\(\int \frac {-56 x^2+62 x^4+28 x^5+10 x^6+4 x^7+e^5 (-14-28 x-2 x^2-4 x^3)+(-112 x^2-168 x^3-72 x^4-24 x^5-8 x^6) \log (5)+(56+112 x+106 x^2+44 x^3+14 x^4+4 x^5) \log ^2(5)+(56 x^2+48 x^3+22 x^4+18 x^5+6 x^6+e^5 (-14-2 x-6 x^2)+(-112 x-112 x^2-60 x^3-40 x^4-12 x^5) \log (5)+(56+64 x+38 x^2+22 x^3+6 x^4) \log ^2(5)) \log (-\frac {5 x}{-e^5+4 x^2+4 x^3+x^4+(-8 x-8 x^2-2 x^3) \log (5)+(4+4 x+x^2) \log ^2(5)})+(-2 e^5 x+8 x^3+8 x^4+2 x^5+(-16 x^2-16 x^3-4 x^4) \log (5)+(8 x+8 x^2+2 x^3) \log ^2(5)) \log ^2(-\frac {5 x}{-e^5+4 x^2+4 x^3+x^4+(-8 x-8 x^2-2 x^3) \log (5)+(4+4 x+x^2) \log ^2(5)})}{-e^5+4 x^2+4 x^3+x^4+(-8 x-8 x^2-2 x^3) \log (5)+(4+4 x+x^2) \log ^2(5)} \, dx\) [1370]

Optimal result

Integrand size = 422, antiderivative size = 33 \[ \int \frac {-56 x^2+62 x^4+28 x^5+10 x^6+4 x^7+e^5 \left (-14-28 x-2 x^2-4 x^3\right )+\left (-112 x^2-168 x^3-72 x^4-24 x^5-8 x^6\right ) \log (5)+\left (56+112 x+106 x^2+44 x^3+14 x^4+4 x^5\right ) \log ^2(5)+\left (56 x^2+48 x^3+22 x^4+18 x^5+6 x^6+e^5 \left (-14-2 x-6 x^2\right )+\left (-112 x-112 x^2-60 x^3-40 x^4-12 x^5\right ) \log (5)+\left (56+64 x+38 x^2+22 x^3+6 x^4\right ) \log ^2(5)\right ) \log \left (-\frac {5 x}{-e^5+4 x^2+4 x^3+x^4+\left (-8 x-8 x^2-2 x^3\right ) \log (5)+\left (4+4 x+x^2\right ) \log ^2(5)}\right )+\left (-2 e^5 x+8 x^3+8 x^4+2 x^5+\left (-16 x^2-16 x^3-4 x^4\right ) \log (5)+\left (8 x+8 x^2+2 x^3\right ) \log ^2(5)\right ) \log ^2\left (-\frac {5 x}{-e^5+4 x^2+4 x^3+x^4+\left (-8 x-8 x^2-2 x^3\right ) \log (5)+\left (4+4 x+x^2\right ) \log ^2(5)}\right )}{-e^5+4 x^2+4 x^3+x^4+\left (-8 x-8 x^2-2 x^3\right ) \log (5)+\left (4+4 x+x^2\right ) \log ^2(5)} \, dx=\left (7+x \left (x+\log \left (\frac {5 x}{e^5-(2+x)^2 (x-\log (5))^2}\right )\right )\right )^2 \] Output:

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

Mathematica [B] (verified)

Leaf count is larger than twice the leaf count of optimal. \(72\) vs. \(2(33)=66\).

Time = 0.18 (sec) , antiderivative size = 72, normalized size of antiderivative = 2.18 \[ \int \frac {-56 x^2+62 x^4+28 x^5+10 x^6+4 x^7+e^5 \left (-14-28 x-2 x^2-4 x^3\right )+\left (-112 x^2-168 x^3-72 x^4-24 x^5-8 x^6\right ) \log (5)+\left (56+112 x+106 x^2+44 x^3+14 x^4+4 x^5\right ) \log ^2(5)+\left (56 x^2+48 x^3+22 x^4+18 x^5+6 x^6+e^5 \left (-14-2 x-6 x^2\right )+\left (-112 x-112 x^2-60 x^3-40 x^4-12 x^5\right ) \log (5)+\left (56+64 x+38 x^2+22 x^3+6 x^4\right ) \log ^2(5)\right ) \log \left (-\frac {5 x}{-e^5+4 x^2+4 x^3+x^4+\left (-8 x-8 x^2-2 x^3\right ) \log (5)+\left (4+4 x+x^2\right ) \log ^2(5)}\right )+\left (-2 e^5 x+8 x^3+8 x^4+2 x^5+\left (-16 x^2-16 x^3-4 x^4\right ) \log (5)+\left (8 x+8 x^2+2 x^3\right ) \log ^2(5)\right ) \log ^2\left (-\frac {5 x}{-e^5+4 x^2+4 x^3+x^4+\left (-8 x-8 x^2-2 x^3\right ) \log (5)+\left (4+4 x+x^2\right ) \log ^2(5)}\right )}{-e^5+4 x^2+4 x^3+x^4+\left (-8 x-8 x^2-2 x^3\right ) \log (5)+\left (4+4 x+x^2\right ) \log ^2(5)} \, dx=x \left (14 x+x^3+2 \left (7+x^2\right ) \log \left (-\frac {5 x}{-e^5+(2+x)^2 (x-\log (5))^2}\right )+x \log ^2\left (-\frac {5 x}{-e^5+(2+x)^2 (x-\log (5))^2}\right )\right ) \] Input:

Integrate[(-56*x^2 + 62*x^4 + 28*x^5 + 10*x^6 + 4*x^7 + E^5*(-14 - 28*x - 
2*x^2 - 4*x^3) + (-112*x^2 - 168*x^3 - 72*x^4 - 24*x^5 - 8*x^6)*Log[5] + ( 
56 + 112*x + 106*x^2 + 44*x^3 + 14*x^4 + 4*x^5)*Log[5]^2 + (56*x^2 + 48*x^ 
3 + 22*x^4 + 18*x^5 + 6*x^6 + E^5*(-14 - 2*x - 6*x^2) + (-112*x - 112*x^2 
- 60*x^3 - 40*x^4 - 12*x^5)*Log[5] + (56 + 64*x + 38*x^2 + 22*x^3 + 6*x^4) 
*Log[5]^2)*Log[(-5*x)/(-E^5 + 4*x^2 + 4*x^3 + x^4 + (-8*x - 8*x^2 - 2*x^3) 
*Log[5] + (4 + 4*x + x^2)*Log[5]^2)] + (-2*E^5*x + 8*x^3 + 8*x^4 + 2*x^5 + 
 (-16*x^2 - 16*x^3 - 4*x^4)*Log[5] + (8*x + 8*x^2 + 2*x^3)*Log[5]^2)*Log[( 
-5*x)/(-E^5 + 4*x^2 + 4*x^3 + x^4 + (-8*x - 8*x^2 - 2*x^3)*Log[5] + (4 + 4 
*x + x^2)*Log[5]^2)]^2)/(-E^5 + 4*x^2 + 4*x^3 + x^4 + (-8*x - 8*x^2 - 2*x^ 
3)*Log[5] + (4 + 4*x + x^2)*Log[5]^2),x]
 

Output:

x*(14*x + x^3 + 2*(7 + x^2)*Log[(-5*x)/(-E^5 + (2 + x)^2*(x - Log[5])^2)] 
+ x*Log[(-5*x)/(-E^5 + (2 + x)^2*(x - Log[5])^2)]^2)
 

Rubi [F]

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.

\(\displaystyle \int \frac {4 x^7+10 x^6+28 x^5+62 x^4-56 x^2+e^5 \left (-4 x^3-2 x^2-28 x-14\right )+\left (2 x^5+8 x^4+8 x^3+\left (2 x^3+8 x^2+8 x\right ) \log ^2(5)+\left (-4 x^4-16 x^3-16 x^2\right ) \log (5)-2 e^5 x\right ) \log ^2\left (-\frac {5 x}{x^4+4 x^3+4 x^2+\left (x^2+4 x+4\right ) \log ^2(5)+\left (-2 x^3-8 x^2-8 x\right ) \log (5)-e^5}\right )+\left (4 x^5+14 x^4+44 x^3+106 x^2+112 x+56\right ) \log ^2(5)+\left (6 x^6+18 x^5+22 x^4+48 x^3+56 x^2+e^5 \left (-6 x^2-2 x-14\right )+\left (6 x^4+22 x^3+38 x^2+64 x+56\right ) \log ^2(5)+\left (-12 x^5-40 x^4-60 x^3-112 x^2-112 x\right ) \log (5)\right ) \log \left (-\frac {5 x}{x^4+4 x^3+4 x^2+\left (x^2+4 x+4\right ) \log ^2(5)+\left (-2 x^3-8 x^2-8 x\right ) \log (5)-e^5}\right )+\left (-8 x^6-24 x^5-72 x^4-168 x^3-112 x^2\right ) \log (5)}{x^4+4 x^3+4 x^2+\left (x^2+4 x+4\right ) \log ^2(5)+\left (-2 x^3-8 x^2-8 x\right ) \log (5)-e^5} \, dx\)

\(\Big \downarrow \) 7292

\(\displaystyle \int \frac {-4 x^7-10 x^6-28 x^5-62 x^4+56 x^2-e^5 \left (-4 x^3-2 x^2-28 x-14\right )-\left (2 x^5+8 x^4+8 x^3+\left (2 x^3+8 x^2+8 x\right ) \log ^2(5)+\left (-4 x^4-16 x^3-16 x^2\right ) \log (5)-2 e^5 x\right ) \log ^2\left (-\frac {5 x}{x^4+4 x^3+4 x^2+\left (x^2+4 x+4\right ) \log ^2(5)+\left (-2 x^3-8 x^2-8 x\right ) \log (5)-e^5}\right )-\left (4 x^5+14 x^4+44 x^3+106 x^2+112 x+56\right ) \log ^2(5)-\left (6 x^6+18 x^5+22 x^4+48 x^3+56 x^2+e^5 \left (-6 x^2-2 x-14\right )+\left (6 x^4+22 x^3+38 x^2+64 x+56\right ) \log ^2(5)+\left (-12 x^5-40 x^4-60 x^3-112 x^2-112 x\right ) \log (5)\right ) \log \left (-\frac {5 x}{x^4+4 x^3+4 x^2+\left (x^2+4 x+4\right ) \log ^2(5)+\left (-2 x^3-8 x^2-8 x\right ) \log (5)-e^5}\right )-\left (-8 x^6-24 x^5-72 x^4-168 x^3-112 x^2\right ) \log (5)}{-x^4-2 x^3 (2-\log (5))-x^2 \left (4+\log ^2(5)-8 \log (5)\right )+4 x (2-\log (5)) \log (5)+e^5-4 \log ^2(5)}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (\frac {4 x^7}{x^4+2 (2-\log (5)) x^3+\left (4-8 \log (5)+\log ^2(5)\right ) x^2-4 (2-\log (5)) \log (5) x+4 \log ^2(5)-e^5}+\frac {10 x^6}{x^4+2 (2-\log (5)) x^3+\left (4-8 \log (5)+\log ^2(5)\right ) x^2-4 (2-\log (5)) \log (5) x+4 \log ^2(5)-e^5}+\frac {28 x^5}{x^4+2 (2-\log (5)) x^3+\left (4-8 \log (5)+\log ^2(5)\right ) x^2-4 (2-\log (5)) \log (5) x+4 \log ^2(5)-e^5}+\frac {62 x^4}{x^4+2 (2-\log (5)) x^3+\left (4-8 \log (5)+\log ^2(5)\right ) x^2-4 (2-\log (5)) \log (5) x+4 \log ^2(5)-e^5}+\frac {8 (x+1) (x+2) \left (x^2+7\right ) \log (5) x^2}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}+\frac {56 x^2}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}+2 \log ^2\left (-\frac {5 x}{x^4+2 (2-\log (5)) x^3+\left (4-8 \log (5)+\log ^2(5)\right ) x^2-4 (2-\log (5)) \log (5) x+4 \log ^2(5)-e^5}\right ) x+\frac {2 \left (-3 x^6-9 \left (1-\frac {2 \log (5)}{3}\right ) x^5-11 \left (1+\frac {1}{11} \log (5) (-20+\log (125))\right ) x^4-24 \left (1+\frac {1}{24} \log (5) (-30+11 \log (5))\right ) x^3-28 \left (1+\frac {1}{28} \left (-3 e^5+\log (5) (-56+19 \log (5))\right )\right ) x^2+e^5 \left (1-\frac {8 \log (5) (-7+\log (625))}{e^5}\right ) x+7 e^5 \left (1-\frac {4 \log ^2(5)}{e^5}\right )\right ) \log \left (-\frac {5 x}{x^4+2 (2-\log (5)) x^3+\left (4-8 \log (5)+\log ^2(5)\right ) x^2-4 (2-\log (5)) \log (5) x+4 \log ^2(5)-e^5}\right )}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}+\frac {2 e^5 (2 x+1) \left (x^2+7\right )}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}+\frac {2 (x+2) \left (-2 x^2-3 x-2\right ) \left (x^2+7\right ) \log ^2(5)}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {2 \left (-2 x^7-5 x^6-14 x^5-31 x^4+28 x^2+e^5 (2 x+1) \left (x^2+7\right )-(x+2) \left (x^2+7\right ) \left (2 x^2+3 x+2\right ) \log ^2(5)+4 (x+1) (x+2) \left (x^2+7\right ) x^2 \log (5)-\left (3 x^6-3 x^5 (\log (25)-3)+x^4 (11+\log (5) (\log (125)-20))+x^3 \left (24+11 \log ^2(5)-30 \log (5)\right )-e^5 \left (3 x^2+x+7\right )+x^2 \left (28+19 \log ^2(5)-56 \log (5)\right )+8 x \log (5) (\log (625)-7)+28 \log ^2(5)\right ) \log \left (-\frac {5 x}{(x+2)^2 (x-\log (5))^2-e^5}\right )+x \left (e^5-(x+2)^2 (x-\log (5))^2\right ) \log ^2\left (-\frac {5 x}{(x+2)^2 (x-\log (5))^2-e^5}\right )\right )}{-x^4-2 x^3 (2-\log (5))-x^2 \left (4+\log ^2(5)-8 \log (5)\right )+4 x (2-\log (5)) \log (5)+e^5-4 \log ^2(5)}dx\)

\(\Big \downarrow \) 27

\(\displaystyle 2 \int \frac {-2 x^7-5 x^6-14 x^5-31 x^4+4 (x+1) (x+2) \left (x^2+7\right ) \log (5) x^2+28 x^2+\left (e^5-(x+2)^2 (x-\log (5))^2\right ) \log ^2\left (\frac {5 x}{e^5-(x+2)^2 (x-\log (5))^2}\right ) x+e^5 (2 x+1) \left (x^2+7\right )-\left (3 x^6+3 (3-\log (25)) x^5+(11-\log (5) (20-\log (125))) x^4+\left (24-30 \log (5)+11 \log ^2(5)\right ) x^3+\left (28-56 \log (5)+19 \log ^2(5)\right ) x^2-8 \log (5) (7-\log (625)) x-e^5 \left (3 x^2+x+7\right )+28 \log ^2(5)\right ) \log \left (\frac {5 x}{e^5-(x+2)^2 (x-\log (5))^2}\right )-(x+2) \left (x^2+7\right ) \left (2 x^2+3 x+2\right ) \log ^2(5)}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle 2 \int \left (\frac {2 x^7}{x^4+2 (2-\log (5)) x^3+\left (4-8 \log (5)+\log ^2(5)\right ) x^2-4 (2-\log (5)) \log (5) x+4 \log ^2(5)-e^5}+\frac {5 x^6}{x^4+2 (2-\log (5)) x^3+\left (4-8 \log (5)+\log ^2(5)\right ) x^2-4 (2-\log (5)) \log (5) x+4 \log ^2(5)-e^5}+\frac {14 x^5}{x^4+2 (2-\log (5)) x^3+\left (4-8 \log (5)+\log ^2(5)\right ) x^2-4 (2-\log (5)) \log (5) x+4 \log ^2(5)-e^5}+\frac {31 x^4}{x^4+2 (2-\log (5)) x^3+\left (4-8 \log (5)+\log ^2(5)\right ) x^2-4 (2-\log (5)) \log (5) x+4 \log ^2(5)-e^5}+\frac {4 (x+1) (x+2) \left (x^2+7\right ) \log (5) x^2}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}+\frac {28 x^2}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}+\log ^2\left (\frac {5 x}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}\right ) x+\frac {\left (-3 x^6-9 \left (1-\frac {2 \log (5)}{3}\right ) x^5-11 \left (1+\frac {1}{11} \log (5) (-20+\log (125))\right ) x^4-24 \left (1+\frac {1}{24} \log (5) (-30+11 \log (5))\right ) x^3-28 \left (1+\frac {1}{28} \left (-3 e^5+\log (5) (-56+19 \log (5))\right )\right ) x^2+e^5 \left (1-\frac {8 \log (5) (-7+\log (625))}{e^5}\right ) x+7 e^5 \left (1-\frac {4 \log ^2(5)}{e^5}\right )\right ) \log \left (\frac {5 x}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}\right )}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}+\frac {e^5 (2 x+1) \left (x^2+7\right )}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}+\frac {(x+2) \left (-2 x^2-3 x-2\right ) \left (x^2+7\right ) \log ^2(5)}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle 2 \int \frac {-2 x^7-5 x^6-14 x^5-31 x^4+4 (x+1) (x+2) \left (x^2+7\right ) \log (5) x^2+28 x^2+\left (e^5-(x+2)^2 (x-\log (5))^2\right ) \log ^2\left (-\frac {5 x}{(x+2)^2 (x-\log (5))^2-e^5}\right ) x+e^5 (2 x+1) \left (x^2+7\right )-\left (3 x^6-3 (-3+\log (25)) x^5+(11+\log (5) (-20+\log (125))) x^4+\left (24-30 \log (5)+11 \log ^2(5)\right ) x^3+\left (28-56 \log (5)+19 \log ^2(5)\right ) x^2+8 \log (5) (-7+\log (625)) x-e^5 \left (3 x^2+x+7\right )+28 \log ^2(5)\right ) \log \left (-\frac {5 x}{(x+2)^2 (x-\log (5))^2-e^5}\right )-(x+2) \left (x^2+7\right ) \left (2 x^2+3 x+2\right ) \log ^2(5)}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle 2 \int \left (\frac {2 x^7}{x^4+2 (2-\log (5)) x^3+\left (4-8 \log (5)+\log ^2(5)\right ) x^2-4 (2-\log (5)) \log (5) x+4 \log ^2(5)-e^5}+\frac {5 x^6}{x^4+2 (2-\log (5)) x^3+\left (4-8 \log (5)+\log ^2(5)\right ) x^2-4 (2-\log (5)) \log (5) x+4 \log ^2(5)-e^5}+\frac {14 x^5}{x^4+2 (2-\log (5)) x^3+\left (4-8 \log (5)+\log ^2(5)\right ) x^2-4 (2-\log (5)) \log (5) x+4 \log ^2(5)-e^5}+\frac {31 x^4}{x^4+2 (2-\log (5)) x^3+\left (4-8 \log (5)+\log ^2(5)\right ) x^2-4 (2-\log (5)) \log (5) x+4 \log ^2(5)-e^5}+\frac {4 (x+1) (x+2) \left (x^2+7\right ) \log (5) x^2}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}+\frac {28 x^2}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}+\log ^2\left (-\frac {5 x}{x^4+2 (2-\log (5)) x^3+\left (4-8 \log (5)+\log ^2(5)\right ) x^2-4 (2-\log (5)) \log (5) x+4 \log ^2(5)-e^5}\right ) x+\frac {\left (-3 x^6-9 \left (1-\frac {2 \log (5)}{3}\right ) x^5-11 \left (1+\frac {1}{11} \log (5) (-20+\log (125))\right ) x^4-24 \left (1+\frac {1}{24} \log (5) (-30+11 \log (5))\right ) x^3-28 \left (1+\frac {1}{28} \left (-3 e^5+\log (5) (-56+19 \log (5))\right )\right ) x^2+e^5 \left (1-\frac {8 \log (5) (-7+\log (625))}{e^5}\right ) x+7 e^5 \left (1-\frac {4 \log ^2(5)}{e^5}\right )\right ) \log \left (-\frac {5 x}{x^4+2 (2-\log (5)) x^3+\left (4-8 \log (5)+\log ^2(5)\right ) x^2-4 (2-\log (5)) \log (5) x+4 \log ^2(5)-e^5}\right )}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}+\frac {e^5 (2 x+1) \left (x^2+7\right )}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}+\frac {(x+2) \left (-2 x^2-3 x-2\right ) \left (x^2+7\right ) \log ^2(5)}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle 2 \int \frac {-2 x^7-5 x^6-14 x^5-31 x^4+4 (x+1) (x+2) \left (x^2+7\right ) \log (5) x^2+28 x^2+\left (e^5-(x+2)^2 (x-\log (5))^2\right ) \log ^2\left (-\frac {5 x}{(x+2)^2 (x-\log (5))^2-e^5}\right ) x+e^5 (2 x+1) \left (x^2+7\right )-\left (3 x^6-3 (-3+\log (25)) x^5+(11+\log (5) (-20+\log (125))) x^4+\left (24-30 \log (5)+11 \log ^2(5)\right ) x^3+\left (28-56 \log (5)+19 \log ^2(5)\right ) x^2+8 \log (5) (-7+\log (625)) x-e^5 \left (3 x^2+x+7\right )+28 \log ^2(5)\right ) \log \left (-\frac {5 x}{(x+2)^2 (x-\log (5))^2-e^5}\right )-(x+2) \left (x^2+7\right ) \left (2 x^2+3 x+2\right ) \log ^2(5)}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle 2 \int \left (\frac {2 x^7}{x^4+2 (2-\log (5)) x^3+\left (4-8 \log (5)+\log ^2(5)\right ) x^2-4 (2-\log (5)) \log (5) x+4 \log ^2(5)-e^5}+\frac {5 x^6}{x^4+2 (2-\log (5)) x^3+\left (4-8 \log (5)+\log ^2(5)\right ) x^2-4 (2-\log (5)) \log (5) x+4 \log ^2(5)-e^5}+\frac {14 x^5}{x^4+2 (2-\log (5)) x^3+\left (4-8 \log (5)+\log ^2(5)\right ) x^2-4 (2-\log (5)) \log (5) x+4 \log ^2(5)-e^5}+\frac {31 x^4}{x^4+2 (2-\log (5)) x^3+\left (4-8 \log (5)+\log ^2(5)\right ) x^2-4 (2-\log (5)) \log (5) x+4 \log ^2(5)-e^5}+\frac {4 (x+1) (x+2) \left (x^2+7\right ) \log (5) x^2}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}+\frac {28 x^2}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}+\log ^2\left (-\frac {5 x}{x^4+2 (2-\log (5)) x^3+\left (4-8 \log (5)+\log ^2(5)\right ) x^2-4 (2-\log (5)) \log (5) x+4 \log ^2(5)-e^5}\right ) x+\frac {\left (-3 x^6-9 \left (1-\frac {2 \log (5)}{3}\right ) x^5-11 \left (1+\frac {1}{11} \log (5) (-20+\log (125))\right ) x^4-24 \left (1+\frac {1}{24} \log (5) (-30+11 \log (5))\right ) x^3-28 \left (1+\frac {1}{28} \left (-3 e^5+\log (5) (-56+19 \log (5))\right )\right ) x^2+e^5 \left (1-\frac {8 \log (5) (-7+\log (625))}{e^5}\right ) x+7 e^5 \left (1-\frac {4 \log ^2(5)}{e^5}\right )\right ) \log \left (-\frac {5 x}{x^4+2 (2-\log (5)) x^3+\left (4-8 \log (5)+\log ^2(5)\right ) x^2-4 (2-\log (5)) \log (5) x+4 \log ^2(5)-e^5}\right )}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}+\frac {e^5 (2 x+1) \left (x^2+7\right )}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}+\frac {(x+2) \left (-2 x^2-3 x-2\right ) \left (x^2+7\right ) \log ^2(5)}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle 2 \int \frac {-2 x^7-5 x^6-14 x^5-31 x^4+4 (x+1) (x+2) \left (x^2+7\right ) \log (5) x^2+28 x^2+\left (e^5-(x+2)^2 (x-\log (5))^2\right ) \log ^2\left (-\frac {5 x}{(x+2)^2 (x-\log (5))^2-e^5}\right ) x+e^5 (2 x+1) \left (x^2+7\right )-\left (3 x^6-3 (-3+\log (25)) x^5+(11+\log (5) (-20+\log (125))) x^4+\left (24-30 \log (5)+11 \log ^2(5)\right ) x^3+\left (28-56 \log (5)+19 \log ^2(5)\right ) x^2+8 \log (5) (-7+\log (625)) x-e^5 \left (3 x^2+x+7\right )+28 \log ^2(5)\right ) \log \left (-\frac {5 x}{(x+2)^2 (x-\log (5))^2-e^5}\right )-(x+2) \left (x^2+7\right ) \left (2 x^2+3 x+2\right ) \log ^2(5)}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle 2 \int \left (\frac {2 x^7}{x^4+2 (2-\log (5)) x^3+\left (4-8 \log (5)+\log ^2(5)\right ) x^2-4 (2-\log (5)) \log (5) x+4 \log ^2(5)-e^5}+\frac {5 x^6}{x^4+2 (2-\log (5)) x^3+\left (4-8 \log (5)+\log ^2(5)\right ) x^2-4 (2-\log (5)) \log (5) x+4 \log ^2(5)-e^5}+\frac {14 x^5}{x^4+2 (2-\log (5)) x^3+\left (4-8 \log (5)+\log ^2(5)\right ) x^2-4 (2-\log (5)) \log (5) x+4 \log ^2(5)-e^5}+\frac {31 x^4}{x^4+2 (2-\log (5)) x^3+\left (4-8 \log (5)+\log ^2(5)\right ) x^2-4 (2-\log (5)) \log (5) x+4 \log ^2(5)-e^5}+\frac {4 (x+1) (x+2) \left (x^2+7\right ) \log (5) x^2}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}+\frac {28 x^2}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}+\log ^2\left (-\frac {5 x}{x^4+2 (2-\log (5)) x^3+\left (4-8 \log (5)+\log ^2(5)\right ) x^2-4 (2-\log (5)) \log (5) x+4 \log ^2(5)-e^5}\right ) x+\frac {\left (-3 x^6-9 \left (1-\frac {2 \log (5)}{3}\right ) x^5-11 \left (1+\frac {1}{11} \log (5) (-20+\log (125))\right ) x^4-24 \left (1+\frac {1}{24} \log (5) (-30+11 \log (5))\right ) x^3-28 \left (1+\frac {1}{28} \left (-3 e^5+\log (5) (-56+19 \log (5))\right )\right ) x^2+e^5 \left (1-\frac {8 \log (5) (-7+\log (625))}{e^5}\right ) x+7 e^5 \left (1-\frac {4 \log ^2(5)}{e^5}\right )\right ) \log \left (-\frac {5 x}{x^4+2 (2-\log (5)) x^3+\left (4-8 \log (5)+\log ^2(5)\right ) x^2-4 (2-\log (5)) \log (5) x+4 \log ^2(5)-e^5}\right )}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}+\frac {e^5 (2 x+1) \left (x^2+7\right )}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}+\frac {(x+2) \left (-2 x^2-3 x-2\right ) \left (x^2+7\right ) \log ^2(5)}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle 2 \int \frac {-2 x^7-5 x^6-14 x^5-31 x^4+4 (x+1) (x+2) \left (x^2+7\right ) \log (5) x^2+28 x^2+\left (e^5-(x+2)^2 (x-\log (5))^2\right ) \log ^2\left (-\frac {5 x}{(x+2)^2 (x-\log (5))^2-e^5}\right ) x+e^5 (2 x+1) \left (x^2+7\right )-\left (3 x^6-3 (-3+\log (25)) x^5+(11+\log (5) (-20+\log (125))) x^4+\left (24-30 \log (5)+11 \log ^2(5)\right ) x^3+\left (28-56 \log (5)+19 \log ^2(5)\right ) x^2+8 \log (5) (-7+\log (625)) x-e^5 \left (3 x^2+x+7\right )+28 \log ^2(5)\right ) \log \left (-\frac {5 x}{(x+2)^2 (x-\log (5))^2-e^5}\right )-(x+2) \left (x^2+7\right ) \left (2 x^2+3 x+2\right ) \log ^2(5)}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle 2 \int \left (\frac {2 x^7}{x^4+2 (2-\log (5)) x^3+\left (4-8 \log (5)+\log ^2(5)\right ) x^2-4 (2-\log (5)) \log (5) x+4 \log ^2(5)-e^5}+\frac {5 x^6}{x^4+2 (2-\log (5)) x^3+\left (4-8 \log (5)+\log ^2(5)\right ) x^2-4 (2-\log (5)) \log (5) x+4 \log ^2(5)-e^5}+\frac {14 x^5}{x^4+2 (2-\log (5)) x^3+\left (4-8 \log (5)+\log ^2(5)\right ) x^2-4 (2-\log (5)) \log (5) x+4 \log ^2(5)-e^5}+\frac {31 x^4}{x^4+2 (2-\log (5)) x^3+\left (4-8 \log (5)+\log ^2(5)\right ) x^2-4 (2-\log (5)) \log (5) x+4 \log ^2(5)-e^5}+\frac {4 (x+1) (x+2) \left (x^2+7\right ) \log (5) x^2}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}+\frac {28 x^2}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}+\log ^2\left (-\frac {5 x}{x^4+2 (2-\log (5)) x^3+\left (4-8 \log (5)+\log ^2(5)\right ) x^2-4 (2-\log (5)) \log (5) x+4 \log ^2(5)-e^5}\right ) x+\frac {\left (-3 x^6-9 \left (1-\frac {2 \log (5)}{3}\right ) x^5-11 \left (1+\frac {1}{11} \log (5) (-20+\log (125))\right ) x^4-24 \left (1+\frac {1}{24} \log (5) (-30+11 \log (5))\right ) x^3-28 \left (1+\frac {1}{28} \left (-3 e^5+\log (5) (-56+19 \log (5))\right )\right ) x^2+e^5 \left (1-\frac {8 \log (5) (-7+\log (625))}{e^5}\right ) x+7 e^5 \left (1-\frac {4 \log ^2(5)}{e^5}\right )\right ) \log \left (-\frac {5 x}{x^4+2 (2-\log (5)) x^3+\left (4-8 \log (5)+\log ^2(5)\right ) x^2-4 (2-\log (5)) \log (5) x+4 \log ^2(5)-e^5}\right )}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}+\frac {e^5 (2 x+1) \left (x^2+7\right )}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}+\frac {(x+2) \left (-2 x^2-3 x-2\right ) \left (x^2+7\right ) \log ^2(5)}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle 2 \int \frac {-2 x^7-5 x^6-14 x^5-31 x^4+4 (x+1) (x+2) \left (x^2+7\right ) \log (5) x^2+28 x^2+\left (e^5-(x+2)^2 (x-\log (5))^2\right ) \log ^2\left (-\frac {5 x}{(x+2)^2 (x-\log (5))^2-e^5}\right ) x+e^5 (2 x+1) \left (x^2+7\right )-\left (3 x^6-3 (-3+\log (25)) x^5+(11+\log (5) (-20+\log (125))) x^4+\left (24-30 \log (5)+11 \log ^2(5)\right ) x^3+\left (28-56 \log (5)+19 \log ^2(5)\right ) x^2+8 \log (5) (-7+\log (625)) x-e^5 \left (3 x^2+x+7\right )+28 \log ^2(5)\right ) \log \left (-\frac {5 x}{(x+2)^2 (x-\log (5))^2-e^5}\right )-(x+2) \left (x^2+7\right ) \left (2 x^2+3 x+2\right ) \log ^2(5)}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle 2 \int \left (\frac {2 x^7}{x^4+2 (2-\log (5)) x^3+\left (4-8 \log (5)+\log ^2(5)\right ) x^2-4 (2-\log (5)) \log (5) x+4 \log ^2(5)-e^5}+\frac {5 x^6}{x^4+2 (2-\log (5)) x^3+\left (4-8 \log (5)+\log ^2(5)\right ) x^2-4 (2-\log (5)) \log (5) x+4 \log ^2(5)-e^5}+\frac {14 x^5}{x^4+2 (2-\log (5)) x^3+\left (4-8 \log (5)+\log ^2(5)\right ) x^2-4 (2-\log (5)) \log (5) x+4 \log ^2(5)-e^5}+\frac {31 x^4}{x^4+2 (2-\log (5)) x^3+\left (4-8 \log (5)+\log ^2(5)\right ) x^2-4 (2-\log (5)) \log (5) x+4 \log ^2(5)-e^5}+\frac {4 (x+1) (x+2) \left (x^2+7\right ) \log (5) x^2}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}+\frac {28 x^2}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}+\log ^2\left (-\frac {5 x}{x^4+2 (2-\log (5)) x^3+\left (4-8 \log (5)+\log ^2(5)\right ) x^2-4 (2-\log (5)) \log (5) x+4 \log ^2(5)-e^5}\right ) x+\frac {\left (-3 x^6-9 \left (1-\frac {2 \log (5)}{3}\right ) x^5-11 \left (1+\frac {1}{11} \log (5) (-20+\log (125))\right ) x^4-24 \left (1+\frac {1}{24} \log (5) (-30+11 \log (5))\right ) x^3-28 \left (1+\frac {1}{28} \left (-3 e^5+\log (5) (-56+19 \log (5))\right )\right ) x^2+e^5 \left (1-\frac {8 \log (5) (-7+\log (625))}{e^5}\right ) x+7 e^5 \left (1-\frac {4 \log ^2(5)}{e^5}\right )\right ) \log \left (-\frac {5 x}{x^4+2 (2-\log (5)) x^3+\left (4-8 \log (5)+\log ^2(5)\right ) x^2-4 (2-\log (5)) \log (5) x+4 \log ^2(5)-e^5}\right )}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}+\frac {e^5 (2 x+1) \left (x^2+7\right )}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}+\frac {(x+2) \left (-2 x^2-3 x-2\right ) \left (x^2+7\right ) \log ^2(5)}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle 2 \int \frac {-2 x^7-5 x^6-14 x^5-31 x^4+4 (x+1) (x+2) \left (x^2+7\right ) \log (5) x^2+28 x^2+\left (e^5-(x+2)^2 (x-\log (5))^2\right ) \log ^2\left (-\frac {5 x}{(x+2)^2 (x-\log (5))^2-e^5}\right ) x+e^5 (2 x+1) \left (x^2+7\right )-\left (3 x^6-3 (-3+\log (25)) x^5+(11+\log (5) (-20+\log (125))) x^4+\left (24-30 \log (5)+11 \log ^2(5)\right ) x^3+\left (28-56 \log (5)+19 \log ^2(5)\right ) x^2+8 \log (5) (-7+\log (625)) x-e^5 \left (3 x^2+x+7\right )+28 \log ^2(5)\right ) \log \left (-\frac {5 x}{(x+2)^2 (x-\log (5))^2-e^5}\right )-(x+2) \left (x^2+7\right ) \left (2 x^2+3 x+2\right ) \log ^2(5)}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle 2 \int \left (\frac {2 x^7}{x^4+2 (2-\log (5)) x^3+\left (4-8 \log (5)+\log ^2(5)\right ) x^2-4 (2-\log (5)) \log (5) x+4 \log ^2(5)-e^5}+\frac {5 x^6}{x^4+2 (2-\log (5)) x^3+\left (4-8 \log (5)+\log ^2(5)\right ) x^2-4 (2-\log (5)) \log (5) x+4 \log ^2(5)-e^5}+\frac {14 x^5}{x^4+2 (2-\log (5)) x^3+\left (4-8 \log (5)+\log ^2(5)\right ) x^2-4 (2-\log (5)) \log (5) x+4 \log ^2(5)-e^5}+\frac {31 x^4}{x^4+2 (2-\log (5)) x^3+\left (4-8 \log (5)+\log ^2(5)\right ) x^2-4 (2-\log (5)) \log (5) x+4 \log ^2(5)-e^5}+\frac {4 (x+1) (x+2) \left (x^2+7\right ) \log (5) x^2}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}+\frac {28 x^2}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}+\log ^2\left (-\frac {5 x}{x^4+2 (2-\log (5)) x^3+\left (4-8 \log (5)+\log ^2(5)\right ) x^2-4 (2-\log (5)) \log (5) x+4 \log ^2(5)-e^5}\right ) x+\frac {\left (-3 x^6-9 \left (1-\frac {2 \log (5)}{3}\right ) x^5-11 \left (1+\frac {1}{11} \log (5) (-20+\log (125))\right ) x^4-24 \left (1+\frac {1}{24} \log (5) (-30+11 \log (5))\right ) x^3-28 \left (1+\frac {1}{28} \left (-3 e^5+\log (5) (-56+19 \log (5))\right )\right ) x^2+e^5 \left (1-\frac {8 \log (5) (-7+\log (625))}{e^5}\right ) x+7 e^5 \left (1-\frac {4 \log ^2(5)}{e^5}\right )\right ) \log \left (-\frac {5 x}{x^4+2 (2-\log (5)) x^3+\left (4-8 \log (5)+\log ^2(5)\right ) x^2-4 (2-\log (5)) \log (5) x+4 \log ^2(5)-e^5}\right )}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}+\frac {e^5 (2 x+1) \left (x^2+7\right )}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}+\frac {(x+2) \left (-2 x^2-3 x-2\right ) \left (x^2+7\right ) \log ^2(5)}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle 2 \int \frac {-2 x^7-5 x^6-14 x^5-31 x^4+4 (x+1) (x+2) \left (x^2+7\right ) \log (5) x^2+28 x^2+\left (e^5-(x+2)^2 (x-\log (5))^2\right ) \log ^2\left (-\frac {5 x}{(x+2)^2 (x-\log (5))^2-e^5}\right ) x+e^5 (2 x+1) \left (x^2+7\right )-\left (3 x^6-3 (-3+\log (25)) x^5+(11+\log (5) (-20+\log (125))) x^4+\left (24-30 \log (5)+11 \log ^2(5)\right ) x^3+\left (28-56 \log (5)+19 \log ^2(5)\right ) x^2+8 \log (5) (-7+\log (625)) x-e^5 \left (3 x^2+x+7\right )+28 \log ^2(5)\right ) \log \left (-\frac {5 x}{(x+2)^2 (x-\log (5))^2-e^5}\right )-(x+2) \left (x^2+7\right ) \left (2 x^2+3 x+2\right ) \log ^2(5)}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle 2 \int \left (\frac {2 x^7}{x^4+2 (2-\log (5)) x^3+\left (4-8 \log (5)+\log ^2(5)\right ) x^2-4 (2-\log (5)) \log (5) x+4 \log ^2(5)-e^5}+\frac {5 x^6}{x^4+2 (2-\log (5)) x^3+\left (4-8 \log (5)+\log ^2(5)\right ) x^2-4 (2-\log (5)) \log (5) x+4 \log ^2(5)-e^5}+\frac {14 x^5}{x^4+2 (2-\log (5)) x^3+\left (4-8 \log (5)+\log ^2(5)\right ) x^2-4 (2-\log (5)) \log (5) x+4 \log ^2(5)-e^5}+\frac {31 x^4}{x^4+2 (2-\log (5)) x^3+\left (4-8 \log (5)+\log ^2(5)\right ) x^2-4 (2-\log (5)) \log (5) x+4 \log ^2(5)-e^5}+\frac {4 (x+1) (x+2) \left (x^2+7\right ) \log (5) x^2}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}+\frac {28 x^2}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}+\log ^2\left (-\frac {5 x}{x^4+2 (2-\log (5)) x^3+\left (4-8 \log (5)+\log ^2(5)\right ) x^2-4 (2-\log (5)) \log (5) x+4 \log ^2(5)-e^5}\right ) x+\frac {\left (-3 x^6-9 \left (1-\frac {2 \log (5)}{3}\right ) x^5-11 \left (1+\frac {1}{11} \log (5) (-20+\log (125))\right ) x^4-24 \left (1+\frac {1}{24} \log (5) (-30+11 \log (5))\right ) x^3-28 \left (1+\frac {1}{28} \left (-3 e^5+\log (5) (-56+19 \log (5))\right )\right ) x^2+e^5 \left (1-\frac {8 \log (5) (-7+\log (625))}{e^5}\right ) x+7 e^5 \left (1-\frac {4 \log ^2(5)}{e^5}\right )\right ) \log \left (-\frac {5 x}{x^4+2 (2-\log (5)) x^3+\left (4-8 \log (5)+\log ^2(5)\right ) x^2-4 (2-\log (5)) \log (5) x+4 \log ^2(5)-e^5}\right )}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}+\frac {e^5 (2 x+1) \left (x^2+7\right )}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}+\frac {(x+2) \left (-2 x^2-3 x-2\right ) \left (x^2+7\right ) \log ^2(5)}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle 2 \int \frac {-2 x^7-5 x^6-14 x^5-31 x^4+4 (x+1) (x+2) \left (x^2+7\right ) \log (5) x^2+28 x^2+\left (e^5-(x+2)^2 (x-\log (5))^2\right ) \log ^2\left (-\frac {5 x}{(x+2)^2 (x-\log (5))^2-e^5}\right ) x+e^5 (2 x+1) \left (x^2+7\right )-\left (3 x^6-3 (-3+\log (25)) x^5+(11+\log (5) (-20+\log (125))) x^4+\left (24-30 \log (5)+11 \log ^2(5)\right ) x^3+\left (28-56 \log (5)+19 \log ^2(5)\right ) x^2+8 \log (5) (-7+\log (625)) x-e^5 \left (3 x^2+x+7\right )+28 \log ^2(5)\right ) \log \left (-\frac {5 x}{(x+2)^2 (x-\log (5))^2-e^5}\right )-(x+2) \left (x^2+7\right ) \left (2 x^2+3 x+2\right ) \log ^2(5)}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle 2 \int \left (\frac {2 x^7}{x^4+2 (2-\log (5)) x^3+\left (4-8 \log (5)+\log ^2(5)\right ) x^2-4 (2-\log (5)) \log (5) x+4 \log ^2(5)-e^5}+\frac {5 x^6}{x^4+2 (2-\log (5)) x^3+\left (4-8 \log (5)+\log ^2(5)\right ) x^2-4 (2-\log (5)) \log (5) x+4 \log ^2(5)-e^5}+\frac {14 x^5}{x^4+2 (2-\log (5)) x^3+\left (4-8 \log (5)+\log ^2(5)\right ) x^2-4 (2-\log (5)) \log (5) x+4 \log ^2(5)-e^5}+\frac {31 x^4}{x^4+2 (2-\log (5)) x^3+\left (4-8 \log (5)+\log ^2(5)\right ) x^2-4 (2-\log (5)) \log (5) x+4 \log ^2(5)-e^5}+\frac {4 (x+1) (x+2) \left (x^2+7\right ) \log (5) x^2}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}+\frac {28 x^2}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}+\log ^2\left (-\frac {5 x}{x^4+2 (2-\log (5)) x^3+\left (4-8 \log (5)+\log ^2(5)\right ) x^2-4 (2-\log (5)) \log (5) x+4 \log ^2(5)-e^5}\right ) x+\frac {\left (-3 x^6-9 \left (1-\frac {2 \log (5)}{3}\right ) x^5-11 \left (1+\frac {1}{11} \log (5) (-20+\log (125))\right ) x^4-24 \left (1+\frac {1}{24} \log (5) (-30+11 \log (5))\right ) x^3-28 \left (1+\frac {1}{28} \left (-3 e^5+\log (5) (-56+19 \log (5))\right )\right ) x^2+e^5 \left (1-\frac {8 \log (5) (-7+\log (625))}{e^5}\right ) x+7 e^5 \left (1-\frac {4 \log ^2(5)}{e^5}\right )\right ) \log \left (-\frac {5 x}{x^4+2 (2-\log (5)) x^3+\left (4-8 \log (5)+\log ^2(5)\right ) x^2-4 (2-\log (5)) \log (5) x+4 \log ^2(5)-e^5}\right )}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}+\frac {e^5 (2 x+1) \left (x^2+7\right )}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}+\frac {(x+2) \left (-2 x^2-3 x-2\right ) \left (x^2+7\right ) \log ^2(5)}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle 2 \int \frac {-2 x^7-5 x^6-14 x^5-31 x^4+4 (x+1) (x+2) \left (x^2+7\right ) \log (5) x^2+28 x^2+\left (e^5-(x+2)^2 (x-\log (5))^2\right ) \log ^2\left (-\frac {5 x}{(x+2)^2 (x-\log (5))^2-e^5}\right ) x+e^5 (2 x+1) \left (x^2+7\right )-\left (3 x^6-3 (-3+\log (25)) x^5+(11+\log (5) (-20+\log (125))) x^4+\left (24-30 \log (5)+11 \log ^2(5)\right ) x^3+\left (28-56 \log (5)+19 \log ^2(5)\right ) x^2+8 \log (5) (-7+\log (625)) x-e^5 \left (3 x^2+x+7\right )+28 \log ^2(5)\right ) \log \left (-\frac {5 x}{(x+2)^2 (x-\log (5))^2-e^5}\right )-(x+2) \left (x^2+7\right ) \left (2 x^2+3 x+2\right ) \log ^2(5)}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle 2 \int \left (\frac {2 x^7}{x^4+2 (2-\log (5)) x^3+\left (4-8 \log (5)+\log ^2(5)\right ) x^2-4 (2-\log (5)) \log (5) x+4 \log ^2(5)-e^5}+\frac {5 x^6}{x^4+2 (2-\log (5)) x^3+\left (4-8 \log (5)+\log ^2(5)\right ) x^2-4 (2-\log (5)) \log (5) x+4 \log ^2(5)-e^5}+\frac {14 x^5}{x^4+2 (2-\log (5)) x^3+\left (4-8 \log (5)+\log ^2(5)\right ) x^2-4 (2-\log (5)) \log (5) x+4 \log ^2(5)-e^5}+\frac {31 x^4}{x^4+2 (2-\log (5)) x^3+\left (4-8 \log (5)+\log ^2(5)\right ) x^2-4 (2-\log (5)) \log (5) x+4 \log ^2(5)-e^5}+\frac {4 (x+1) (x+2) \left (x^2+7\right ) \log (5) x^2}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}+\frac {28 x^2}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}+\log ^2\left (-\frac {5 x}{x^4+2 (2-\log (5)) x^3+\left (4-8 \log (5)+\log ^2(5)\right ) x^2-4 (2-\log (5)) \log (5) x+4 \log ^2(5)-e^5}\right ) x+\frac {\left (-3 x^6-9 \left (1-\frac {2 \log (5)}{3}\right ) x^5-11 \left (1+\frac {1}{11} \log (5) (-20+\log (125))\right ) x^4-24 \left (1+\frac {1}{24} \log (5) (-30+11 \log (5))\right ) x^3-28 \left (1+\frac {1}{28} \left (-3 e^5+\log (5) (-56+19 \log (5))\right )\right ) x^2+e^5 \left (1-\frac {8 \log (5) (-7+\log (625))}{e^5}\right ) x+7 e^5 \left (1-\frac {4 \log ^2(5)}{e^5}\right )\right ) \log \left (-\frac {5 x}{x^4+2 (2-\log (5)) x^3+\left (4-8 \log (5)+\log ^2(5)\right ) x^2-4 (2-\log (5)) \log (5) x+4 \log ^2(5)-e^5}\right )}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}+\frac {e^5 (2 x+1) \left (x^2+7\right )}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}+\frac {(x+2) \left (-2 x^2-3 x-2\right ) \left (x^2+7\right ) \log ^2(5)}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle 2 \int \frac {-2 x^7-5 x^6-14 x^5-31 x^4+4 (x+1) (x+2) \left (x^2+7\right ) \log (5) x^2+28 x^2+\left (e^5-(x+2)^2 (x-\log (5))^2\right ) \log ^2\left (-\frac {5 x}{(x+2)^2 (x-\log (5))^2-e^5}\right ) x+e^5 (2 x+1) \left (x^2+7\right )-\left (3 x^6-3 (-3+\log (25)) x^5+(11+\log (5) (-20+\log (125))) x^4+\left (24-30 \log (5)+11 \log ^2(5)\right ) x^3+\left (28-56 \log (5)+19 \log ^2(5)\right ) x^2+8 \log (5) (-7+\log (625)) x-e^5 \left (3 x^2+x+7\right )+28 \log ^2(5)\right ) \log \left (-\frac {5 x}{(x+2)^2 (x-\log (5))^2-e^5}\right )-(x+2) \left (x^2+7\right ) \left (2 x^2+3 x+2\right ) \log ^2(5)}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle 2 \int \left (\frac {2 x^7}{x^4+2 (2-\log (5)) x^3+\left (4-8 \log (5)+\log ^2(5)\right ) x^2-4 (2-\log (5)) \log (5) x+4 \log ^2(5)-e^5}+\frac {5 x^6}{x^4+2 (2-\log (5)) x^3+\left (4-8 \log (5)+\log ^2(5)\right ) x^2-4 (2-\log (5)) \log (5) x+4 \log ^2(5)-e^5}+\frac {14 x^5}{x^4+2 (2-\log (5)) x^3+\left (4-8 \log (5)+\log ^2(5)\right ) x^2-4 (2-\log (5)) \log (5) x+4 \log ^2(5)-e^5}+\frac {31 x^4}{x^4+2 (2-\log (5)) x^3+\left (4-8 \log (5)+\log ^2(5)\right ) x^2-4 (2-\log (5)) \log (5) x+4 \log ^2(5)-e^5}+\frac {4 (x+1) (x+2) \left (x^2+7\right ) \log (5) x^2}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}+\frac {28 x^2}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}+\log ^2\left (-\frac {5 x}{x^4+2 (2-\log (5)) x^3+\left (4-8 \log (5)+\log ^2(5)\right ) x^2-4 (2-\log (5)) \log (5) x+4 \log ^2(5)-e^5}\right ) x+\frac {\left (-3 x^6-9 \left (1-\frac {2 \log (5)}{3}\right ) x^5-11 \left (1+\frac {1}{11} \log (5) (-20+\log (125))\right ) x^4-24 \left (1+\frac {1}{24} \log (5) (-30+11 \log (5))\right ) x^3-28 \left (1+\frac {1}{28} \left (-3 e^5+\log (5) (-56+19 \log (5))\right )\right ) x^2+e^5 \left (1-\frac {8 \log (5) (-7+\log (625))}{e^5}\right ) x+7 e^5 \left (1-\frac {4 \log ^2(5)}{e^5}\right )\right ) \log \left (-\frac {5 x}{x^4+2 (2-\log (5)) x^3+\left (4-8 \log (5)+\log ^2(5)\right ) x^2-4 (2-\log (5)) \log (5) x+4 \log ^2(5)-e^5}\right )}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}+\frac {e^5 (2 x+1) \left (x^2+7\right )}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}+\frac {(x+2) \left (-2 x^2-3 x-2\right ) \left (x^2+7\right ) \log ^2(5)}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle 2 \int \frac {-2 x^7-5 x^6-14 x^5-31 x^4+4 (x+1) (x+2) \left (x^2+7\right ) \log (5) x^2+28 x^2+\left (e^5-(x+2)^2 (x-\log (5))^2\right ) \log ^2\left (-\frac {5 x}{(x+2)^2 (x-\log (5))^2-e^5}\right ) x+e^5 (2 x+1) \left (x^2+7\right )-\left (3 x^6-3 (-3+\log (25)) x^5+(11+\log (5) (-20+\log (125))) x^4+\left (24-30 \log (5)+11 \log ^2(5)\right ) x^3+\left (28-56 \log (5)+19 \log ^2(5)\right ) x^2+8 \log (5) (-7+\log (625)) x-e^5 \left (3 x^2+x+7\right )+28 \log ^2(5)\right ) \log \left (-\frac {5 x}{(x+2)^2 (x-\log (5))^2-e^5}\right )-(x+2) \left (x^2+7\right ) \left (2 x^2+3 x+2\right ) \log ^2(5)}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle 2 \int \left (\frac {2 x^7}{x^4+2 (2-\log (5)) x^3+\left (4-8 \log (5)+\log ^2(5)\right ) x^2-4 (2-\log (5)) \log (5) x+4 \log ^2(5)-e^5}+\frac {5 x^6}{x^4+2 (2-\log (5)) x^3+\left (4-8 \log (5)+\log ^2(5)\right ) x^2-4 (2-\log (5)) \log (5) x+4 \log ^2(5)-e^5}+\frac {14 x^5}{x^4+2 (2-\log (5)) x^3+\left (4-8 \log (5)+\log ^2(5)\right ) x^2-4 (2-\log (5)) \log (5) x+4 \log ^2(5)-e^5}+\frac {31 x^4}{x^4+2 (2-\log (5)) x^3+\left (4-8 \log (5)+\log ^2(5)\right ) x^2-4 (2-\log (5)) \log (5) x+4 \log ^2(5)-e^5}+\frac {4 (x+1) (x+2) \left (x^2+7\right ) \log (5) x^2}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}+\frac {28 x^2}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}+\log ^2\left (-\frac {5 x}{x^4+2 (2-\log (5)) x^3+\left (4-8 \log (5)+\log ^2(5)\right ) x^2-4 (2-\log (5)) \log (5) x+4 \log ^2(5)-e^5}\right ) x+\frac {\left (-3 x^6-9 \left (1-\frac {2 \log (5)}{3}\right ) x^5-11 \left (1+\frac {1}{11} \log (5) (-20+\log (125))\right ) x^4-24 \left (1+\frac {1}{24} \log (5) (-30+11 \log (5))\right ) x^3-28 \left (1+\frac {1}{28} \left (-3 e^5+\log (5) (-56+19 \log (5))\right )\right ) x^2+e^5 \left (1-\frac {8 \log (5) (-7+\log (625))}{e^5}\right ) x+7 e^5 \left (1-\frac {4 \log ^2(5)}{e^5}\right )\right ) \log \left (-\frac {5 x}{x^4+2 (2-\log (5)) x^3+\left (4-8 \log (5)+\log ^2(5)\right ) x^2-4 (2-\log (5)) \log (5) x+4 \log ^2(5)-e^5}\right )}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}+\frac {e^5 (2 x+1) \left (x^2+7\right )}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}+\frac {(x+2) \left (-2 x^2-3 x-2\right ) \left (x^2+7\right ) \log ^2(5)}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle 2 \int \frac {-2 x^7-5 x^6-14 x^5-31 x^4+4 (x+1) (x+2) \left (x^2+7\right ) \log (5) x^2+28 x^2+\left (e^5-(x+2)^2 (x-\log (5))^2\right ) \log ^2\left (-\frac {5 x}{(x+2)^2 (x-\log (5))^2-e^5}\right ) x+e^5 (2 x+1) \left (x^2+7\right )-\left (3 x^6-3 (-3+\log (25)) x^5+(11+\log (5) (-20+\log (125))) x^4+\left (24-30 \log (5)+11 \log ^2(5)\right ) x^3+\left (28-56 \log (5)+19 \log ^2(5)\right ) x^2+8 \log (5) (-7+\log (625)) x-e^5 \left (3 x^2+x+7\right )+28 \log ^2(5)\right ) \log \left (-\frac {5 x}{(x+2)^2 (x-\log (5))^2-e^5}\right )-(x+2) \left (x^2+7\right ) \left (2 x^2+3 x+2\right ) \log ^2(5)}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle 2 \int \left (\frac {2 x^7}{x^4+2 (2-\log (5)) x^3+\left (4-8 \log (5)+\log ^2(5)\right ) x^2-4 (2-\log (5)) \log (5) x+4 \log ^2(5)-e^5}+\frac {5 x^6}{x^4+2 (2-\log (5)) x^3+\left (4-8 \log (5)+\log ^2(5)\right ) x^2-4 (2-\log (5)) \log (5) x+4 \log ^2(5)-e^5}+\frac {14 x^5}{x^4+2 (2-\log (5)) x^3+\left (4-8 \log (5)+\log ^2(5)\right ) x^2-4 (2-\log (5)) \log (5) x+4 \log ^2(5)-e^5}+\frac {31 x^4}{x^4+2 (2-\log (5)) x^3+\left (4-8 \log (5)+\log ^2(5)\right ) x^2-4 (2-\log (5)) \log (5) x+4 \log ^2(5)-e^5}+\frac {4 (x+1) (x+2) \left (x^2+7\right ) \log (5) x^2}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}+\frac {28 x^2}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}+\log ^2\left (-\frac {5 x}{x^4+2 (2-\log (5)) x^3+\left (4-8 \log (5)+\log ^2(5)\right ) x^2-4 (2-\log (5)) \log (5) x+4 \log ^2(5)-e^5}\right ) x+\frac {\left (-3 x^6-9 \left (1-\frac {2 \log (5)}{3}\right ) x^5-11 \left (1+\frac {1}{11} \log (5) (-20+\log (125))\right ) x^4-24 \left (1+\frac {1}{24} \log (5) (-30+11 \log (5))\right ) x^3-28 \left (1+\frac {1}{28} \left (-3 e^5+\log (5) (-56+19 \log (5))\right )\right ) x^2+e^5 \left (1-\frac {8 \log (5) (-7+\log (625))}{e^5}\right ) x+7 e^5 \left (1-\frac {4 \log ^2(5)}{e^5}\right )\right ) \log \left (-\frac {5 x}{x^4+2 (2-\log (5)) x^3+\left (4-8 \log (5)+\log ^2(5)\right ) x^2-4 (2-\log (5)) \log (5) x+4 \log ^2(5)-e^5}\right )}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}+\frac {e^5 (2 x+1) \left (x^2+7\right )}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}+\frac {(x+2) \left (-2 x^2-3 x-2\right ) \left (x^2+7\right ) \log ^2(5)}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle 2 \int \frac {-2 x^7-5 x^6-14 x^5-31 x^4+4 (x+1) (x+2) \left (x^2+7\right ) \log (5) x^2+28 x^2+\left (e^5-(x+2)^2 (x-\log (5))^2\right ) \log ^2\left (-\frac {5 x}{(x+2)^2 (x-\log (5))^2-e^5}\right ) x+e^5 (2 x+1) \left (x^2+7\right )-\left (3 x^6-3 (-3+\log (25)) x^5+(11+\log (5) (-20+\log (125))) x^4+\left (24-30 \log (5)+11 \log ^2(5)\right ) x^3+\left (28-56 \log (5)+19 \log ^2(5)\right ) x^2+8 \log (5) (-7+\log (625)) x-e^5 \left (3 x^2+x+7\right )+28 \log ^2(5)\right ) \log \left (-\frac {5 x}{(x+2)^2 (x-\log (5))^2-e^5}\right )-(x+2) \left (x^2+7\right ) \left (2 x^2+3 x+2\right ) \log ^2(5)}{-x^4-2 (2-\log (5)) x^3-\left (4-8 \log (5)+\log ^2(5)\right ) x^2+4 (2-\log (5)) \log (5) x-4 \log ^2(5)+e^5}dx\)

Input:

Int[(-56*x^2 + 62*x^4 + 28*x^5 + 10*x^6 + 4*x^7 + E^5*(-14 - 28*x - 2*x^2 
- 4*x^3) + (-112*x^2 - 168*x^3 - 72*x^4 - 24*x^5 - 8*x^6)*Log[5] + (56 + 1 
12*x + 106*x^2 + 44*x^3 + 14*x^4 + 4*x^5)*Log[5]^2 + (56*x^2 + 48*x^3 + 22 
*x^4 + 18*x^5 + 6*x^6 + E^5*(-14 - 2*x - 6*x^2) + (-112*x - 112*x^2 - 60*x 
^3 - 40*x^4 - 12*x^5)*Log[5] + (56 + 64*x + 38*x^2 + 22*x^3 + 6*x^4)*Log[5 
]^2)*Log[(-5*x)/(-E^5 + 4*x^2 + 4*x^3 + x^4 + (-8*x - 8*x^2 - 2*x^3)*Log[5 
] + (4 + 4*x + x^2)*Log[5]^2)] + (-2*E^5*x + 8*x^3 + 8*x^4 + 2*x^5 + (-16* 
x^2 - 16*x^3 - 4*x^4)*Log[5] + (8*x + 8*x^2 + 2*x^3)*Log[5]^2)*Log[(-5*x)/ 
(-E^5 + 4*x^2 + 4*x^3 + x^4 + (-8*x - 8*x^2 - 2*x^3)*Log[5] + (4 + 4*x + x 
^2)*Log[5]^2)]^2)/(-E^5 + 4*x^2 + 4*x^3 + x^4 + (-8*x - 8*x^2 - 2*x^3)*Log 
[5] + (4 + 4*x + x^2)*Log[5]^2),x]
 

Output:

$Aborted
 

Maple [B] (verified)

Leaf count of result is larger than twice the leaf count of optimal. \(185\) vs. \(2(32)=64\).

Time = 1.14 (sec) , antiderivative size = 186, normalized size of antiderivative = 5.64

\[x^{4}+x^{2} {\ln \left (-\frac {5 x}{\left (x^{2}+4 x +4\right ) \ln \left (5\right )^{2}+\left (-2 x^{3}-8 x^{2}-8 x \right ) \ln \left (5\right )-{\mathrm e}^{5}+x^{4}+4 x^{3}+4 x^{2}}\right )}^{2}+14 x^{2}+14 x \ln \left (-\frac {5 x}{\left (x^{2}+4 x +4\right ) \ln \left (5\right )^{2}+\left (-2 x^{3}-8 x^{2}-8 x \right ) \ln \left (5\right )-{\mathrm e}^{5}+x^{4}+4 x^{3}+4 x^{2}}\right )+2 x^{3} \ln \left (-\frac {5 x}{\left (x^{2}+4 x +4\right ) \ln \left (5\right )^{2}+\left (-2 x^{3}-8 x^{2}-8 x \right ) \ln \left (5\right )-{\mathrm e}^{5}+x^{4}+4 x^{3}+4 x^{2}}\right )\]

Input:

int((((2*x^3+8*x^2+8*x)*ln(5)^2+(-4*x^4-16*x^3-16*x^2)*ln(5)-2*x*exp(5)+2* 
x^5+8*x^4+8*x^3)*ln(-5*x/((x^2+4*x+4)*ln(5)^2+(-2*x^3-8*x^2-8*x)*ln(5)-exp 
(5)+x^4+4*x^3+4*x^2))^2+((6*x^4+22*x^3+38*x^2+64*x+56)*ln(5)^2+(-12*x^5-40 
*x^4-60*x^3-112*x^2-112*x)*ln(5)+(-6*x^2-2*x-14)*exp(5)+6*x^6+18*x^5+22*x^ 
4+48*x^3+56*x^2)*ln(-5*x/((x^2+4*x+4)*ln(5)^2+(-2*x^3-8*x^2-8*x)*ln(5)-exp 
(5)+x^4+4*x^3+4*x^2))+(4*x^5+14*x^4+44*x^3+106*x^2+112*x+56)*ln(5)^2+(-8*x 
^6-24*x^5-72*x^4-168*x^3-112*x^2)*ln(5)+(-4*x^3-2*x^2-28*x-14)*exp(5)+4*x^ 
7+10*x^6+28*x^5+62*x^4-56*x^2)/((x^2+4*x+4)*ln(5)^2+(-2*x^3-8*x^2-8*x)*ln( 
5)-exp(5)+x^4+4*x^3+4*x^2),x)
 

Output:

x^4+x^2*ln(-5*x/((x^2+4*x+4)*ln(5)^2+(-2*x^3-8*x^2-8*x)*ln(5)-exp(5)+x^4+4 
*x^3+4*x^2))^2+14*x^2+14*x*ln(-5*x/((x^2+4*x+4)*ln(5)^2+(-2*x^3-8*x^2-8*x) 
*ln(5)-exp(5)+x^4+4*x^3+4*x^2))+2*x^3*ln(-5*x/((x^2+4*x+4)*ln(5)^2+(-2*x^3 
-8*x^2-8*x)*ln(5)-exp(5)+x^4+4*x^3+4*x^2))
 

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 130 vs. \(2 (33) = 66\).

Time = 0.08 (sec) , antiderivative size = 130, normalized size of antiderivative = 3.94 \[ \int \frac {-56 x^2+62 x^4+28 x^5+10 x^6+4 x^7+e^5 \left (-14-28 x-2 x^2-4 x^3\right )+\left (-112 x^2-168 x^3-72 x^4-24 x^5-8 x^6\right ) \log (5)+\left (56+112 x+106 x^2+44 x^3+14 x^4+4 x^5\right ) \log ^2(5)+\left (56 x^2+48 x^3+22 x^4+18 x^5+6 x^6+e^5 \left (-14-2 x-6 x^2\right )+\left (-112 x-112 x^2-60 x^3-40 x^4-12 x^5\right ) \log (5)+\left (56+64 x+38 x^2+22 x^3+6 x^4\right ) \log ^2(5)\right ) \log \left (-\frac {5 x}{-e^5+4 x^2+4 x^3+x^4+\left (-8 x-8 x^2-2 x^3\right ) \log (5)+\left (4+4 x+x^2\right ) \log ^2(5)}\right )+\left (-2 e^5 x+8 x^3+8 x^4+2 x^5+\left (-16 x^2-16 x^3-4 x^4\right ) \log (5)+\left (8 x+8 x^2+2 x^3\right ) \log ^2(5)\right ) \log ^2\left (-\frac {5 x}{-e^5+4 x^2+4 x^3+x^4+\left (-8 x-8 x^2-2 x^3\right ) \log (5)+\left (4+4 x+x^2\right ) \log ^2(5)}\right )}{-e^5+4 x^2+4 x^3+x^4+\left (-8 x-8 x^2-2 x^3\right ) \log (5)+\left (4+4 x+x^2\right ) \log ^2(5)} \, dx=x^{4} + x^{2} \log \left (-\frac {5 \, x}{x^{4} + 4 \, x^{3} + {\left (x^{2} + 4 \, x + 4\right )} \log \left (5\right )^{2} + 4 \, x^{2} - 2 \, {\left (x^{3} + 4 \, x^{2} + 4 \, x\right )} \log \left (5\right ) - e^{5}}\right )^{2} + 14 \, x^{2} + 2 \, {\left (x^{3} + 7 \, x\right )} \log \left (-\frac {5 \, x}{x^{4} + 4 \, x^{3} + {\left (x^{2} + 4 \, x + 4\right )} \log \left (5\right )^{2} + 4 \, x^{2} - 2 \, {\left (x^{3} + 4 \, x^{2} + 4 \, x\right )} \log \left (5\right ) - e^{5}}\right ) \] Input:

integrate((((2*x^3+8*x^2+8*x)*log(5)^2+(-4*x^4-16*x^3-16*x^2)*log(5)-2*x*e 
xp(5)+2*x^5+8*x^4+8*x^3)*log(-5*x/((x^2+4*x+4)*log(5)^2+(-2*x^3-8*x^2-8*x) 
*log(5)-exp(5)+x^4+4*x^3+4*x^2))^2+((6*x^4+22*x^3+38*x^2+64*x+56)*log(5)^2 
+(-12*x^5-40*x^4-60*x^3-112*x^2-112*x)*log(5)+(-6*x^2-2*x-14)*exp(5)+6*x^6 
+18*x^5+22*x^4+48*x^3+56*x^2)*log(-5*x/((x^2+4*x+4)*log(5)^2+(-2*x^3-8*x^2 
-8*x)*log(5)-exp(5)+x^4+4*x^3+4*x^2))+(4*x^5+14*x^4+44*x^3+106*x^2+112*x+5 
6)*log(5)^2+(-8*x^6-24*x^5-72*x^4-168*x^3-112*x^2)*log(5)+(-4*x^3-2*x^2-28 
*x-14)*exp(5)+4*x^7+10*x^6+28*x^5+62*x^4-56*x^2)/((x^2+4*x+4)*log(5)^2+(-2 
*x^3-8*x^2-8*x)*log(5)-exp(5)+x^4+4*x^3+4*x^2),x, algorithm="fricas")
 

Output:

x^4 + x^2*log(-5*x/(x^4 + 4*x^3 + (x^2 + 4*x + 4)*log(5)^2 + 4*x^2 - 2*(x^ 
3 + 4*x^2 + 4*x)*log(5) - e^5))^2 + 14*x^2 + 2*(x^3 + 7*x)*log(-5*x/(x^4 + 
 4*x^3 + (x^2 + 4*x + 4)*log(5)^2 + 4*x^2 - 2*(x^3 + 4*x^2 + 4*x)*log(5) - 
 e^5))
 

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 133 vs. \(2 (26) = 52\).

Time = 0.37 (sec) , antiderivative size = 133, normalized size of antiderivative = 4.03 \[ \int \frac {-56 x^2+62 x^4+28 x^5+10 x^6+4 x^7+e^5 \left (-14-28 x-2 x^2-4 x^3\right )+\left (-112 x^2-168 x^3-72 x^4-24 x^5-8 x^6\right ) \log (5)+\left (56+112 x+106 x^2+44 x^3+14 x^4+4 x^5\right ) \log ^2(5)+\left (56 x^2+48 x^3+22 x^4+18 x^5+6 x^6+e^5 \left (-14-2 x-6 x^2\right )+\left (-112 x-112 x^2-60 x^3-40 x^4-12 x^5\right ) \log (5)+\left (56+64 x+38 x^2+22 x^3+6 x^4\right ) \log ^2(5)\right ) \log \left (-\frac {5 x}{-e^5+4 x^2+4 x^3+x^4+\left (-8 x-8 x^2-2 x^3\right ) \log (5)+\left (4+4 x+x^2\right ) \log ^2(5)}\right )+\left (-2 e^5 x+8 x^3+8 x^4+2 x^5+\left (-16 x^2-16 x^3-4 x^4\right ) \log (5)+\left (8 x+8 x^2+2 x^3\right ) \log ^2(5)\right ) \log ^2\left (-\frac {5 x}{-e^5+4 x^2+4 x^3+x^4+\left (-8 x-8 x^2-2 x^3\right ) \log (5)+\left (4+4 x+x^2\right ) \log ^2(5)}\right )}{-e^5+4 x^2+4 x^3+x^4+\left (-8 x-8 x^2-2 x^3\right ) \log (5)+\left (4+4 x+x^2\right ) \log ^2(5)} \, dx=x^{4} + x^{2} \log {\left (- \frac {5 x}{x^{4} + 4 x^{3} + 4 x^{2} + \left (x^{2} + 4 x + 4\right ) \log {\left (5 \right )}^{2} + \left (- 2 x^{3} - 8 x^{2} - 8 x\right ) \log {\left (5 \right )} - e^{5}} \right )}^{2} + 14 x^{2} + \left (2 x^{3} + 14 x\right ) \log {\left (- \frac {5 x}{x^{4} + 4 x^{3} + 4 x^{2} + \left (x^{2} + 4 x + 4\right ) \log {\left (5 \right )}^{2} + \left (- 2 x^{3} - 8 x^{2} - 8 x\right ) \log {\left (5 \right )} - e^{5}} \right )} \] Input:

integrate((((2*x**3+8*x**2+8*x)*ln(5)**2+(-4*x**4-16*x**3-16*x**2)*ln(5)-2 
*x*exp(5)+2*x**5+8*x**4+8*x**3)*ln(-5*x/((x**2+4*x+4)*ln(5)**2+(-2*x**3-8* 
x**2-8*x)*ln(5)-exp(5)+x**4+4*x**3+4*x**2))**2+((6*x**4+22*x**3+38*x**2+64 
*x+56)*ln(5)**2+(-12*x**5-40*x**4-60*x**3-112*x**2-112*x)*ln(5)+(-6*x**2-2 
*x-14)*exp(5)+6*x**6+18*x**5+22*x**4+48*x**3+56*x**2)*ln(-5*x/((x**2+4*x+4 
)*ln(5)**2+(-2*x**3-8*x**2-8*x)*ln(5)-exp(5)+x**4+4*x**3+4*x**2))+(4*x**5+ 
14*x**4+44*x**3+106*x**2+112*x+56)*ln(5)**2+(-8*x**6-24*x**5-72*x**4-168*x 
**3-112*x**2)*ln(5)+(-4*x**3-2*x**2-28*x-14)*exp(5)+4*x**7+10*x**6+28*x**5 
+62*x**4-56*x**2)/((x**2+4*x+4)*ln(5)**2+(-2*x**3-8*x**2-8*x)*ln(5)-exp(5) 
+x**4+4*x**3+4*x**2),x)
 

Output:

x**4 + x**2*log(-5*x/(x**4 + 4*x**3 + 4*x**2 + (x**2 + 4*x + 4)*log(5)**2 
+ (-2*x**3 - 8*x**2 - 8*x)*log(5) - exp(5)))**2 + 14*x**2 + (2*x**3 + 14*x 
)*log(-5*x/(x**4 + 4*x**3 + 4*x**2 + (x**2 + 4*x + 4)*log(5)**2 + (-2*x**3 
 - 8*x**2 - 8*x)*log(5) - exp(5)))
 

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 180 vs. \(2 (33) = 66\).

Time = 0.14 (sec) , antiderivative size = 180, normalized size of antiderivative = 5.45 \[ \int \frac {-56 x^2+62 x^4+28 x^5+10 x^6+4 x^7+e^5 \left (-14-28 x-2 x^2-4 x^3\right )+\left (-112 x^2-168 x^3-72 x^4-24 x^5-8 x^6\right ) \log (5)+\left (56+112 x+106 x^2+44 x^3+14 x^4+4 x^5\right ) \log ^2(5)+\left (56 x^2+48 x^3+22 x^4+18 x^5+6 x^6+e^5 \left (-14-2 x-6 x^2\right )+\left (-112 x-112 x^2-60 x^3-40 x^4-12 x^5\right ) \log (5)+\left (56+64 x+38 x^2+22 x^3+6 x^4\right ) \log ^2(5)\right ) \log \left (-\frac {5 x}{-e^5+4 x^2+4 x^3+x^4+\left (-8 x-8 x^2-2 x^3\right ) \log (5)+\left (4+4 x+x^2\right ) \log ^2(5)}\right )+\left (-2 e^5 x+8 x^3+8 x^4+2 x^5+\left (-16 x^2-16 x^3-4 x^4\right ) \log (5)+\left (8 x+8 x^2+2 x^3\right ) \log ^2(5)\right ) \log ^2\left (-\frac {5 x}{-e^5+4 x^2+4 x^3+x^4+\left (-8 x-8 x^2-2 x^3\right ) \log (5)+\left (4+4 x+x^2\right ) \log ^2(5)}\right )}{-e^5+4 x^2+4 x^3+x^4+\left (-8 x-8 x^2-2 x^3\right ) \log (5)+\left (4+4 x+x^2\right ) \log ^2(5)} \, dx=x^{4} + 2 \, x^{3} \log \left (5\right ) + x^{2} \log \left (-x^{4} + 2 \, x^{3} {\left (\log \left (5\right ) - 2\right )} - {\left (\log \left (5\right )^{2} - 8 \, \log \left (5\right ) + 4\right )} x^{2} - 4 \, {\left (\log \left (5\right )^{2} - 2 \, \log \left (5\right )\right )} x - 4 \, \log \left (5\right )^{2} + e^{5}\right )^{2} + x^{2} \log \left (x\right )^{2} + {\left (\log \left (5\right )^{2} + 14\right )} x^{2} + 14 \, x \log \left (5\right ) - 2 \, {\left (x^{3} + x^{2} \log \left (5\right ) + x^{2} \log \left (x\right ) + 7 \, x\right )} \log \left (-x^{4} + 2 \, x^{3} {\left (\log \left (5\right ) - 2\right )} - {\left (\log \left (5\right )^{2} - 8 \, \log \left (5\right ) + 4\right )} x^{2} - 4 \, {\left (\log \left (5\right )^{2} - 2 \, \log \left (5\right )\right )} x - 4 \, \log \left (5\right )^{2} + e^{5}\right ) + 2 \, {\left (x^{3} + x^{2} \log \left (5\right ) + 7 \, x\right )} \log \left (x\right ) \] Input:

integrate((((2*x^3+8*x^2+8*x)*log(5)^2+(-4*x^4-16*x^3-16*x^2)*log(5)-2*x*e 
xp(5)+2*x^5+8*x^4+8*x^3)*log(-5*x/((x^2+4*x+4)*log(5)^2+(-2*x^3-8*x^2-8*x) 
*log(5)-exp(5)+x^4+4*x^3+4*x^2))^2+((6*x^4+22*x^3+38*x^2+64*x+56)*log(5)^2 
+(-12*x^5-40*x^4-60*x^3-112*x^2-112*x)*log(5)+(-6*x^2-2*x-14)*exp(5)+6*x^6 
+18*x^5+22*x^4+48*x^3+56*x^2)*log(-5*x/((x^2+4*x+4)*log(5)^2+(-2*x^3-8*x^2 
-8*x)*log(5)-exp(5)+x^4+4*x^3+4*x^2))+(4*x^5+14*x^4+44*x^3+106*x^2+112*x+5 
6)*log(5)^2+(-8*x^6-24*x^5-72*x^4-168*x^3-112*x^2)*log(5)+(-4*x^3-2*x^2-28 
*x-14)*exp(5)+4*x^7+10*x^6+28*x^5+62*x^4-56*x^2)/((x^2+4*x+4)*log(5)^2+(-2 
*x^3-8*x^2-8*x)*log(5)-exp(5)+x^4+4*x^3+4*x^2),x, algorithm="maxima")
 

Output:

x^4 + 2*x^3*log(5) + x^2*log(-x^4 + 2*x^3*(log(5) - 2) - (log(5)^2 - 8*log 
(5) + 4)*x^2 - 4*(log(5)^2 - 2*log(5))*x - 4*log(5)^2 + e^5)^2 + x^2*log(x 
)^2 + (log(5)^2 + 14)*x^2 + 14*x*log(5) - 2*(x^3 + x^2*log(5) + x^2*log(x) 
 + 7*x)*log(-x^4 + 2*x^3*(log(5) - 2) - (log(5)^2 - 8*log(5) + 4)*x^2 - 4* 
(log(5)^2 - 2*log(5))*x - 4*log(5)^2 + e^5) + 2*(x^3 + x^2*log(5) + 7*x)*l 
og(x)
 

Giac [F(-1)]

Timed out. \[ \int \frac {-56 x^2+62 x^4+28 x^5+10 x^6+4 x^7+e^5 \left (-14-28 x-2 x^2-4 x^3\right )+\left (-112 x^2-168 x^3-72 x^4-24 x^5-8 x^6\right ) \log (5)+\left (56+112 x+106 x^2+44 x^3+14 x^4+4 x^5\right ) \log ^2(5)+\left (56 x^2+48 x^3+22 x^4+18 x^5+6 x^6+e^5 \left (-14-2 x-6 x^2\right )+\left (-112 x-112 x^2-60 x^3-40 x^4-12 x^5\right ) \log (5)+\left (56+64 x+38 x^2+22 x^3+6 x^4\right ) \log ^2(5)\right ) \log \left (-\frac {5 x}{-e^5+4 x^2+4 x^3+x^4+\left (-8 x-8 x^2-2 x^3\right ) \log (5)+\left (4+4 x+x^2\right ) \log ^2(5)}\right )+\left (-2 e^5 x+8 x^3+8 x^4+2 x^5+\left (-16 x^2-16 x^3-4 x^4\right ) \log (5)+\left (8 x+8 x^2+2 x^3\right ) \log ^2(5)\right ) \log ^2\left (-\frac {5 x}{-e^5+4 x^2+4 x^3+x^4+\left (-8 x-8 x^2-2 x^3\right ) \log (5)+\left (4+4 x+x^2\right ) \log ^2(5)}\right )}{-e^5+4 x^2+4 x^3+x^4+\left (-8 x-8 x^2-2 x^3\right ) \log (5)+\left (4+4 x+x^2\right ) \log ^2(5)} \, dx=\text {Timed out} \] Input:

integrate((((2*x^3+8*x^2+8*x)*log(5)^2+(-4*x^4-16*x^3-16*x^2)*log(5)-2*x*e 
xp(5)+2*x^5+8*x^4+8*x^3)*log(-5*x/((x^2+4*x+4)*log(5)^2+(-2*x^3-8*x^2-8*x) 
*log(5)-exp(5)+x^4+4*x^3+4*x^2))^2+((6*x^4+22*x^3+38*x^2+64*x+56)*log(5)^2 
+(-12*x^5-40*x^4-60*x^3-112*x^2-112*x)*log(5)+(-6*x^2-2*x-14)*exp(5)+6*x^6 
+18*x^5+22*x^4+48*x^3+56*x^2)*log(-5*x/((x^2+4*x+4)*log(5)^2+(-2*x^3-8*x^2 
-8*x)*log(5)-exp(5)+x^4+4*x^3+4*x^2))+(4*x^5+14*x^4+44*x^3+106*x^2+112*x+5 
6)*log(5)^2+(-8*x^6-24*x^5-72*x^4-168*x^3-112*x^2)*log(5)+(-4*x^3-2*x^2-28 
*x-14)*exp(5)+4*x^7+10*x^6+28*x^5+62*x^4-56*x^2)/((x^2+4*x+4)*log(5)^2+(-2 
*x^3-8*x^2-8*x)*log(5)-exp(5)+x^4+4*x^3+4*x^2),x, algorithm="giac")
 

Output:

Timed out
 

Mupad [B] (verification not implemented)

Time = 3.08 (sec) , antiderivative size = 135, normalized size of antiderivative = 4.09 \[ \int \frac {-56 x^2+62 x^4+28 x^5+10 x^6+4 x^7+e^5 \left (-14-28 x-2 x^2-4 x^3\right )+\left (-112 x^2-168 x^3-72 x^4-24 x^5-8 x^6\right ) \log (5)+\left (56+112 x+106 x^2+44 x^3+14 x^4+4 x^5\right ) \log ^2(5)+\left (56 x^2+48 x^3+22 x^4+18 x^5+6 x^6+e^5 \left (-14-2 x-6 x^2\right )+\left (-112 x-112 x^2-60 x^3-40 x^4-12 x^5\right ) \log (5)+\left (56+64 x+38 x^2+22 x^3+6 x^4\right ) \log ^2(5)\right ) \log \left (-\frac {5 x}{-e^5+4 x^2+4 x^3+x^4+\left (-8 x-8 x^2-2 x^3\right ) \log (5)+\left (4+4 x+x^2\right ) \log ^2(5)}\right )+\left (-2 e^5 x+8 x^3+8 x^4+2 x^5+\left (-16 x^2-16 x^3-4 x^4\right ) \log (5)+\left (8 x+8 x^2+2 x^3\right ) \log ^2(5)\right ) \log ^2\left (-\frac {5 x}{-e^5+4 x^2+4 x^3+x^4+\left (-8 x-8 x^2-2 x^3\right ) \log (5)+\left (4+4 x+x^2\right ) \log ^2(5)}\right )}{-e^5+4 x^2+4 x^3+x^4+\left (-8 x-8 x^2-2 x^3\right ) \log (5)+\left (4+4 x+x^2\right ) \log ^2(5)} \, dx=x^2\,{\ln \left (-\frac {5\,x}{{\ln \left (5\right )}^2\,\left (x^2+4\,x+4\right )-{\mathrm {e}}^5-\ln \left (5\right )\,\left (2\,x^3+8\,x^2+8\,x\right )+4\,x^2+4\,x^3+x^4}\right )}^2+\ln \left (-\frac {5\,x}{{\ln \left (5\right )}^2\,\left (x^2+4\,x+4\right )-{\mathrm {e}}^5-\ln \left (5\right )\,\left (2\,x^3+8\,x^2+8\,x\right )+4\,x^2+4\,x^3+x^4}\right )\,\left (2\,x^3+14\,x\right )+14\,x^2+x^4 \] Input:

int((log(5)^2*(112*x + 106*x^2 + 44*x^3 + 14*x^4 + 4*x^5 + 56) - log(5)*(1 
12*x^2 + 168*x^3 + 72*x^4 + 24*x^5 + 8*x^6) + log(-(5*x)/(log(5)^2*(4*x + 
x^2 + 4) - exp(5) - log(5)*(8*x + 8*x^2 + 2*x^3) + 4*x^2 + 4*x^3 + x^4))^2 
*(log(5)^2*(8*x + 8*x^2 + 2*x^3) - 2*x*exp(5) - log(5)*(16*x^2 + 16*x^3 + 
4*x^4) + 8*x^3 + 8*x^4 + 2*x^5) - exp(5)*(28*x + 2*x^2 + 4*x^3 + 14) + log 
(-(5*x)/(log(5)^2*(4*x + x^2 + 4) - exp(5) - log(5)*(8*x + 8*x^2 + 2*x^3) 
+ 4*x^2 + 4*x^3 + x^4))*(log(5)^2*(64*x + 38*x^2 + 22*x^3 + 6*x^4 + 56) - 
exp(5)*(2*x + 6*x^2 + 14) + 56*x^2 + 48*x^3 + 22*x^4 + 18*x^5 + 6*x^6 - lo 
g(5)*(112*x + 112*x^2 + 60*x^3 + 40*x^4 + 12*x^5)) - 56*x^2 + 62*x^4 + 28* 
x^5 + 10*x^6 + 4*x^7)/(log(5)^2*(4*x + x^2 + 4) - exp(5) - log(5)*(8*x + 8 
*x^2 + 2*x^3) + 4*x^2 + 4*x^3 + x^4),x)
 

Output:

x^2*log(-(5*x)/(log(5)^2*(4*x + x^2 + 4) - exp(5) - log(5)*(8*x + 8*x^2 + 
2*x^3) + 4*x^2 + 4*x^3 + x^4))^2 + log(-(5*x)/(log(5)^2*(4*x + x^2 + 4) - 
exp(5) - log(5)*(8*x + 8*x^2 + 2*x^3) + 4*x^2 + 4*x^3 + x^4))*(14*x + 2*x^ 
3) + 14*x^2 + x^4
 

Reduce [F]

\[ \int \frac {-56 x^2+62 x^4+28 x^5+10 x^6+4 x^7+e^5 \left (-14-28 x-2 x^2-4 x^3\right )+\left (-112 x^2-168 x^3-72 x^4-24 x^5-8 x^6\right ) \log (5)+\left (56+112 x+106 x^2+44 x^3+14 x^4+4 x^5\right ) \log ^2(5)+\left (56 x^2+48 x^3+22 x^4+18 x^5+6 x^6+e^5 \left (-14-2 x-6 x^2\right )+\left (-112 x-112 x^2-60 x^3-40 x^4-12 x^5\right ) \log (5)+\left (56+64 x+38 x^2+22 x^3+6 x^4\right ) \log ^2(5)\right ) \log \left (-\frac {5 x}{-e^5+4 x^2+4 x^3+x^4+\left (-8 x-8 x^2-2 x^3\right ) \log (5)+\left (4+4 x+x^2\right ) \log ^2(5)}\right )+\left (-2 e^5 x+8 x^3+8 x^4+2 x^5+\left (-16 x^2-16 x^3-4 x^4\right ) \log (5)+\left (8 x+8 x^2+2 x^3\right ) \log ^2(5)\right ) \log ^2\left (-\frac {5 x}{-e^5+4 x^2+4 x^3+x^4+\left (-8 x-8 x^2-2 x^3\right ) \log (5)+\left (4+4 x+x^2\right ) \log ^2(5)}\right )}{-e^5+4 x^2+4 x^3+x^4+\left (-8 x-8 x^2-2 x^3\right ) \log (5)+\left (4+4 x+x^2\right ) \log ^2(5)} \, dx=\int \frac {\left (\left (2 x^{3}+8 x^{2}+8 x \right ) \mathrm {log}\left (5\right )^{2}+\left (-4 x^{4}-16 x^{3}-16 x^{2}\right ) \mathrm {log}\left (5\right )-2 x \,{\mathrm e}^{5}+2 x^{5}+8 x^{4}+8 x^{3}\right ) {\mathrm {log}\left (-\frac {5 x}{\left (x^{2}+4 x +4\right ) \mathrm {log}\left (5\right )^{2}+\left (-2 x^{3}-8 x^{2}-8 x \right ) \mathrm {log}\left (5\right )-{\mathrm e}^{5}+x^{4}+4 x^{3}+4 x^{2}}\right )}^{2}+\left (\left (6 x^{4}+22 x^{3}+38 x^{2}+64 x +56\right ) \mathrm {log}\left (5\right )^{2}+\left (-12 x^{5}-40 x^{4}-60 x^{3}-112 x^{2}-112 x \right ) \mathrm {log}\left (5\right )+\left (-6 x^{2}-2 x -14\right ) {\mathrm e}^{5}+6 x^{6}+18 x^{5}+22 x^{4}+48 x^{3}+56 x^{2}\right ) \mathrm {log}\left (-\frac {5 x}{\left (x^{2}+4 x +4\right ) \mathrm {log}\left (5\right )^{2}+\left (-2 x^{3}-8 x^{2}-8 x \right ) \mathrm {log}\left (5\right )-{\mathrm e}^{5}+x^{4}+4 x^{3}+4 x^{2}}\right )+\left (4 x^{5}+14 x^{4}+44 x^{3}+106 x^{2}+112 x +56\right ) \mathrm {log}\left (5\right )^{2}+\left (-8 x^{6}-24 x^{5}-72 x^{4}-168 x^{3}-112 x^{2}\right ) \mathrm {log}\left (5\right )+\left (-4 x^{3}-2 x^{2}-28 x -14\right ) {\mathrm e}^{5}+4 x^{7}+10 x^{6}+28 x^{5}+62 x^{4}-56 x^{2}}{\left (x^{2}+4 x +4\right ) \mathrm {log}\left (5\right )^{2}+\left (-2 x^{3}-8 x^{2}-8 x \right ) \mathrm {log}\left (5\right )-{\mathrm e}^{5}+x^{4}+4 x^{3}+4 x^{2}}d x \] Input:

int((((2*x^3+8*x^2+8*x)*log(5)^2+(-4*x^4-16*x^3-16*x^2)*log(5)-2*x*exp(5)+ 
2*x^5+8*x^4+8*x^3)*log(-5*x/((x^2+4*x+4)*log(5)^2+(-2*x^3-8*x^2-8*x)*log(5 
)-exp(5)+x^4+4*x^3+4*x^2))^2+((6*x^4+22*x^3+38*x^2+64*x+56)*log(5)^2+(-12* 
x^5-40*x^4-60*x^3-112*x^2-112*x)*log(5)+(-6*x^2-2*x-14)*exp(5)+6*x^6+18*x^ 
5+22*x^4+48*x^3+56*x^2)*log(-5*x/((x^2+4*x+4)*log(5)^2+(-2*x^3-8*x^2-8*x)* 
log(5)-exp(5)+x^4+4*x^3+4*x^2))+(4*x^5+14*x^4+44*x^3+106*x^2+112*x+56)*log 
(5)^2+(-8*x^6-24*x^5-72*x^4-168*x^3-112*x^2)*log(5)+(-4*x^3-2*x^2-28*x-14) 
*exp(5)+4*x^7+10*x^6+28*x^5+62*x^4-56*x^2)/((x^2+4*x+4)*log(5)^2+(-2*x^3-8 
*x^2-8*x)*log(5)-exp(5)+x^4+4*x^3+4*x^2),x)
 

Output:

int((((2*x^3+8*x^2+8*x)*log(5)^2+(-4*x^4-16*x^3-16*x^2)*log(5)-2*x*exp(5)+ 
2*x^5+8*x^4+8*x^3)*log(-5*x/((x^2+4*x+4)*log(5)^2+(-2*x^3-8*x^2-8*x)*log(5 
)-exp(5)+x^4+4*x^3+4*x^2))^2+((6*x^4+22*x^3+38*x^2+64*x+56)*log(5)^2+(-12* 
x^5-40*x^4-60*x^3-112*x^2-112*x)*log(5)+(-6*x^2-2*x-14)*exp(5)+6*x^6+18*x^ 
5+22*x^4+48*x^3+56*x^2)*log(-5*x/((x^2+4*x+4)*log(5)^2+(-2*x^3-8*x^2-8*x)* 
log(5)-exp(5)+x^4+4*x^3+4*x^2))+(4*x^5+14*x^4+44*x^3+106*x^2+112*x+56)*log 
(5)^2+(-8*x^6-24*x^5-72*x^4-168*x^3-112*x^2)*log(5)+(-4*x^3-2*x^2-28*x-14) 
*exp(5)+4*x^7+10*x^6+28*x^5+62*x^4-56*x^2)/((x^2+4*x+4)*log(5)^2+(-2*x^3-8 
*x^2-8*x)*log(5)-exp(5)+x^4+4*x^3+4*x^2),x)