\(\int \frac {(-10 x^4-2 x^5) \log (\log (4))+(5+x)^{\frac {2}{\log (\log (4))}} (4 x^4+(-20 x^3-4 x^4) \log (\log (4)))+(5+x)^{\frac {1}{\log (\log (4))}} (4 x^5+(-20 x^4-4 x^5) \log (\log (4)))}{(5+x)^{1+\frac {6}{\log (\log (4))}} \log (\log (4))+(5+x)^{\frac {5}{\log (\log (4))}} (30 x+6 x^2) \log (\log (4))+(5+x)^{\frac {4}{\log (\log (4))}} (15 x+78 x^2+15 x^3) \log (\log (4))+(5+x)^{\frac {3}{\log (\log (4))}} (60 x^2+112 x^3+20 x^4) \log (\log (4))+(5+x)^{\frac {2}{\log (\log (4))}} (15 x^2+93 x^3+93 x^4+15 x^5) \log (\log (4))+(5+x)^{\frac {1}{\log (\log (4))}} (30 x^3+66 x^4+42 x^5+6 x^6) \log (\log (4))+(5 x^3+16 x^4+18 x^5+8 x^6+x^7) \log (\log (4))} \, dx\) [291]

Optimal result

Integrand size = 283, antiderivative size = 24 \[ \int \frac {\left (-10 x^4-2 x^5\right ) \log (\log (4))+(5+x)^{\frac {2}{\log (\log (4))}} \left (4 x^4+\left (-20 x^3-4 x^4\right ) \log (\log (4))\right )+(5+x)^{\frac {1}{\log (\log (4))}} \left (4 x^5+\left (-20 x^4-4 x^5\right ) \log (\log (4))\right )}{(5+x)^{1+\frac {6}{\log (\log (4))}} \log (\log (4))+(5+x)^{\frac {5}{\log (\log (4))}} \left (30 x+6 x^2\right ) \log (\log (4))+(5+x)^{\frac {4}{\log (\log (4))}} \left (15 x+78 x^2+15 x^3\right ) \log (\log (4))+(5+x)^{\frac {3}{\log (\log (4))}} \left (60 x^2+112 x^3+20 x^4\right ) \log (\log (4))+(5+x)^{\frac {2}{\log (\log (4))}} \left (15 x^2+93 x^3+93 x^4+15 x^5\right ) \log (\log (4))+(5+x)^{\frac {1}{\log (\log (4))}} \left (30 x^3+66 x^4+42 x^5+6 x^6\right ) \log (\log (4))+\left (5 x^3+16 x^4+18 x^5+8 x^6+x^7\right ) \log (\log (4))} \, dx=2-\frac {x^4}{\left (x+\left (x+(5+x)^{\frac {1}{\log (\log (4))}}\right )^2\right )^2} \]

[Out]

2-1/(x+(exp(ln(5+x)/ln(2*ln(2)))+x)^2)^2*x^4

Rubi [F]

\[ \int \frac {\left (-10 x^4-2 x^5\right ) \log (\log (4))+(5+x)^{\frac {2}{\log (\log (4))}} \left (4 x^4+\left (-20 x^3-4 x^4\right ) \log (\log (4))\right )+(5+x)^{\frac {1}{\log (\log (4))}} \left (4 x^5+\left (-20 x^4-4 x^5\right ) \log (\log (4))\right )}{(5+x)^{1+\frac {6}{\log (\log (4))}} \log (\log (4))+(5+x)^{\frac {5}{\log (\log (4))}} \left (30 x+6 x^2\right ) \log (\log (4))+(5+x)^{\frac {4}{\log (\log (4))}} \left (15 x+78 x^2+15 x^3\right ) \log (\log (4))+(5+x)^{\frac {3}{\log (\log (4))}} \left (60 x^2+112 x^3+20 x^4\right ) \log (\log (4))+(5+x)^{\frac {2}{\log (\log (4))}} \left (15 x^2+93 x^3+93 x^4+15 x^5\right ) \log (\log (4))+(5+x)^{\frac {1}{\log (\log (4))}} \left (30 x^3+66 x^4+42 x^5+6 x^6\right ) \log (\log (4))+\left (5 x^3+16 x^4+18 x^5+8 x^6+x^7\right ) \log (\log (4))} \, dx=\int \frac {\left (-10 x^4-2 x^5\right ) \log (\log (4))+(5+x)^{\frac {2}{\log (\log (4))}} \left (4 x^4+\left (-20 x^3-4 x^4\right ) \log (\log (4))\right )+(5+x)^{\frac {1}{\log (\log (4))}} \left (4 x^5+\left (-20 x^4-4 x^5\right ) \log (\log (4))\right )}{(5+x)^{1+\frac {6}{\log (\log (4))}} \log (\log (4))+(5+x)^{\frac {5}{\log (\log (4))}} \left (30 x+6 x^2\right ) \log (\log (4))+(5+x)^{\frac {4}{\log (\log (4))}} \left (15 x+78 x^2+15 x^3\right ) \log (\log (4))+(5+x)^{\frac {3}{\log (\log (4))}} \left (60 x^2+112 x^3+20 x^4\right ) \log (\log (4))+(5+x)^{\frac {2}{\log (\log (4))}} \left (15 x^2+93 x^3+93 x^4+15 x^5\right ) \log (\log (4))+(5+x)^{\frac {1}{\log (\log (4))}} \left (30 x^3+66 x^4+42 x^5+6 x^6\right ) \log (\log (4))+\left (5 x^3+16 x^4+18 x^5+8 x^6+x^7\right ) \log (\log (4))} \, dx \]

[In]

Int[((-10*x^4 - 2*x^5)*Log[Log[4]] + (5 + x)^(2/Log[Log[4]])*(4*x^4 + (-20*x^3 - 4*x^4)*Log[Log[4]]) + (5 + x)
^Log[Log[4]]^(-1)*(4*x^5 + (-20*x^4 - 4*x^5)*Log[Log[4]]))/((5 + x)^(1 + 6/Log[Log[4]])*Log[Log[4]] + (5 + x)^
(5/Log[Log[4]])*(30*x + 6*x^2)*Log[Log[4]] + (5 + x)^(4/Log[Log[4]])*(15*x + 78*x^2 + 15*x^3)*Log[Log[4]] + (5
+ x)^(3/Log[Log[4]])*(60*x^2 + 112*x^3 + 20*x^4)*Log[Log[4]] + (5 + x)^(2/Log[Log[4]])*(15*x^2 + 93*x^3 + 93*
x^4 + 15*x^5)*Log[Log[4]] + (5 + x)^Log[Log[4]]^(-1)*(30*x^3 + 66*x^4 + 42*x^5 + 6*x^6)*Log[Log[4]] + (5*x^3 +
16*x^4 + 18*x^5 + 8*x^6 + x^7)*Log[Log[4]]),x]

[Out]

-1250*Defer[Int][(x + x^2 + 2*x*(5 + x)^Log[Log[4]]^(-1) + (5 + x)^(2/Log[Log[4]]))^(-3), x] - 12500*(1 - Log[
Log[4]]^(-1))*Defer[Int][(x + x^2 + 2*x*(5 + x)^Log[Log[4]]^(-1) + (5 + x)^(2/Log[Log[4]]))^(-3), x] - (1250*(
2 - 11*Log[Log[4]])*Defer[Int][(x + x^2 + 2*x*(5 + x)^Log[Log[4]]^(-1) + (5 + x)^(2/Log[Log[4]]))^(-3), x])/Lo
g[Log[4]] + 250*Defer[Int][x/(x + x^2 + 2*x*(5 + x)^Log[Log[4]]^(-1) + (5 + x)^(2/Log[Log[4]]))^3, x] + 2500*(
1 - Log[Log[4]]^(-1))*Defer[Int][x/(x + x^2 + 2*x*(5 + x)^Log[Log[4]]^(-1) + (5 + x)^(2/Log[Log[4]]))^3, x] +
(250*(2 - 11*Log[Log[4]])*Defer[Int][x/(x + x^2 + 2*x*(5 + x)^Log[Log[4]]^(-1) + (5 + x)^(2/Log[Log[4]]))^3, x
])/Log[Log[4]] - 50*Defer[Int][x^2/(x + x^2 + 2*x*(5 + x)^Log[Log[4]]^(-1) + (5 + x)^(2/Log[Log[4]]))^3, x] -
500*(1 - Log[Log[4]]^(-1))*Defer[Int][x^2/(x + x^2 + 2*x*(5 + x)^Log[Log[4]]^(-1) + (5 + x)^(2/Log[Log[4]]))^3
, x] - (50*(2 - 11*Log[Log[4]])*Defer[Int][x^2/(x + x^2 + 2*x*(5 + x)^Log[Log[4]]^(-1) + (5 + x)^(2/Log[Log[4]
]))^3, x])/Log[Log[4]] + 10*Defer[Int][x^3/(x + x^2 + 2*x*(5 + x)^Log[Log[4]]^(-1) + (5 + x)^(2/Log[Log[4]]))^
3, x] + 100*(1 - Log[Log[4]]^(-1))*Defer[Int][x^3/(x + x^2 + 2*x*(5 + x)^Log[Log[4]]^(-1) + (5 + x)^(2/Log[Log
[4]]))^3, x] + (10*(2 - 11*Log[Log[4]])*Defer[Int][x^3/(x + x^2 + 2*x*(5 + x)^Log[Log[4]]^(-1) + (5 + x)^(2/Lo
g[Log[4]]))^3, x])/Log[Log[4]] - 20*(1 - Log[Log[4]]^(-1))*Defer[Int][x^4/(x + x^2 + 2*x*(5 + x)^Log[Log[4]]^(
-1) + (5 + x)^(2/Log[Log[4]]))^3, x] - (2*(2 - 11*Log[Log[4]])*Defer[Int][x^4/(x + x^2 + 2*x*(5 + x)^Log[Log[4
]]^(-1) + (5 + x)^(2/Log[Log[4]]))^3, x])/Log[Log[4]] + 4*(1 - Log[Log[4]]^(-1))*Defer[Int][x^5/(x + x^2 + 2*x
*(5 + x)^Log[Log[4]]^(-1) + (5 + x)^(2/Log[Log[4]]))^3, x] + 6250*Defer[Int][1/((5 + x)*(x + x^2 + 2*x*(5 + x)
^Log[Log[4]]^(-1) + (5 + x)^(2/Log[Log[4]]))^3), x] + 62500*(1 - Log[Log[4]]^(-1))*Defer[Int][1/((5 + x)*(x +
x^2 + 2*x*(5 + x)^Log[Log[4]]^(-1) + (5 + x)^(2/Log[Log[4]]))^3), x] + (6250*(2 - 11*Log[Log[4]])*Defer[Int][1
/((5 + x)*(x + x^2 + 2*x*(5 + x)^Log[Log[4]]^(-1) + (5 + x)^(2/Log[Log[4]]))^3), x])/Log[Log[4]] + 12500*Defer
[Int][(5 + x)^(-1 + Log[Log[4]]^(-1))/(x + x^2 + 2*x*(5 + x)^Log[Log[4]]^(-1) + (5 + x)^(2/Log[Log[4]]))^3, x]
+ 2500*(1 - Log[Log[4]]^(-1))*Defer[Int][(x*(5 + x)^(-1 + Log[Log[4]]^(-1)))/(x + x^2 + 2*x*(5 + x)^Log[Log[4
]]^(-1) + (5 + x)^(2/Log[Log[4]]))^3, x] - 2500*Defer[Int][(5 + x)^Log[Log[4]]^(-1)/(x + x^2 + 2*x*(5 + x)^Log
[Log[4]]^(-1) + (5 + x)^(2/Log[Log[4]]))^3, x] + 500*Defer[Int][(x*(5 + x)^Log[Log[4]]^(-1))/(x + x^2 + 2*x*(5
+ x)^Log[Log[4]]^(-1) + (5 + x)^(2/Log[Log[4]]))^3, x] - 500*(1 - Log[Log[4]]^(-1))*Defer[Int][(x*(5 + x)^Log
[Log[4]]^(-1))/(x + x^2 + 2*x*(5 + x)^Log[Log[4]]^(-1) + (5 + x)^(2/Log[Log[4]]))^3, x] - 100*Defer[Int][(x^2*
(5 + x)^Log[Log[4]]^(-1))/(x + x^2 + 2*x*(5 + x)^Log[Log[4]]^(-1) + (5 + x)^(2/Log[Log[4]]))^3, x] + 100*(1 -
Log[Log[4]]^(-1))*Defer[Int][(x^2*(5 + x)^Log[Log[4]]^(-1))/(x + x^2 + 2*x*(5 + x)^Log[Log[4]]^(-1) + (5 + x)^
(2/Log[Log[4]]))^3, x] + 20*Defer[Int][(x^3*(5 + x)^Log[Log[4]]^(-1))/(x + x^2 + 2*x*(5 + x)^Log[Log[4]]^(-1)
+ (5 + x)^(2/Log[Log[4]]))^3, x] - 20*(1 - Log[Log[4]]^(-1))*Defer[Int][(x^3*(5 + x)^Log[Log[4]]^(-1))/(x + x^
2 + 2*x*(5 + x)^Log[Log[4]]^(-1) + (5 + x)^(2/Log[Log[4]]))^3, x] + 4*(1 - Log[Log[4]]^(-1))*Defer[Int][(x^4*(
5 + x)^Log[Log[4]]^(-1))/(x + x^2 + 2*x*(5 + x)^Log[Log[4]]^(-1) + (5 + x)^(2/Log[Log[4]]))^3, x] - (500*Defer
[Int][(x + x^2 + 2*x*(5 + x)^Log[Log[4]]^(-1) + (5 + x)^(2/Log[Log[4]]))^(-2), x])/Log[Log[4]] + (100*Defer[In
t][x/(x + x^2 + 2*x*(5 + x)^Log[Log[4]]^(-1) + (5 + x)^(2/Log[Log[4]]))^2, x])/Log[Log[4]] - (20*Defer[Int][x^
2/(x + x^2 + 2*x*(5 + x)^Log[Log[4]]^(-1) + (5 + x)^(2/Log[Log[4]]))^2, x])/Log[Log[4]] - 4*(1 - Log[Log[4]]^(
-1))*Defer[Int][x^3/(x + x^2 + 2*x*(5 + x)^Log[Log[4]]^(-1) + (5 + x)^(2/Log[Log[4]]))^2, x] + (2500*Defer[Int
][1/((5 + x)*(x + x^2 + 2*x*(5 + x)^Log[Log[4]]^(-1) + (5 + x)^(2/Log[Log[4]]))^2), x])/Log[Log[4]]

Rubi steps \begin{align*} \text {integral}& = \int \frac {2 x^3 \left (-10 (5+x)^{\frac {2}{\log (\log (4))}} \log (\log (4))-x^2 \left (-2 (5+x)^{\frac {1}{\log (\log (4))}}+\left (1+2 (5+x)^{\frac {1}{\log (\log (4))}}\right ) \log (\log (4))\right )-x \left (-2 (5+x)^{\frac {2}{\log (\log (4))}}+\left (5+10 (5+x)^{\frac {1}{\log (\log (4))}}+2 (5+x)^{\frac {2}{\log (\log (4))}}\right ) \log (\log (4))\right )\right )}{(5+x) \left (x+x^2+2 x (5+x)^{\frac {1}{\log (\log (4))}}+(5+x)^{\frac {2}{\log (\log (4))}}\right )^3 \log (\log (4))} \, dx \\ & = \frac {2 \int \frac {x^3 \left (-10 (5+x)^{\frac {2}{\log (\log (4))}} \log (\log (4))-x^2 \left (-2 (5+x)^{\frac {1}{\log (\log (4))}}+\left (1+2 (5+x)^{\frac {1}{\log (\log (4))}}\right ) \log (\log (4))\right )-x \left (-2 (5+x)^{\frac {2}{\log (\log (4))}}+\left (5+10 (5+x)^{\frac {1}{\log (\log (4))}}+2 (5+x)^{\frac {2}{\log (\log (4))}}\right ) \log (\log (4))\right )\right )}{(5+x) \left (x+x^2+2 x (5+x)^{\frac {1}{\log (\log (4))}}+(5+x)^{\frac {2}{\log (\log (4))}}\right )^3} \, dx}{\log (\log (4))} \\ & = \frac {2 \int \left (\frac {2 x^3 (x (1-\log (\log (4)))-5 \log (\log (4)))}{(5+x) \left (x+x^2+2 x (5+x)^{\frac {1}{\log (\log (4))}}+(5+x)^{\frac {2}{\log (\log (4))}}\right )^2}+\frac {x^4 \left (-2 x \left (1-\frac {11}{2} \log (\log (4))\right )-2 x^2 (1-\log (\log (4)))-2 x (5+x)^{\frac {1}{\log (\log (4))}} (1-\log (\log (4)))+5 \log (\log (4))+10 (5+x)^{\frac {1}{\log (\log (4))}} \log (\log (4))\right )}{(5+x) \left (x+x^2+2 x (5+x)^{\frac {1}{\log (\log (4))}}+(5+x)^{\frac {2}{\log (\log (4))}}\right )^3}\right ) \, dx}{\log (\log (4))} \\ & = \frac {2 \int \frac {x^4 \left (-2 x \left (1-\frac {11}{2} \log (\log (4))\right )-2 x^2 (1-\log (\log (4)))-2 x (5+x)^{\frac {1}{\log (\log (4))}} (1-\log (\log (4)))+5 \log (\log (4))+10 (5+x)^{\frac {1}{\log (\log (4))}} \log (\log (4))\right )}{(5+x) \left (x+x^2+2 x (5+x)^{\frac {1}{\log (\log (4))}}+(5+x)^{\frac {2}{\log (\log (4))}}\right )^3} \, dx}{\log (\log (4))}+\frac {4 \int \frac {x^3 (x (1-\log (\log (4)))-5 \log (\log (4)))}{(5+x) \left (x+x^2+2 x (5+x)^{\frac {1}{\log (\log (4))}}+(5+x)^{\frac {2}{\log (\log (4))}}\right )^2} \, dx}{\log (\log (4))} \\ & = \frac {2 \int \left (\frac {125 \left (2 x \left (1-\frac {11}{2} \log (\log (4))\right )+2 x^2 (1-\log (\log (4)))+2 x (5+x)^{\frac {1}{\log (\log (4))}} (1-\log (\log (4)))-5 \log (\log (4))-10 (5+x)^{\frac {1}{\log (\log (4))}} \log (\log (4))\right )}{\left (x+x^2+2 x (5+x)^{\frac {1}{\log (\log (4))}}+(5+x)^{\frac {2}{\log (\log (4))}}\right )^3}+\frac {5 x^2 \left (2 x \left (1-\frac {11}{2} \log (\log (4))\right )+2 x^2 (1-\log (\log (4)))+2 x (5+x)^{\frac {1}{\log (\log (4))}} (1-\log (\log (4)))-5 \log (\log (4))-10 (5+x)^{\frac {1}{\log (\log (4))}} \log (\log (4))\right )}{\left (x+x^2+2 x (5+x)^{\frac {1}{\log (\log (4))}}+(5+x)^{\frac {2}{\log (\log (4))}}\right )^3}+\frac {25 x \left (-2 x \left (1-\frac {11}{2} \log (\log (4))\right )-2 x^2 (1-\log (\log (4)))-2 x (5+x)^{\frac {1}{\log (\log (4))}} (1-\log (\log (4)))+5 \log (\log (4))+10 (5+x)^{\frac {1}{\log (\log (4))}} \log (\log (4))\right )}{\left (x+x^2+2 x (5+x)^{\frac {1}{\log (\log (4))}}+(5+x)^{\frac {2}{\log (\log (4))}}\right )^3}+\frac {x^3 \left (-2 x \left (1-\frac {11}{2} \log (\log (4))\right )-2 x^2 (1-\log (\log (4)))-2 x (5+x)^{\frac {1}{\log (\log (4))}} (1-\log (\log (4)))+5 \log (\log (4))+10 (5+x)^{\frac {1}{\log (\log (4))}} \log (\log (4))\right )}{\left (x+x^2+2 x (5+x)^{\frac {1}{\log (\log (4))}}+(5+x)^{\frac {2}{\log (\log (4))}}\right )^3}+\frac {625 \left (-2 x \left (1-\frac {11}{2} \log (\log (4))\right )-2 x^2 (1-\log (\log (4)))-2 x (5+x)^{\frac {1}{\log (\log (4))}} (1-\log (\log (4)))+5 \log (\log (4))+10 (5+x)^{\frac {1}{\log (\log (4))}} \log (\log (4))\right )}{(5+x) \left (x+x^2+2 x (5+x)^{\frac {1}{\log (\log (4))}}+(5+x)^{\frac {2}{\log (\log (4))}}\right )^3}\right ) \, dx}{\log (\log (4))}+\frac {4 \int \left (-\frac {125}{\left (x+x^2+2 x (5+x)^{\frac {1}{\log (\log (4))}}+(5+x)^{\frac {2}{\log (\log (4))}}\right )^2}+\frac {25 x}{\left (x+x^2+2 x (5+x)^{\frac {1}{\log (\log (4))}}+(5+x)^{\frac {2}{\log (\log (4))}}\right )^2}-\frac {5 x^2}{\left (x+x^2+2 x (5+x)^{\frac {1}{\log (\log (4))}}+(5+x)^{\frac {2}{\log (\log (4))}}\right )^2}+\frac {625}{(5+x) \left (x+x^2+2 x (5+x)^{\frac {1}{\log (\log (4))}}+(5+x)^{\frac {2}{\log (\log (4))}}\right )^2}-\frac {x^3 (-1+\log (\log (4)))}{\left (x+x^2+2 x (5+x)^{\frac {1}{\log (\log (4))}}+(5+x)^{\frac {2}{\log (\log (4))}}\right )^2}\right ) \, dx}{\log (\log (4))} \\ & = -\left (\left (4 \left (1-\frac {1}{\log (\log (4))}\right )\right ) \int \frac {x^3}{\left (x+x^2+2 x (5+x)^{\frac {1}{\log (\log (4))}}+(5+x)^{\frac {2}{\log (\log (4))}}\right )^2} \, dx\right )+\frac {2 \int \frac {x^3 \left (-2 x \left (1-\frac {11}{2} \log (\log (4))\right )-2 x^2 (1-\log (\log (4)))-2 x (5+x)^{\frac {1}{\log (\log (4))}} (1-\log (\log (4)))+5 \log (\log (4))+10 (5+x)^{\frac {1}{\log (\log (4))}} \log (\log (4))\right )}{\left (x+x^2+2 x (5+x)^{\frac {1}{\log (\log (4))}}+(5+x)^{\frac {2}{\log (\log (4))}}\right )^3} \, dx}{\log (\log (4))}+\frac {10 \int \frac {x^2 \left (2 x \left (1-\frac {11}{2} \log (\log (4))\right )+2 x^2 (1-\log (\log (4)))+2 x (5+x)^{\frac {1}{\log (\log (4))}} (1-\log (\log (4)))-5 \log (\log (4))-10 (5+x)^{\frac {1}{\log (\log (4))}} \log (\log (4))\right )}{\left (x+x^2+2 x (5+x)^{\frac {1}{\log (\log (4))}}+(5+x)^{\frac {2}{\log (\log (4))}}\right )^3} \, dx}{\log (\log (4))}-\frac {20 \int \frac {x^2}{\left (x+x^2+2 x (5+x)^{\frac {1}{\log (\log (4))}}+(5+x)^{\frac {2}{\log (\log (4))}}\right )^2} \, dx}{\log (\log (4))}+\frac {50 \int \frac {x \left (-2 x \left (1-\frac {11}{2} \log (\log (4))\right )-2 x^2 (1-\log (\log (4)))-2 x (5+x)^{\frac {1}{\log (\log (4))}} (1-\log (\log (4)))+5 \log (\log (4))+10 (5+x)^{\frac {1}{\log (\log (4))}} \log (\log (4))\right )}{\left (x+x^2+2 x (5+x)^{\frac {1}{\log (\log (4))}}+(5+x)^{\frac {2}{\log (\log (4))}}\right )^3} \, dx}{\log (\log (4))}+\frac {100 \int \frac {x}{\left (x+x^2+2 x (5+x)^{\frac {1}{\log (\log (4))}}+(5+x)^{\frac {2}{\log (\log (4))}}\right )^2} \, dx}{\log (\log (4))}+\frac {250 \int \frac {2 x \left (1-\frac {11}{2} \log (\log (4))\right )+2 x^2 (1-\log (\log (4)))+2 x (5+x)^{\frac {1}{\log (\log (4))}} (1-\log (\log (4)))-5 \log (\log (4))-10 (5+x)^{\frac {1}{\log (\log (4))}} \log (\log (4))}{\left (x+x^2+2 x (5+x)^{\frac {1}{\log (\log (4))}}+(5+x)^{\frac {2}{\log (\log (4))}}\right )^3} \, dx}{\log (\log (4))}-\frac {500 \int \frac {1}{\left (x+x^2+2 x (5+x)^{\frac {1}{\log (\log (4))}}+(5+x)^{\frac {2}{\log (\log (4))}}\right )^2} \, dx}{\log (\log (4))}+\frac {1250 \int \frac {-2 x \left (1-\frac {11}{2} \log (\log (4))\right )-2 x^2 (1-\log (\log (4)))-2 x (5+x)^{\frac {1}{\log (\log (4))}} (1-\log (\log (4)))+5 \log (\log (4))+10 (5+x)^{\frac {1}{\log (\log (4))}} \log (\log (4))}{(5+x) \left (x+x^2+2 x (5+x)^{\frac {1}{\log (\log (4))}}+(5+x)^{\frac {2}{\log (\log (4))}}\right )^3} \, dx}{\log (\log (4))}+\frac {2500 \int \frac {1}{(5+x) \left (x+x^2+2 x (5+x)^{\frac {1}{\log (\log (4))}}+(5+x)^{\frac {2}{\log (\log (4))}}\right )^2} \, dx}{\log (\log (4))} \\ & = \text {Too large to display} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.19 (sec) , antiderivative size = 35, normalized size of antiderivative = 1.46 \[ \int \frac {\left (-10 x^4-2 x^5\right ) \log (\log (4))+(5+x)^{\frac {2}{\log (\log (4))}} \left (4 x^4+\left (-20 x^3-4 x^4\right ) \log (\log (4))\right )+(5+x)^{\frac {1}{\log (\log (4))}} \left (4 x^5+\left (-20 x^4-4 x^5\right ) \log (\log (4))\right )}{(5+x)^{1+\frac {6}{\log (\log (4))}} \log (\log (4))+(5+x)^{\frac {5}{\log (\log (4))}} \left (30 x+6 x^2\right ) \log (\log (4))+(5+x)^{\frac {4}{\log (\log (4))}} \left (15 x+78 x^2+15 x^3\right ) \log (\log (4))+(5+x)^{\frac {3}{\log (\log (4))}} \left (60 x^2+112 x^3+20 x^4\right ) \log (\log (4))+(5+x)^{\frac {2}{\log (\log (4))}} \left (15 x^2+93 x^3+93 x^4+15 x^5\right ) \log (\log (4))+(5+x)^{\frac {1}{\log (\log (4))}} \left (30 x^3+66 x^4+42 x^5+6 x^6\right ) \log (\log (4))+\left (5 x^3+16 x^4+18 x^5+8 x^6+x^7\right ) \log (\log (4))} \, dx=-\frac {x^4}{\left (x+x^2+2 x (5+x)^{\frac {1}{\log (\log (4))}}+(5+x)^{\frac {2}{\log (\log (4))}}\right )^2} \]

[In]

Integrate[((-10*x^4 - 2*x^5)*Log[Log[4]] + (5 + x)^(2/Log[Log[4]])*(4*x^4 + (-20*x^3 - 4*x^4)*Log[Log[4]]) + (
5 + x)^Log[Log[4]]^(-1)*(4*x^5 + (-20*x^4 - 4*x^5)*Log[Log[4]]))/((5 + x)^(1 + 6/Log[Log[4]])*Log[Log[4]] + (5
+ x)^(5/Log[Log[4]])*(30*x + 6*x^2)*Log[Log[4]] + (5 + x)^(4/Log[Log[4]])*(15*x + 78*x^2 + 15*x^3)*Log[Log[4]
] + (5 + x)^(3/Log[Log[4]])*(60*x^2 + 112*x^3 + 20*x^4)*Log[Log[4]] + (5 + x)^(2/Log[Log[4]])*(15*x^2 + 93*x^3
+ 93*x^4 + 15*x^5)*Log[Log[4]] + (5 + x)^Log[Log[4]]^(-1)*(30*x^3 + 66*x^4 + 42*x^5 + 6*x^6)*Log[Log[4]] + (5
*x^3 + 16*x^4 + 18*x^5 + 8*x^6 + x^7)*Log[Log[4]]),x]

[Out]

-(x^4/(x + x^2 + 2*x*(5 + x)^Log[Log[4]]^(-1) + (5 + x)^(2/Log[Log[4]]))^2)

Maple [A] (verified)

Time = 2.27 (sec) , antiderivative size = 42, normalized size of antiderivative = 1.75

method	result	size
risch	\(-\frac {x^{4}}{\left (x^{2}+2 \left (5+x \right )^{\frac {1}{\ln \left (2\right )+\ln \left (\ln \left (2\right )\right )}} x +\left (5+x \right )^{\frac {2}{\ln \left (2 \ln \left (2\right )\right )}}+x \right )^{2}}\)	\(42\)
parallelrisch	\(-\frac {x^{4}}{x^{4}+4 x^{3} {\mathrm e}^{\frac {\ln \left (5+x \right )}{\ln \left (2 \ln \left (2\right )\right )}}+6 \,{\mathrm e}^{\frac {2 \ln \left (5+x \right )}{\ln \left (2 \ln \left (2\right )\right )}} x^{2}+4 x \,{\mathrm e}^{\frac {3 \ln \left (5+x \right )}{\ln \left (2 \ln \left (2\right )\right )}}+{\mathrm e}^{\frac {4 \ln \left (5+x \right )}{\ln \left (2 \ln \left (2\right )\right )}}+2 x^{3}+4 x^{2} {\mathrm e}^{\frac {\ln \left (5+x \right )}{\ln \left (2 \ln \left (2\right )\right )}}+2 \,{\mathrm e}^{\frac {2 \ln \left (5+x \right )}{\ln \left (2 \ln \left (2\right )\right )}} x +x^{2}}\)	\(127\)

[In]

int((((-4*x^4-20*x^3)*ln(2*ln(2))+4*x^4)*exp(ln(5+x)/ln(2*ln(2)))^2+((-4*x^5-20*x^4)*ln(2*ln(2))+4*x^5)*exp(ln
(5+x)/ln(2*ln(2)))+(-2*x^5-10*x^4)*ln(2*ln(2)))/((5+x)*ln(2*ln(2))*exp(ln(5+x)/ln(2*ln(2)))^6+(6*x^2+30*x)*ln(
2*ln(2))*exp(ln(5+x)/ln(2*ln(2)))^5+(15*x^3+78*x^2+15*x)*ln(2*ln(2))*exp(ln(5+x)/ln(2*ln(2)))^4+(20*x^4+112*x^
3+60*x^2)*ln(2*ln(2))*exp(ln(5+x)/ln(2*ln(2)))^3+(15*x^5+93*x^4+93*x^3+15*x^2)*ln(2*ln(2))*exp(ln(5+x)/ln(2*ln
(2)))^2+(6*x^6+42*x^5+66*x^4+30*x^3)*ln(2*ln(2))*exp(ln(5+x)/ln(2*ln(2)))+(x^7+8*x^6+18*x^5+16*x^4+5*x^3)*ln(2
*ln(2))),x,method=_RETURNVERBOSE)

[Out]

-x^4/(x^2+2*(5+x)^(1/(ln(2)+ln(ln(2))))*x+((5+x)^(1/(ln(2)+ln(ln(2)))))^2+x)^2

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 90 vs. \(2 (26) = 52\).

Time = 0.27 (sec) , antiderivative size = 90, normalized size of antiderivative = 3.75 \[ \int \frac {\left (-10 x^4-2 x^5\right ) \log (\log (4))+(5+x)^{\frac {2}{\log (\log (4))}} \left (4 x^4+\left (-20 x^3-4 x^4\right ) \log (\log (4))\right )+(5+x)^{\frac {1}{\log (\log (4))}} \left (4 x^5+\left (-20 x^4-4 x^5\right ) \log (\log (4))\right )}{(5+x)^{1+\frac {6}{\log (\log (4))}} \log (\log (4))+(5+x)^{\frac {5}{\log (\log (4))}} \left (30 x+6 x^2\right ) \log (\log (4))+(5+x)^{\frac {4}{\log (\log (4))}} \left (15 x+78 x^2+15 x^3\right ) \log (\log (4))+(5+x)^{\frac {3}{\log (\log (4))}} \left (60 x^2+112 x^3+20 x^4\right ) \log (\log (4))+(5+x)^{\frac {2}{\log (\log (4))}} \left (15 x^2+93 x^3+93 x^4+15 x^5\right ) \log (\log (4))+(5+x)^{\frac {1}{\log (\log (4))}} \left (30 x^3+66 x^4+42 x^5+6 x^6\right ) \log (\log (4))+\left (5 x^3+16 x^4+18 x^5+8 x^6+x^7\right ) \log (\log (4))} \, dx=-\frac {x^{4}}{x^{4} + 2 \, x^{3} + 2 \, {\left (3 \, x^{2} + x\right )} {\left (x + 5\right )}^{\frac {2}{\log \left (2 \, \log \left (2\right )\right )}} + 4 \, {\left (x^{3} + x^{2}\right )} {\left (x + 5\right )}^{\left (\frac {1}{\log \left (2 \, \log \left (2\right )\right )}\right )} + 4 \, {\left (x + 5\right )}^{\frac {3}{\log \left (2 \, \log \left (2\right )\right )}} x + x^{2} + {\left (x + 5\right )}^{\frac {4}{\log \left (2 \, \log \left (2\right )\right )}}} \]

[In]

integrate((((-4*x^4-20*x^3)*log(2*log(2))+4*x^4)*exp(log(5+x)/log(2*log(2)))^2+((-4*x^5-20*x^4)*log(2*log(2))+
4*x^5)*exp(log(5+x)/log(2*log(2)))+(-2*x^5-10*x^4)*log(2*log(2)))/((5+x)*log(2*log(2))*exp(log(5+x)/log(2*log(
2)))^6+(6*x^2+30*x)*log(2*log(2))*exp(log(5+x)/log(2*log(2)))^5+(15*x^3+78*x^2+15*x)*log(2*log(2))*exp(log(5+x
)/log(2*log(2)))^4+(20*x^4+112*x^3+60*x^2)*log(2*log(2))*exp(log(5+x)/log(2*log(2)))^3+(15*x^5+93*x^4+93*x^3+1
5*x^2)*log(2*log(2))*exp(log(5+x)/log(2*log(2)))^2+(6*x^6+42*x^5+66*x^4+30*x^3)*log(2*log(2))*exp(log(5+x)/log
(2*log(2)))+(x^7+8*x^6+18*x^5+16*x^4+5*x^3)*log(2*log(2))),x, algorithm="fricas")

[Out]

-x^4/(x^4 + 2*x^3 + 2*(3*x^2 + x)*(x + 5)^(2/log(2*log(2))) + 4*(x^3 + x^2)*(x + 5)^(1/log(2*log(2))) + 4*(x +
5)^(3/log(2*log(2)))*x + x^2 + (x + 5)^(4/log(2*log(2))))

Sympy [F(-1)]

Timed out. \[ \int \frac {\left (-10 x^4-2 x^5\right ) \log (\log (4))+(5+x)^{\frac {2}{\log (\log (4))}} \left (4 x^4+\left (-20 x^3-4 x^4\right ) \log (\log (4))\right )+(5+x)^{\frac {1}{\log (\log (4))}} \left (4 x^5+\left (-20 x^4-4 x^5\right ) \log (\log (4))\right )}{(5+x)^{1+\frac {6}{\log (\log (4))}} \log (\log (4))+(5+x)^{\frac {5}{\log (\log (4))}} \left (30 x+6 x^2\right ) \log (\log (4))+(5+x)^{\frac {4}{\log (\log (4))}} \left (15 x+78 x^2+15 x^3\right ) \log (\log (4))+(5+x)^{\frac {3}{\log (\log (4))}} \left (60 x^2+112 x^3+20 x^4\right ) \log (\log (4))+(5+x)^{\frac {2}{\log (\log (4))}} \left (15 x^2+93 x^3+93 x^4+15 x^5\right ) \log (\log (4))+(5+x)^{\frac {1}{\log (\log (4))}} \left (30 x^3+66 x^4+42 x^5+6 x^6\right ) \log (\log (4))+\left (5 x^3+16 x^4+18 x^5+8 x^6+x^7\right ) \log (\log (4))} \, dx=\text {Timed out} \]

[In]

integrate((((-4*x**4-20*x**3)*ln(2*ln(2))+4*x**4)*exp(ln(5+x)/ln(2*ln(2)))**2+((-4*x**5-20*x**4)*ln(2*ln(2))+4
*x**5)*exp(ln(5+x)/ln(2*ln(2)))+(-2*x**5-10*x**4)*ln(2*ln(2)))/((5+x)*ln(2*ln(2))*exp(ln(5+x)/ln(2*ln(2)))**6+
(6*x**2+30*x)*ln(2*ln(2))*exp(ln(5+x)/ln(2*ln(2)))**5+(15*x**3+78*x**2+15*x)*ln(2*ln(2))*exp(ln(5+x)/ln(2*ln(2
)))**4+(20*x**4+112*x**3+60*x**2)*ln(2*ln(2))*exp(ln(5+x)/ln(2*ln(2)))**3+(15*x**5+93*x**4+93*x**3+15*x**2)*ln
(2*ln(2))*exp(ln(5+x)/ln(2*ln(2)))**2+(6*x**6+42*x**5+66*x**4+30*x**3)*ln(2*ln(2))*exp(ln(5+x)/ln(2*ln(2)))+(x
**7+8*x**6+18*x**5+16*x**4+5*x**3)*ln(2*ln(2))),x)

[Out]

Timed out

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 94 vs. \(2 (26) = 52\).

Time = 2.44 (sec) , antiderivative size = 94, normalized size of antiderivative = 3.92 \[ \int \frac {\left (-10 x^4-2 x^5\right ) \log (\log (4))+(5+x)^{\frac {2}{\log (\log (4))}} \left (4 x^4+\left (-20 x^3-4 x^4\right ) \log (\log (4))\right )+(5+x)^{\frac {1}{\log (\log (4))}} \left (4 x^5+\left (-20 x^4-4 x^5\right ) \log (\log (4))\right )}{(5+x)^{1+\frac {6}{\log (\log (4))}} \log (\log (4))+(5+x)^{\frac {5}{\log (\log (4))}} \left (30 x+6 x^2\right ) \log (\log (4))+(5+x)^{\frac {4}{\log (\log (4))}} \left (15 x+78 x^2+15 x^3\right ) \log (\log (4))+(5+x)^{\frac {3}{\log (\log (4))}} \left (60 x^2+112 x^3+20 x^4\right ) \log (\log (4))+(5+x)^{\frac {2}{\log (\log (4))}} \left (15 x^2+93 x^3+93 x^4+15 x^5\right ) \log (\log (4))+(5+x)^{\frac {1}{\log (\log (4))}} \left (30 x^3+66 x^4+42 x^5+6 x^6\right ) \log (\log (4))+\left (5 x^3+16 x^4+18 x^5+8 x^6+x^7\right ) \log (\log (4))} \, dx=-\frac {x^{4}}{x^{4} + 2 \, x^{3} + 2 \, {\left (3 \, x^{2} + x\right )} {\left (x + 5\right )}^{\frac {2}{\log \left (2\right ) + \log \left (\log \left (2\right )\right )}} + 4 \, {\left (x^{3} + x^{2}\right )} {\left (x + 5\right )}^{\left (\frac {1}{\log \left (2\right ) + \log \left (\log \left (2\right )\right )}\right )} + 4 \, {\left (x + 5\right )}^{\frac {3}{\log \left (2\right ) + \log \left (\log \left (2\right )\right )}} x + x^{2} + {\left (x + 5\right )}^{\frac {4}{\log \left (2\right ) + \log \left (\log \left (2\right )\right )}}} \]

[In]

integrate((((-4*x^4-20*x^3)*log(2*log(2))+4*x^4)*exp(log(5+x)/log(2*log(2)))^2+((-4*x^5-20*x^4)*log(2*log(2))+
4*x^5)*exp(log(5+x)/log(2*log(2)))+(-2*x^5-10*x^4)*log(2*log(2)))/((5+x)*log(2*log(2))*exp(log(5+x)/log(2*log(
2)))^6+(6*x^2+30*x)*log(2*log(2))*exp(log(5+x)/log(2*log(2)))^5+(15*x^3+78*x^2+15*x)*log(2*log(2))*exp(log(5+x
)/log(2*log(2)))^4+(20*x^4+112*x^3+60*x^2)*log(2*log(2))*exp(log(5+x)/log(2*log(2)))^3+(15*x^5+93*x^4+93*x^3+1
5*x^2)*log(2*log(2))*exp(log(5+x)/log(2*log(2)))^2+(6*x^6+42*x^5+66*x^4+30*x^3)*log(2*log(2))*exp(log(5+x)/log
(2*log(2)))+(x^7+8*x^6+18*x^5+16*x^4+5*x^3)*log(2*log(2))),x, algorithm="maxima")

[Out]

-x^4/(x^4 + 2*x^3 + 2*(3*x^2 + x)*(x + 5)^(2/(log(2) + log(log(2)))) + 4*(x^3 + x^2)*(x + 5)^(1/(log(2) + log(
log(2)))) + 4*(x + 5)^(3/(log(2) + log(log(2))))*x + x^2 + (x + 5)^(4/(log(2) + log(log(2)))))

Giac [F]

\[ \int \frac {\left (-10 x^4-2 x^5\right ) \log (\log (4))+(5+x)^{\frac {2}{\log (\log (4))}} \left (4 x^4+\left (-20 x^3-4 x^4\right ) \log (\log (4))\right )+(5+x)^{\frac {1}{\log (\log (4))}} \left (4 x^5+\left (-20 x^4-4 x^5\right ) \log (\log (4))\right )}{(5+x)^{1+\frac {6}{\log (\log (4))}} \log (\log (4))+(5+x)^{\frac {5}{\log (\log (4))}} \left (30 x+6 x^2\right ) \log (\log (4))+(5+x)^{\frac {4}{\log (\log (4))}} \left (15 x+78 x^2+15 x^3\right ) \log (\log (4))+(5+x)^{\frac {3}{\log (\log (4))}} \left (60 x^2+112 x^3+20 x^4\right ) \log (\log (4))+(5+x)^{\frac {2}{\log (\log (4))}} \left (15 x^2+93 x^3+93 x^4+15 x^5\right ) \log (\log (4))+(5+x)^{\frac {1}{\log (\log (4))}} \left (30 x^3+66 x^4+42 x^5+6 x^6\right ) \log (\log (4))+\left (5 x^3+16 x^4+18 x^5+8 x^6+x^7\right ) \log (\log (4))} \, dx=\int { \frac {2 \, {\left (2 \, {\left (x^{4} - {\left (x^{4} + 5 \, x^{3}\right )} \log \left (2 \, \log \left (2\right )\right )\right )} {\left (x + 5\right )}^{\frac {2}{\log \left (2 \, \log \left (2\right )\right )}} + 2 \, {\left (x^{5} - {\left (x^{5} + 5 \, x^{4}\right )} \log \left (2 \, \log \left (2\right )\right )\right )} {\left (x + 5\right )}^{\left (\frac {1}{\log \left (2 \, \log \left (2\right )\right )}\right )} - {\left (x^{5} + 5 \, x^{4}\right )} \log \left (2 \, \log \left (2\right )\right )\right )}}{6 \, {\left (x^{2} + 5 \, x\right )} {\left (x + 5\right )}^{\frac {5}{\log \left (2 \, \log \left (2\right )\right )}} \log \left (2 \, \log \left (2\right )\right ) + 3 \, {\left (5 \, x^{3} + 26 \, x^{2} + 5 \, x\right )} {\left (x + 5\right )}^{\frac {4}{\log \left (2 \, \log \left (2\right )\right )}} \log \left (2 \, \log \left (2\right )\right ) + 4 \, {\left (5 \, x^{4} + 28 \, x^{3} + 15 \, x^{2}\right )} {\left (x + 5\right )}^{\frac {3}{\log \left (2 \, \log \left (2\right )\right )}} \log \left (2 \, \log \left (2\right )\right ) + 3 \, {\left (5 \, x^{5} + 31 \, x^{4} + 31 \, x^{3} + 5 \, x^{2}\right )} {\left (x + 5\right )}^{\frac {2}{\log \left (2 \, \log \left (2\right )\right )}} \log \left (2 \, \log \left (2\right )\right ) + 6 \, {\left (x^{6} + 7 \, x^{5} + 11 \, x^{4} + 5 \, x^{3}\right )} {\left (x + 5\right )}^{\left (\frac {1}{\log \left (2 \, \log \left (2\right )\right )}\right )} \log \left (2 \, \log \left (2\right )\right ) + {\left (x + 5\right )}^{\frac {6}{\log \left (2 \, \log \left (2\right )\right )}} {\left (x + 5\right )} \log \left (2 \, \log \left (2\right )\right ) + {\left (x^{7} + 8 \, x^{6} + 18 \, x^{5} + 16 \, x^{4} + 5 \, x^{3}\right )} \log \left (2 \, \log \left (2\right )\right )} \,d x } \]

[In]

integrate((((-4*x^4-20*x^3)*log(2*log(2))+4*x^4)*exp(log(5+x)/log(2*log(2)))^2+((-4*x^5-20*x^4)*log(2*log(2))+
4*x^5)*exp(log(5+x)/log(2*log(2)))+(-2*x^5-10*x^4)*log(2*log(2)))/((5+x)*log(2*log(2))*exp(log(5+x)/log(2*log(
2)))^6+(6*x^2+30*x)*log(2*log(2))*exp(log(5+x)/log(2*log(2)))^5+(15*x^3+78*x^2+15*x)*log(2*log(2))*exp(log(5+x
)/log(2*log(2)))^4+(20*x^4+112*x^3+60*x^2)*log(2*log(2))*exp(log(5+x)/log(2*log(2)))^3+(15*x^5+93*x^4+93*x^3+1
5*x^2)*log(2*log(2))*exp(log(5+x)/log(2*log(2)))^2+(6*x^6+42*x^5+66*x^4+30*x^3)*log(2*log(2))*exp(log(5+x)/log
(2*log(2)))+(x^7+8*x^6+18*x^5+16*x^4+5*x^3)*log(2*log(2))),x, algorithm="giac")

[Out]

integrate(2*(2*(x^4 - (x^4 + 5*x^3)*log(2*log(2)))*(x + 5)^(2/log(2*log(2))) + 2*(x^5 - (x^5 + 5*x^4)*log(2*lo
g(2)))*(x + 5)^(1/log(2*log(2))) - (x^5 + 5*x^4)*log(2*log(2)))/(6*(x^2 + 5*x)*(x + 5)^(5/log(2*log(2)))*log(2
*log(2)) + 3*(5*x^3 + 26*x^2 + 5*x)*(x + 5)^(4/log(2*log(2)))*log(2*log(2)) + 4*(5*x^4 + 28*x^3 + 15*x^2)*(x +
5)^(3/log(2*log(2)))*log(2*log(2)) + 3*(5*x^5 + 31*x^4 + 31*x^3 + 5*x^2)*(x + 5)^(2/log(2*log(2)))*log(2*log(
2)) + 6*(x^6 + 7*x^5 + 11*x^4 + 5*x^3)*(x + 5)^(1/log(2*log(2)))*log(2*log(2)) + (x + 5)^(6/log(2*log(2)))*(x
+ 5)*log(2*log(2)) + (x^7 + 8*x^6 + 18*x^5 + 16*x^4 + 5*x^3)*log(2*log(2))), x)

Mupad [F(-1)]

Timed out. \[ \int \frac {\left (-10 x^4-2 x^5\right ) \log (\log (4))+(5+x)^{\frac {2}{\log (\log (4))}} \left (4 x^4+\left (-20 x^3-4 x^4\right ) \log (\log (4))\right )+(5+x)^{\frac {1}{\log (\log (4))}} \left (4 x^5+\left (-20 x^4-4 x^5\right ) \log (\log (4))\right )}{(5+x)^{1+\frac {6}{\log (\log (4))}} \log (\log (4))+(5+x)^{\frac {5}{\log (\log (4))}} \left (30 x+6 x^2\right ) \log (\log (4))+(5+x)^{\frac {4}{\log (\log (4))}} \left (15 x+78 x^2+15 x^3\right ) \log (\log (4))+(5+x)^{\frac {3}{\log (\log (4))}} \left (60 x^2+112 x^3+20 x^4\right ) \log (\log (4))+(5+x)^{\frac {2}{\log (\log (4))}} \left (15 x^2+93 x^3+93 x^4+15 x^5\right ) \log (\log (4))+(5+x)^{\frac {1}{\log (\log (4))}} \left (30 x^3+66 x^4+42 x^5+6 x^6\right ) \log (\log (4))+\left (5 x^3+16 x^4+18 x^5+8 x^6+x^7\right ) \log (\log (4))} \, dx=\int -\frac {{\left (x+5\right )}^{\frac {1}{\ln \left (2\,\ln \left (2\right )\right )}}\,\left (\ln \left (2\,\ln \left (2\right )\right )\,\left (4\,x^5+20\,x^4\right )-4\,x^5\right )+\ln \left (2\,\ln \left (2\right )\right )\,\left (2\,x^5+10\,x^4\right )+{\left (x+5\right )}^{\frac {2}{\ln \left (2\,\ln \left (2\right )\right )}}\,\left (\ln \left (2\,\ln \left (2\right )\right )\,\left (4\,x^4+20\,x^3\right )-4\,x^4\right )}{\ln \left (2\,\ln \left (2\right )\right )\,\left (x^7+8\,x^6+18\,x^5+16\,x^4+5\,x^3\right )+\ln \left (2\,\ln \left (2\right )\right )\,{\left (x+5\right )}^{\frac {2}{\ln \left (2\,\ln \left (2\right )\right )}}\,\left (15\,x^5+93\,x^4+93\,x^3+15\,x^2\right )+\ln \left (2\,\ln \left (2\right )\right )\,\left (6\,x^2+30\,x\right )\,{\left (x+5\right )}^{\frac {5}{\ln \left (2\,\ln \left (2\right )\right )}}+\ln \left (2\,\ln \left (2\right )\right )\,{\left (x+5\right )}^{\frac {4}{\ln \left (2\,\ln \left (2\right )\right )}}\,\left (15\,x^3+78\,x^2+15\,x\right )+\ln \left (2\,\ln \left (2\right )\right )\,{\left (x+5\right )}^{\frac {6}{\ln \left (2\,\ln \left (2\right )\right )}}\,\left (x+5\right )+\ln \left (2\,\ln \left (2\right )\right )\,{\left (x+5\right )}^{\frac {1}{\ln \left (2\,\ln \left (2\right )\right )}}\,\left (6\,x^6+42\,x^5+66\,x^4+30\,x^3\right )+\ln \left (2\,\ln \left (2\right )\right )\,{\left (x+5\right )}^{\frac {3}{\ln \left (2\,\ln \left (2\right )\right )}}\,\left (20\,x^4+112\,x^3+60\,x^2\right )} \,d x \]

[In]

int(-((x + 5)^(1/log(2*log(2)))*(log(2*log(2))*(20*x^4 + 4*x^5) - 4*x^5) + log(2*log(2))*(10*x^4 + 2*x^5) + (x
+ 5)^(2/log(2*log(2)))*(log(2*log(2))*(20*x^3 + 4*x^4) - 4*x^4))/(log(2*log(2))*(5*x^3 + 16*x^4 + 18*x^5 + 8*
x^6 + x^7) + log(2*log(2))*(x + 5)^(2/log(2*log(2)))*(15*x^2 + 93*x^3 + 93*x^4 + 15*x^5) + log(2*log(2))*(30*x
+ 6*x^2)*(x + 5)^(5/log(2*log(2))) + log(2*log(2))*(x + 5)^(4/log(2*log(2)))*(15*x + 78*x^2 + 15*x^3) + log(2
*log(2))*(x + 5)^(6/log(2*log(2)))*(x + 5) + log(2*log(2))*(x + 5)^(1/log(2*log(2)))*(30*x^3 + 66*x^4 + 42*x^5
+ 6*x^6) + log(2*log(2))*(x + 5)^(3/log(2*log(2)))*(60*x^2 + 112*x^3 + 20*x^4)),x)

[Out]

int(-((x + 5)^(1/log(2*log(2)))*(log(2*log(2))*(20*x^4 + 4*x^5) - 4*x^5) + log(2*log(2))*(10*x^4 + 2*x^5) + (x
+ 5)^(2/log(2*log(2)))*(log(2*log(2))*(20*x^3 + 4*x^4) - 4*x^4))/(log(2*log(2))*(5*x^3 + 16*x^4 + 18*x^5 + 8*
x^6 + x^7) + log(2*log(2))*(x + 5)^(2/log(2*log(2)))*(15*x^2 + 93*x^3 + 93*x^4 + 15*x^5) + log(2*log(2))*(30*x
+ 6*x^2)*(x + 5)^(5/log(2*log(2))) + log(2*log(2))*(x + 5)^(4/log(2*log(2)))*(15*x + 78*x^2 + 15*x^3) + log(2
*log(2))*(x + 5)^(6/log(2*log(2)))*(x + 5) + log(2*log(2))*(x + 5)^(1/log(2*log(2)))*(30*x^3 + 66*x^4 + 42*x^5
+ 6*x^6) + log(2*log(2))*(x + 5)^(3/log(2*log(2)))*(60*x^2 + 112*x^3 + 20*x^4)), x)