Integrand size = 263, antiderivative size = 30 \[ \int \frac {\left (-20+14 x-2 x^2+25 x^4-5 x^5+e^{2 x} \left (15 x^2+7 x^3-2 x^4\right )+e^x \left (40 x^3+2 x^4-2 x^5\right )+(-5+x) \log (4)\right ) \log (x)+\left (-4+x+e^{2 x} x^2+2 e^x x^3+x^4-\log (4)+\left (4 x-x^2-e^{2 x} x^3-2 e^x x^4-x^5+x \log (4)\right ) \log (x)\right ) \log \left (-4 x+x^2+e^{2 x} x^3+2 e^x x^4+x^5-x \log (4)\right )+\left (-4+2 x+5 x^4+e^{2 x} \left (3 x^2+2 x^3\right )+e^x \left (8 x^3+2 x^4\right )-\log (4)\right ) \log (x) \log (\log (x))}{\left (-4 x+x^2+e^{2 x} x^3+2 e^x x^4+x^5-x \log (4)\right ) \log (x)} \, dx=\log \left (x \left (-4+x+x^2 \left (e^x+x\right )^2-\log (4)\right )\right ) (5-x+\log (\log (x))) \] Output:
(ln(ln(x))+5-x)*ln(x*(x+(exp(x)+x)^2*x^2-4-2*ln(2)))
\[ \int \frac {\left (-20+14 x-2 x^2+25 x^4-5 x^5+e^{2 x} \left (15 x^2+7 x^3-2 x^4\right )+e^x \left (40 x^3+2 x^4-2 x^5\right )+(-5+x) \log (4)\right ) \log (x)+\left (-4+x+e^{2 x} x^2+2 e^x x^3+x^4-\log (4)+\left (4 x-x^2-e^{2 x} x^3-2 e^x x^4-x^5+x \log (4)\right ) \log (x)\right ) \log \left (-4 x+x^2+e^{2 x} x^3+2 e^x x^4+x^5-x \log (4)\right )+\left (-4+2 x+5 x^4+e^{2 x} \left (3 x^2+2 x^3\right )+e^x \left (8 x^3+2 x^4\right )-\log (4)\right ) \log (x) \log (\log (x))}{\left (-4 x+x^2+e^{2 x} x^3+2 e^x x^4+x^5-x \log (4)\right ) \log (x)} \, dx=\int \frac {\left (-20+14 x-2 x^2+25 x^4-5 x^5+e^{2 x} \left (15 x^2+7 x^3-2 x^4\right )+e^x \left (40 x^3+2 x^4-2 x^5\right )+(-5+x) \log (4)\right ) \log (x)+\left (-4+x+e^{2 x} x^2+2 e^x x^3+x^4-\log (4)+\left (4 x-x^2-e^{2 x} x^3-2 e^x x^4-x^5+x \log (4)\right ) \log (x)\right ) \log \left (-4 x+x^2+e^{2 x} x^3+2 e^x x^4+x^5-x \log (4)\right )+\left (-4+2 x+5 x^4+e^{2 x} \left (3 x^2+2 x^3\right )+e^x \left (8 x^3+2 x^4\right )-\log (4)\right ) \log (x) \log (\log (x))}{\left (-4 x+x^2+e^{2 x} x^3+2 e^x x^4+x^5-x \log (4)\right ) \log (x)} \, dx \] Input:
Integrate[((-20 + 14*x - 2*x^2 + 25*x^4 - 5*x^5 + E^(2*x)*(15*x^2 + 7*x^3 - 2*x^4) + E^x*(40*x^3 + 2*x^4 - 2*x^5) + (-5 + x)*Log[4])*Log[x] + (-4 + x + E^(2*x)*x^2 + 2*E^x*x^3 + x^4 - Log[4] + (4*x - x^2 - E^(2*x)*x^3 - 2* E^x*x^4 - x^5 + x*Log[4])*Log[x])*Log[-4*x + x^2 + E^(2*x)*x^3 + 2*E^x*x^4 + x^5 - x*Log[4]] + (-4 + 2*x + 5*x^4 + E^(2*x)*(3*x^2 + 2*x^3) + E^x*(8* x^3 + 2*x^4) - Log[4])*Log[x]*Log[Log[x]])/((-4*x + x^2 + E^(2*x)*x^3 + 2* E^x*x^4 + x^5 - x*Log[4])*Log[x]),x]
Output:
Integrate[((-20 + 14*x - 2*x^2 + 25*x^4 - 5*x^5 + E^(2*x)*(15*x^2 + 7*x^3 - 2*x^4) + E^x*(40*x^3 + 2*x^4 - 2*x^5) + (-5 + x)*Log[4])*Log[x] + (-4 + x + E^(2*x)*x^2 + 2*E^x*x^3 + x^4 - Log[4] + (4*x - x^2 - E^(2*x)*x^3 - 2* E^x*x^4 - x^5 + x*Log[4])*Log[x])*Log[-4*x + x^2 + E^(2*x)*x^3 + 2*E^x*x^4 + x^5 - x*Log[4]] + (-4 + 2*x + 5*x^4 + E^(2*x)*(3*x^2 + 2*x^3) + E^x*(8* x^3 + 2*x^4) - Log[4])*Log[x]*Log[Log[x]])/((-4*x + x^2 + E^(2*x)*x^3 + 2* E^x*x^4 + x^5 - x*Log[4])*Log[x]), 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.
| \(\displaystyle \int \frac {\left (5 x^4+e^x \left (2 x^4+8 x^3\right )+e^{2 x} \left (2 x^3+3 x^2\right )+2 x-4-\log (4)\right ) \log (\log (x)) \log (x)+\left (-5 x^5+25 x^4-2 x^2+e^x \left (-2 x^5+2 x^4+40 x^3\right )+e^{2 x} \left (-2 x^4+7 x^3+15 x^2\right )+14 x+(x-5) \log (4)-20\right ) \log (x)+\left (x^4+2 e^x x^3+e^{2 x} x^2+\left (-x^5-2 e^x x^4-e^{2 x} x^3-x^2+4 x+x \log (4)\right ) \log (x)+x-4-\log (4)\right ) \log \left (x^5+2 e^x x^4+e^{2 x} x^3+x^2-4 x-x \log (4)\right )}{\left (x^5+2 e^x x^4+e^{2 x} x^3+x^2-4 x-x \log (4)\right ) \log (x)} \, dx\) |
| \(\Big \downarrow \) 6 |
| \(\displaystyle \int \frac {\left (5 x^4+e^x \left (2 x^4+8 x^3\right )+e^{2 x} \left (2 x^3+3 x^2\right )+2 x-4-\log (4)\right ) \log (\log (x)) \log (x)+\left (-5 x^5+25 x^4-2 x^2+e^x \left (-2 x^5+2 x^4+40 x^3\right )+e^{2 x} \left (-2 x^4+7 x^3+15 x^2\right )+14 x+(x-5) \log (4)-20\right ) \log (x)+\left (x^4+2 e^x x^3+e^{2 x} x^2+\left (-x^5-2 e^x x^4-e^{2 x} x^3-x^2+4 x+x \log (4)\right ) \log (x)+x-4-\log (4)\right ) \log \left (x^5+2 e^x x^4+e^{2 x} x^3+x^2-4 x-x \log (4)\right )}{\left (x^5+2 e^x x^4+e^{2 x} x^3+x^2+x (-4-\log (4))\right ) \log (x)}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {-2 x^2 \log (x)-x \log (x) \log \left (x \left (x^4+2 e^x x^3+e^{2 x} x^2+x-4-\log (4)\right )\right )+\log \left (x \left (x^4+2 e^x x^3+e^{2 x} x^2+x-4-\log (4)\right )\right )+7 x \log (x)+2 x \log (x) \log (\log (x))+15 \log (x)+3 \log (x) \log (\log (x))}{x \log (x)}+\frac {\left (2 x^5+2 e^x x^4-2 x^4-2 e^x x^3+2 x^2-7 x \left (1+\frac {4 \log (2)}{7}\right )-8 \left (1+\frac {\log (2)}{2}\right )\right ) (x-\log (\log (x))-5)}{x \left (x^4+2 e^x x^3+e^{2 x} x^2+x-4 \left (1+\frac {\log (2)}{2}\right )\right )}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle -\log \left (x^5+2 e^x x^4+e^{2 x} x^3+x^2-2 (2+\log (2)) x\right ) x+2 \log (\log (x)) x+10 x+12 \log (x)+3 \log (x) \log (\log (x))-2 \operatorname {LogIntegral}(x)+\frac {4 (2+\log (2)) (27+4 \log (16)) \int \frac {1}{x^4+2 e^x x^3+e^{2 x} x^2+x-4 \left (1+\frac {\log (2)}{2}\right )}dx}{8+\log (16)}+4 (2+\log (2)) \int \frac {1}{x^4+2 e^x x^3+e^{2 x} x^2+x-4 \left (1+\frac {\log (2)}{2}\right )}dx+20 (2+\log (2)) \int \frac {1}{x \left (x^4+2 e^x x^3+e^{2 x} x^2+x-4 \left (1+\frac {\log (2)}{2}\right )\right )}dx+(7+\log (16)) \int \frac {x}{x^4+2 e^x x^3+e^{2 x} x^2+x-4 \left (1+\frac {\log (2)}{2}\right )}dx+2 \int \frac {x^2}{x^4+2 e^x x^3+e^{2 x} x^2+x-4 \left (1+\frac {\log (2)}{2}\right )}dx+10 \int \frac {e^x x^2}{x^4+2 e^x x^3+e^{2 x} x^2+x-4 \left (1+\frac {\log (2)}{2}\right )}dx+10 \int \frac {x^3}{x^4+2 e^x x^3+e^{2 x} x^2+x-4 \left (1+\frac {\log (2)}{2}\right )}dx+2 \int \frac {e^x x^3}{x^4+2 e^x x^3+e^{2 x} x^2+x-4 \left (1+\frac {\log (2)}{2}\right )}dx+2 \int \frac {x^4}{x^4+2 e^x x^3+e^{2 x} x^2+x-4 \left (1+\frac {\log (2)}{2}\right )}dx+2 \int \frac {e^x x^4}{x^4+2 e^x x^3+e^{2 x} x^2+x-4 \left (1+\frac {\log (2)}{2}\right )}dx+2 \int \frac {x^5}{x^4+2 e^x x^3+e^{2 x} x^2+x-4 \left (1+\frac {\log (2)}{2}\right )}dx+(17+\log (16)) \int \frac {x}{-x^4-2 e^x x^3-e^{2 x} x^2-x+4 \left (1+\frac {\log (2)}{2}\right )}dx+2 \int \frac {x^2}{-x^4-2 e^x x^3-e^{2 x} x^2-x+4 \left (1+\frac {\log (2)}{2}\right )}dx+12 \int \frac {e^x x^3}{-x^4-2 e^x x^3-e^{2 x} x^2-x+4 \left (1+\frac {\log (2)}{2}\right )}dx+12 \int \frac {x^4}{-x^4-2 e^x x^3-e^{2 x} x^2-x+4 \left (1+\frac {\log (2)}{2}\right )}dx+2 \int \frac {e^x x^4}{-x^4-2 e^x x^3-e^{2 x} x^2-x+4 \left (1+\frac {\log (2)}{2}\right )}dx+2 \int \frac {x^5}{-x^4-2 e^x x^3-e^{2 x} x^2-x+4 \left (1+\frac {\log (2)}{2}\right )}dx+\int \frac {\log \left (x^5+2 e^x x^4+e^{2 x} x^3+x^2-4 \left (1+\frac {\log (2)}{2}\right ) x\right )}{x \log (x)}dx+(7+\log (16)) \int \frac {\log (\log (x))}{x^4+2 e^x x^3+e^{2 x} x^2+x-4 \left (1+\frac {\log (2)}{2}\right )}dx+4 (2+\log (2)) \int \frac {\log (\log (x))}{x \left (x^4+2 e^x x^3+e^{2 x} x^2+x-4 \left (1+\frac {\log (2)}{2}\right )\right )}dx+2 \int \frac {e^x x^2 \log (\log (x))}{x^4+2 e^x x^3+e^{2 x} x^2+x-4 \left (1+\frac {\log (2)}{2}\right )}dx+2 \int \frac {x^3 \log (\log (x))}{x^4+2 e^x x^3+e^{2 x} x^2+x-4 \left (1+\frac {\log (2)}{2}\right )}dx+2 \int \frac {x \log (\log (x))}{-x^4-2 e^x x^3-e^{2 x} x^2-x+4 \left (1+\frac {\log (2)}{2}\right )}dx+2 \int \frac {e^x x^3 \log (\log (x))}{-x^4-2 e^x x^3-e^{2 x} x^2-x+4 \left (1+\frac {\log (2)}{2}\right )}dx+2 \int \frac {x^4 \log (\log (x))}{-x^4-2 e^x x^3-e^{2 x} x^2-x+4 \left (1+\frac {\log (2)}{2}\right )}dx\) |
Input:
Int[((-20 + 14*x - 2*x^2 + 25*x^4 - 5*x^5 + E^(2*x)*(15*x^2 + 7*x^3 - 2*x^ 4) + E^x*(40*x^3 + 2*x^4 - 2*x^5) + (-5 + x)*Log[4])*Log[x] + (-4 + x + E^ (2*x)*x^2 + 2*E^x*x^3 + x^4 - Log[4] + (4*x - x^2 - E^(2*x)*x^3 - 2*E^x*x^ 4 - x^5 + x*Log[4])*Log[x])*Log[-4*x + x^2 + E^(2*x)*x^3 + 2*E^x*x^4 + x^5 - x*Log[4]] + (-4 + 2*x + 5*x^4 + E^(2*x)*(3*x^2 + 2*x^3) + E^x*(8*x^3 + 2*x^4) - Log[4])*Log[x]*Log[Log[x]])/((-4*x + x^2 + E^(2*x)*x^3 + 2*E^x*x^ 4 + x^5 - x*Log[4])*Log[x]),x]
Output:
$Aborted
Result contains higher order function than in optimal. Order 9 vs. order 3.
Time = 0.05 (sec) , antiderivative size = 666, normalized size of antiderivative = 22.20
\[\text {Expression too large to display}\]
Input:
int((((2*x^3+3*x^2)*exp(x)^2+(2*x^4+8*x^3)*exp(x)-2*ln(2)+5*x^4+2*x-4)*ln( x)*ln(ln(x))+((-exp(x)^2*x^3-2*exp(x)*x^4+2*x*ln(2)-x^5-x^2+4*x)*ln(x)+exp (x)^2*x^2+2*exp(x)*x^3-2*ln(2)+x^4+x-4)*ln(exp(x)^2*x^3+2*exp(x)*x^4-2*x*l n(2)+x^5+x^2-4*x)+((-2*x^4+7*x^3+15*x^2)*exp(x)^2+(-2*x^5+2*x^4+40*x^3)*ex p(x)+2*(-5+x)*ln(2)-5*x^5+25*x^4-2*x^2+14*x-20)*ln(x))/(exp(x)^2*x^3+2*exp (x)*x^4-2*x*ln(2)+x^5+x^2-4*x)/ln(x),x)
Output:
(ln(ln(x))-x)*ln(-1/2*x^4-exp(x)*x^3-1/2*exp(2*x)*x^2+ln(2)-1/2*x+2)+ln(x) *ln(ln(x))-x*ln(x)-I*Pi*x+I*Pi*x*csgn(I*(1/2*x^4+exp(x)*x^3+1/2*exp(2*x)*x ^2-ln(2)+1/2*x-2)*x)^2-1/2*I*ln(ln(x))*Pi*csgn(I*(1/2*x^4+exp(x)*x^3+1/2*e xp(2*x)*x^2-ln(2)+1/2*x-2)*x)^3+1/2*I*Pi*x*csgn(I*(1/2*x^4+exp(x)*x^3+1/2* exp(2*x)*x^2-ln(2)+1/2*x-2))*csgn(I*(1/2*x^4+exp(x)*x^3+1/2*exp(2*x)*x^2-l n(2)+1/2*x-2)*x)^2+1/2*I*Pi*x*csgn(I*(1/2*x^4+exp(x)*x^3+1/2*exp(2*x)*x^2- ln(2)+1/2*x-2))*csgn(I*(1/2*x^4+exp(x)*x^3+1/2*exp(2*x)*x^2-ln(2)+1/2*x-2) *x)*csgn(I*x)-I*ln(ln(x))*Pi*csgn(I*(1/2*x^4+exp(x)*x^3+1/2*exp(2*x)*x^2-l n(2)+1/2*x-2)*x)^2+I*Pi*ln(ln(x))-1/2*I*ln(ln(x))*Pi*csgn(I*(1/2*x^4+exp(x )*x^3+1/2*exp(2*x)*x^2-ln(2)+1/2*x-2))*csgn(I*(1/2*x^4+exp(x)*x^3+1/2*exp( 2*x)*x^2-ln(2)+1/2*x-2)*x)^2+1/2*I*ln(ln(x))*Pi*csgn(I*(1/2*x^4+exp(x)*x^3 +1/2*exp(2*x)*x^2-ln(2)+1/2*x-2)*x)^2*csgn(I*x)+15*ln(x)+5*ln(exp(2*x)+2*e xp(x)*x-(-x^4+2*ln(2)-x+4)/x^2)+1/2*I*Pi*x*csgn(I*(1/2*x^4+exp(x)*x^3+1/2* exp(2*x)*x^2-ln(2)+1/2*x-2)*x)^3-1/2*I*Pi*x*csgn(I*(1/2*x^4+exp(x)*x^3+1/2 *exp(2*x)*x^2-ln(2)+1/2*x-2)*x)^2*csgn(I*x)-1/2*I*ln(ln(x))*Pi*csgn(I*(1/2 *x^4+exp(x)*x^3+1/2*exp(2*x)*x^2-ln(2)+1/2*x-2))*csgn(I*(1/2*x^4+exp(x)*x^ 3+1/2*exp(2*x)*x^2-ln(2)+1/2*x-2)*x)*csgn(I*x)
Leaf count of result is larger than twice the leaf count of optimal. 72 vs. \(2 (30) = 60\).
Time = 0.08 (sec) , antiderivative size = 72, normalized size of antiderivative = 2.40 \[ \int \frac {\left (-20+14 x-2 x^2+25 x^4-5 x^5+e^{2 x} \left (15 x^2+7 x^3-2 x^4\right )+e^x \left (40 x^3+2 x^4-2 x^5\right )+(-5+x) \log (4)\right ) \log (x)+\left (-4+x+e^{2 x} x^2+2 e^x x^3+x^4-\log (4)+\left (4 x-x^2-e^{2 x} x^3-2 e^x x^4-x^5+x \log (4)\right ) \log (x)\right ) \log \left (-4 x+x^2+e^{2 x} x^3+2 e^x x^4+x^5-x \log (4)\right )+\left (-4+2 x+5 x^4+e^{2 x} \left (3 x^2+2 x^3\right )+e^x \left (8 x^3+2 x^4\right )-\log (4)\right ) \log (x) \log (\log (x))}{\left (-4 x+x^2+e^{2 x} x^3+2 e^x x^4+x^5-x \log (4)\right ) \log (x)} \, dx=-{\left (x - 5\right )} \log \left (x^{5} + 2 \, x^{4} e^{x} + x^{3} e^{\left (2 \, x\right )} + x^{2} - 2 \, x \log \left (2\right ) - 4 \, x\right ) + \log \left (x^{5} + 2 \, x^{4} e^{x} + x^{3} e^{\left (2 \, x\right )} + x^{2} - 2 \, x \log \left (2\right ) - 4 \, x\right ) \log \left (\log \left (x\right )\right ) \] Input:
integrate((((2*x^3+3*x^2)*exp(x)^2+(2*x^4+8*x^3)*exp(x)-2*log(2)+5*x^4+2*x -4)*log(x)*log(log(x))+((-exp(x)^2*x^3-2*exp(x)*x^4+2*x*log(2)-x^5-x^2+4*x )*log(x)+exp(x)^2*x^2+2*exp(x)*x^3-2*log(2)+x^4+x-4)*log(exp(x)^2*x^3+2*ex p(x)*x^4-2*x*log(2)+x^5+x^2-4*x)+((-2*x^4+7*x^3+15*x^2)*exp(x)^2+(-2*x^5+2 *x^4+40*x^3)*exp(x)+2*(-5+x)*log(2)-5*x^5+25*x^4-2*x^2+14*x-20)*log(x))/(e xp(x)^2*x^3+2*exp(x)*x^4-2*x*log(2)+x^5+x^2-4*x)/log(x),x, algorithm="fric as")
Output:
-(x - 5)*log(x^5 + 2*x^4*e^x + x^3*e^(2*x) + x^2 - 2*x*log(2) - 4*x) + log (x^5 + 2*x^4*e^x + x^3*e^(2*x) + x^2 - 2*x*log(2) - 4*x)*log(log(x))
Leaf count of result is larger than twice the leaf count of optimal. 76 vs. \(2 (29) = 58\).
Time = 43.70 (sec) , antiderivative size = 76, normalized size of antiderivative = 2.53 \[ \int \frac {\left (-20+14 x-2 x^2+25 x^4-5 x^5+e^{2 x} \left (15 x^2+7 x^3-2 x^4\right )+e^x \left (40 x^3+2 x^4-2 x^5\right )+(-5+x) \log (4)\right ) \log (x)+\left (-4+x+e^{2 x} x^2+2 e^x x^3+x^4-\log (4)+\left (4 x-x^2-e^{2 x} x^3-2 e^x x^4-x^5+x \log (4)\right ) \log (x)\right ) \log \left (-4 x+x^2+e^{2 x} x^3+2 e^x x^4+x^5-x \log (4)\right )+\left (-4+2 x+5 x^4+e^{2 x} \left (3 x^2+2 x^3\right )+e^x \left (8 x^3+2 x^4\right )-\log (4)\right ) \log (x) \log (\log (x))}{\left (-4 x+x^2+e^{2 x} x^3+2 e^x x^4+x^5-x \log (4)\right ) \log (x)} \, dx=\left (- x + \log {\left (\log {\left (x \right )} \right )}\right ) \log {\left (x^{5} + 2 x^{4} e^{x} + x^{3} e^{2 x} + x^{2} - 4 x - 2 x \log {\left (2 \right )} \right )} + 15 \log {\left (x \right )} + 5 \log {\left (2 x e^{x} + e^{2 x} + \frac {x^{4} + x - 4 - 2 \log {\left (2 \right )}}{x^{2}} \right )} \] Input:
integrate((((2*x**3+3*x**2)*exp(x)**2+(2*x**4+8*x**3)*exp(x)-2*ln(2)+5*x** 4+2*x-4)*ln(x)*ln(ln(x))+((-exp(x)**2*x**3-2*exp(x)*x**4+2*x*ln(2)-x**5-x* *2+4*x)*ln(x)+exp(x)**2*x**2+2*exp(x)*x**3-2*ln(2)+x**4+x-4)*ln(exp(x)**2* x**3+2*exp(x)*x**4-2*x*ln(2)+x**5+x**2-4*x)+((-2*x**4+7*x**3+15*x**2)*exp( x)**2+(-2*x**5+2*x**4+40*x**3)*exp(x)+2*(-5+x)*ln(2)-5*x**5+25*x**4-2*x**2 +14*x-20)*ln(x))/(exp(x)**2*x**3+2*exp(x)*x**4-2*x*ln(2)+x**5+x**2-4*x)/ln (x),x)
Output:
(-x + log(log(x)))*log(x**5 + 2*x**4*exp(x) + x**3*exp(2*x) + x**2 - 4*x - 2*x*log(2)) + 15*log(x) + 5*log(2*x*exp(x) + exp(2*x) + (x**4 + x - 4 - 2 *log(2))/x**2)
Leaf count of result is larger than twice the leaf count of optimal. 81 vs. \(2 (30) = 60\).
Time = 0.19 (sec) , antiderivative size = 81, normalized size of antiderivative = 2.70 \[ \int \frac {\left (-20+14 x-2 x^2+25 x^4-5 x^5+e^{2 x} \left (15 x^2+7 x^3-2 x^4\right )+e^x \left (40 x^3+2 x^4-2 x^5\right )+(-5+x) \log (4)\right ) \log (x)+\left (-4+x+e^{2 x} x^2+2 e^x x^3+x^4-\log (4)+\left (4 x-x^2-e^{2 x} x^3-2 e^x x^4-x^5+x \log (4)\right ) \log (x)\right ) \log \left (-4 x+x^2+e^{2 x} x^3+2 e^x x^4+x^5-x \log (4)\right )+\left (-4+2 x+5 x^4+e^{2 x} \left (3 x^2+2 x^3\right )+e^x \left (8 x^3+2 x^4\right )-\log (4)\right ) \log (x) \log (\log (x))}{\left (-4 x+x^2+e^{2 x} x^3+2 e^x x^4+x^5-x \log (4)\right ) \log (x)} \, dx=-{\left (x - \log \left (\log \left (x\right )\right )\right )} \log \left (x^{4} + 2 \, x^{3} e^{x} + x^{2} e^{\left (2 \, x\right )} + x - 2 \, \log \left (2\right ) - 4\right ) - {\left (x - 15\right )} \log \left (x\right ) + \log \left (x\right ) \log \left (\log \left (x\right )\right ) + 5 \, \log \left (\frac {x^{4} + 2 \, x^{3} e^{x} + x^{2} e^{\left (2 \, x\right )} + x - 2 \, \log \left (2\right ) - 4}{x^{2}}\right ) \] Input:
integrate((((2*x^3+3*x^2)*exp(x)^2+(2*x^4+8*x^3)*exp(x)-2*log(2)+5*x^4+2*x -4)*log(x)*log(log(x))+((-exp(x)^2*x^3-2*exp(x)*x^4+2*x*log(2)-x^5-x^2+4*x )*log(x)+exp(x)^2*x^2+2*exp(x)*x^3-2*log(2)+x^4+x-4)*log(exp(x)^2*x^3+2*ex p(x)*x^4-2*x*log(2)+x^5+x^2-4*x)+((-2*x^4+7*x^3+15*x^2)*exp(x)^2+(-2*x^5+2 *x^4+40*x^3)*exp(x)+2*(-5+x)*log(2)-5*x^5+25*x^4-2*x^2+14*x-20)*log(x))/(e xp(x)^2*x^3+2*exp(x)*x^4-2*x*log(2)+x^5+x^2-4*x)/log(x),x, algorithm="maxi ma")
Output:
-(x - log(log(x)))*log(x^4 + 2*x^3*e^x + x^2*e^(2*x) + x - 2*log(2) - 4) - (x - 15)*log(x) + log(x)*log(log(x)) + 5*log((x^4 + 2*x^3*e^x + x^2*e^(2* x) + x - 2*log(2) - 4)/x^2)
\[ \int \frac {\left (-20+14 x-2 x^2+25 x^4-5 x^5+e^{2 x} \left (15 x^2+7 x^3-2 x^4\right )+e^x \left (40 x^3+2 x^4-2 x^5\right )+(-5+x) \log (4)\right ) \log (x)+\left (-4+x+e^{2 x} x^2+2 e^x x^3+x^4-\log (4)+\left (4 x-x^2-e^{2 x} x^3-2 e^x x^4-x^5+x \log (4)\right ) \log (x)\right ) \log \left (-4 x+x^2+e^{2 x} x^3+2 e^x x^4+x^5-x \log (4)\right )+\left (-4+2 x+5 x^4+e^{2 x} \left (3 x^2+2 x^3\right )+e^x \left (8 x^3+2 x^4\right )-\log (4)\right ) \log (x) \log (\log (x))}{\left (-4 x+x^2+e^{2 x} x^3+2 e^x x^4+x^5-x \log (4)\right ) \log (x)} \, dx=\int { \frac {{\left (5 \, x^{4} + {\left (2 \, x^{3} + 3 \, x^{2}\right )} e^{\left (2 \, x\right )} + 2 \, {\left (x^{4} + 4 \, x^{3}\right )} e^{x} + 2 \, x - 2 \, \log \left (2\right ) - 4\right )} \log \left (x\right ) \log \left (\log \left (x\right )\right ) + {\left (x^{4} + 2 \, x^{3} e^{x} + x^{2} e^{\left (2 \, x\right )} - {\left (x^{5} + 2 \, x^{4} e^{x} + x^{3} e^{\left (2 \, x\right )} + x^{2} - 2 \, x \log \left (2\right ) - 4 \, x\right )} \log \left (x\right ) + x - 2 \, \log \left (2\right ) - 4\right )} \log \left (x^{5} + 2 \, x^{4} e^{x} + x^{3} e^{\left (2 \, x\right )} + x^{2} - 2 \, x \log \left (2\right ) - 4 \, x\right ) - {\left (5 \, x^{5} - 25 \, x^{4} + 2 \, x^{2} + {\left (2 \, x^{4} - 7 \, x^{3} - 15 \, x^{2}\right )} e^{\left (2 \, x\right )} + 2 \, {\left (x^{5} - x^{4} - 20 \, x^{3}\right )} e^{x} - 2 \, {\left (x - 5\right )} \log \left (2\right ) - 14 \, x + 20\right )} \log \left (x\right )}{{\left (x^{5} + 2 \, x^{4} e^{x} + x^{3} e^{\left (2 \, x\right )} + x^{2} - 2 \, x \log \left (2\right ) - 4 \, x\right )} \log \left (x\right )} \,d x } \] Input:
integrate((((2*x^3+3*x^2)*exp(x)^2+(2*x^4+8*x^3)*exp(x)-2*log(2)+5*x^4+2*x -4)*log(x)*log(log(x))+((-exp(x)^2*x^3-2*exp(x)*x^4+2*x*log(2)-x^5-x^2+4*x )*log(x)+exp(x)^2*x^2+2*exp(x)*x^3-2*log(2)+x^4+x-4)*log(exp(x)^2*x^3+2*ex p(x)*x^4-2*x*log(2)+x^5+x^2-4*x)+((-2*x^4+7*x^3+15*x^2)*exp(x)^2+(-2*x^5+2 *x^4+40*x^3)*exp(x)+2*(-5+x)*log(2)-5*x^5+25*x^4-2*x^2+14*x-20)*log(x))/(e xp(x)^2*x^3+2*exp(x)*x^4-2*x*log(2)+x^5+x^2-4*x)/log(x),x, algorithm="giac ")
Output:
integrate(((5*x^4 + (2*x^3 + 3*x^2)*e^(2*x) + 2*(x^4 + 4*x^3)*e^x + 2*x - 2*log(2) - 4)*log(x)*log(log(x)) + (x^4 + 2*x^3*e^x + x^2*e^(2*x) - (x^5 + 2*x^4*e^x + x^3*e^(2*x) + x^2 - 2*x*log(2) - 4*x)*log(x) + x - 2*log(2) - 4)*log(x^5 + 2*x^4*e^x + x^3*e^(2*x) + x^2 - 2*x*log(2) - 4*x) - (5*x^5 - 25*x^4 + 2*x^2 + (2*x^4 - 7*x^3 - 15*x^2)*e^(2*x) + 2*(x^5 - x^4 - 20*x^3 )*e^x - 2*(x - 5)*log(2) - 14*x + 20)*log(x))/((x^5 + 2*x^4*e^x + x^3*e^(2 *x) + x^2 - 2*x*log(2) - 4*x)*log(x)), x)
Timed out. \[ \int \frac {\left (-20+14 x-2 x^2+25 x^4-5 x^5+e^{2 x} \left (15 x^2+7 x^3-2 x^4\right )+e^x \left (40 x^3+2 x^4-2 x^5\right )+(-5+x) \log (4)\right ) \log (x)+\left (-4+x+e^{2 x} x^2+2 e^x x^3+x^4-\log (4)+\left (4 x-x^2-e^{2 x} x^3-2 e^x x^4-x^5+x \log (4)\right ) \log (x)\right ) \log \left (-4 x+x^2+e^{2 x} x^3+2 e^x x^4+x^5-x \log (4)\right )+\left (-4+2 x+5 x^4+e^{2 x} \left (3 x^2+2 x^3\right )+e^x \left (8 x^3+2 x^4\right )-\log (4)\right ) \log (x) \log (\log (x))}{\left (-4 x+x^2+e^{2 x} x^3+2 e^x x^4+x^5-x \log (4)\right ) \log (x)} \, dx=\int \frac {\ln \left (2\,x^4\,{\mathrm {e}}^x-4\,x-2\,x\,\ln \left (2\right )+x^3\,{\mathrm {e}}^{2\,x}+x^2+x^5\right )\,\left (x-2\,\ln \left (2\right )+2\,x^3\,{\mathrm {e}}^x+x^2\,{\mathrm {e}}^{2\,x}+x^4-\ln \left (x\right )\,\left (2\,x^4\,{\mathrm {e}}^x-4\,x-2\,x\,\ln \left (2\right )+x^3\,{\mathrm {e}}^{2\,x}+x^2+x^5\right )-4\right )+\ln \left (x\right )\,\left (14\,x+{\mathrm {e}}^x\,\left (-2\,x^5+2\,x^4+40\,x^3\right )+{\mathrm {e}}^{2\,x}\,\left (-2\,x^4+7\,x^3+15\,x^2\right )+2\,\ln \left (2\right )\,\left (x-5\right )-2\,x^2+25\,x^4-5\,x^5-20\right )+\ln \left (\ln \left (x\right )\right )\,\ln \left (x\right )\,\left (2\,x-2\,\ln \left (2\right )+{\mathrm {e}}^x\,\left (2\,x^4+8\,x^3\right )+{\mathrm {e}}^{2\,x}\,\left (2\,x^3+3\,x^2\right )+5\,x^4-4\right )}{\ln \left (x\right )\,\left (2\,x^4\,{\mathrm {e}}^x-4\,x-2\,x\,\ln \left (2\right )+x^3\,{\mathrm {e}}^{2\,x}+x^2+x^5\right )} \,d x \] Input:
int((log(2*x^4*exp(x) - 4*x - 2*x*log(2) + x^3*exp(2*x) + x^2 + x^5)*(x - 2*log(2) + 2*x^3*exp(x) + x^2*exp(2*x) + x^4 - log(x)*(2*x^4*exp(x) - 4*x - 2*x*log(2) + x^3*exp(2*x) + x^2 + x^5) - 4) + log(x)*(14*x + exp(x)*(40* x^3 + 2*x^4 - 2*x^5) + exp(2*x)*(15*x^2 + 7*x^3 - 2*x^4) + 2*log(2)*(x - 5 ) - 2*x^2 + 25*x^4 - 5*x^5 - 20) + log(log(x))*log(x)*(2*x - 2*log(2) + ex p(x)*(8*x^3 + 2*x^4) + exp(2*x)*(3*x^2 + 2*x^3) + 5*x^4 - 4))/(log(x)*(2*x ^4*exp(x) - 4*x - 2*x*log(2) + x^3*exp(2*x) + x^2 + x^5)),x)
Output:
int((log(2*x^4*exp(x) - 4*x - 2*x*log(2) + x^3*exp(2*x) + x^2 + x^5)*(x - 2*log(2) + 2*x^3*exp(x) + x^2*exp(2*x) + x^4 - log(x)*(2*x^4*exp(x) - 4*x - 2*x*log(2) + x^3*exp(2*x) + x^2 + x^5) - 4) + log(x)*(14*x + exp(x)*(40* x^3 + 2*x^4 - 2*x^5) + exp(2*x)*(15*x^2 + 7*x^3 - 2*x^4) + 2*log(2)*(x - 5 ) - 2*x^2 + 25*x^4 - 5*x^5 - 20) + log(log(x))*log(x)*(2*x - 2*log(2) + ex p(x)*(8*x^3 + 2*x^4) + exp(2*x)*(3*x^2 + 2*x^3) + 5*x^4 - 4))/(log(x)*(2*x ^4*exp(x) - 4*x - 2*x*log(2) + x^3*exp(2*x) + x^2 + x^5)), x)
\[ \int \frac {\left (-20+14 x-2 x^2+25 x^4-5 x^5+e^{2 x} \left (15 x^2+7 x^3-2 x^4\right )+e^x \left (40 x^3+2 x^4-2 x^5\right )+(-5+x) \log (4)\right ) \log (x)+\left (-4+x+e^{2 x} x^2+2 e^x x^3+x^4-\log (4)+\left (4 x-x^2-e^{2 x} x^3-2 e^x x^4-x^5+x \log (4)\right ) \log (x)\right ) \log \left (-4 x+x^2+e^{2 x} x^3+2 e^x x^4+x^5-x \log (4)\right )+\left (-4+2 x+5 x^4+e^{2 x} \left (3 x^2+2 x^3\right )+e^x \left (8 x^3+2 x^4\right )-\log (4)\right ) \log (x) \log (\log (x))}{\left (-4 x+x^2+e^{2 x} x^3+2 e^x x^4+x^5-x \log (4)\right ) \log (x)} \, dx=\int \frac {\left (\left (2 x^{3}+3 x^{2}\right ) \left ({\mathrm e}^{x}\right )^{2}+\left (2 x^{4}+8 x^{3}\right ) {\mathrm e}^{x}-2 \,\mathrm {log}\left (2\right )+5 x^{4}+2 x -4\right ) \mathrm {log}\left (x \right ) \mathrm {log}\left (\mathrm {log}\left (x \right )\right )+\left (\left (-\left ({\mathrm e}^{x}\right )^{2} x^{3}-2 \,{\mathrm e}^{x} x^{4}+2 \,\mathrm {log}\left (2\right ) x -x^{5}-x^{2}+4 x \right ) \mathrm {log}\left (x \right )+\left ({\mathrm e}^{x}\right )^{2} x^{2}+2 \,{\mathrm e}^{x} x^{3}-2 \,\mathrm {log}\left (2\right )+x^{4}+x -4\right ) \mathrm {log}\left (\left ({\mathrm e}^{x}\right )^{2} x^{3}+2 \,{\mathrm e}^{x} x^{4}-2 \,\mathrm {log}\left (2\right ) x +x^{5}+x^{2}-4 x \right )+\left (\left (-2 x^{4}+7 x^{3}+15 x^{2}\right ) \left ({\mathrm e}^{x}\right )^{2}+\left (-2 x^{5}+2 x^{4}+40 x^{3}\right ) {\mathrm e}^{x}+2 \left (-5+x \right ) \mathrm {log}\left (2\right )-5 x^{5}+25 x^{4}-2 x^{2}+14 x -20\right ) \mathrm {log}\left (x \right )}{\left (\left ({\mathrm e}^{x}\right )^{2} x^{3}+2 \,{\mathrm e}^{x} x^{4}-2 \,\mathrm {log}\left (2\right ) x +x^{5}+x^{2}-4 x \right ) \mathrm {log}\left (x \right )}d x \] Input:
int((((2*x^3+3*x^2)*exp(x)^2+(2*x^4+8*x^3)*exp(x)-2*log(2)+5*x^4+2*x-4)*lo g(x)*log(log(x))+((-exp(x)^2*x^3-2*exp(x)*x^4+2*x*log(2)-x^5-x^2+4*x)*log( x)+exp(x)^2*x^2+2*exp(x)*x^3-2*log(2)+x^4+x-4)*log(exp(x)^2*x^3+2*exp(x)*x ^4-2*x*log(2)+x^5+x^2-4*x)+((-2*x^4+7*x^3+15*x^2)*exp(x)^2+(-2*x^5+2*x^4+4 0*x^3)*exp(x)+2*(-5+x)*log(2)-5*x^5+25*x^4-2*x^2+14*x-20)*log(x))/(exp(x)^ 2*x^3+2*exp(x)*x^4-2*x*log(2)+x^5+x^2-4*x)/log(x),x)
Output:
int((((2*x^3+3*x^2)*exp(x)^2+(2*x^4+8*x^3)*exp(x)-2*log(2)+5*x^4+2*x-4)*lo g(x)*log(log(x))+((-exp(x)^2*x^3-2*exp(x)*x^4+2*x*log(2)-x^5-x^2+4*x)*log( x)+exp(x)^2*x^2+2*exp(x)*x^3-2*log(2)+x^4+x-4)*log(exp(x)^2*x^3+2*exp(x)*x ^4-2*x*log(2)+x^5+x^2-4*x)+((-2*x^4+7*x^3+15*x^2)*exp(x)^2+(-2*x^5+2*x^4+4 0*x^3)*exp(x)+2*(-5+x)*log(2)-5*x^5+25*x^4-2*x^2+14*x-20)*log(x))/(exp(x)^ 2*x^3+2*exp(x)*x^4-2*x*log(2)+x^5+x^2-4*x)/log(x),x)