(( - log(x)*x - 5*log(x) - 18*log(2) + 3*e**4*x**2 + 15*e**4*x)/(6*log(2))) + 4*x**2