\(\int \frac {-486 x-486 x^2+324 x^3+468 x^4+162 x^5+18 x^6+(162 x+324 x^2+216 x^3+60 x^4+6 x^5) \log (5)+(648 x^4+648 x^5+216 x^6+24 x^7) \log (\frac {1}{2} (3-3 x-\log (5)))+(-1296 x^3-324 x^4+972 x^5+564 x^6+84 x^7+(432 x^3+540 x^4+216 x^5+28 x^6) \log (5)) \log ^2(\frac {1}{2} (3-3 x-\log (5)))+(648 x^6+432 x^7+72 x^8) \log ^3(\frac {1}{2} (3-3 x-\log (5)))+(-972 x^5+216 x^6+612 x^7+144 x^8+(324 x^5+252 x^6+48 x^7) \log (5)) \log ^4(\frac {1}{2} (3-3 x-\log (5)))+(216 x^8+72 x^9) \log ^5(\frac {1}{2} (3-3 x-\log (5)))+(-288 x^7+180 x^8+108 x^9+(96 x^7+36 x^8) \log (5)) \log ^6(\frac {1}{2} (3-3 x-\log (5)))+24 x^{10} \log ^7(\frac {1}{2} (3-3 x-\log (5)))+(-30 x^9+30 x^{10}+10 x^9 \log (5)) \log ^8(\frac {1}{2} (3-3 x-\log (5)))}{-3+3 x+\log (5)} \, dx\) [99]

Optimal result

Integrand size = 390, antiderivative size = 33 \[ \int \frac {-486 x-486 x^2+324 x^3+468 x^4+162 x^5+18 x^6+\left (162 x+324 x^2+216 x^3+60 x^4+6 x^5\right ) \log (5)+\left (648 x^4+648 x^5+216 x^6+24 x^7\right ) \log \left (\frac {1}{2} (3-3 x-\log (5))\right )+\left (-1296 x^3-324 x^4+972 x^5+564 x^6+84 x^7+\left (432 x^3+540 x^4+216 x^5+28 x^6\right ) \log (5)\right ) \log ^2\left (\frac {1}{2} (3-3 x-\log (5))\right )+\left (648 x^6+432 x^7+72 x^8\right ) \log ^3\left (\frac {1}{2} (3-3 x-\log (5))\right )+\left (-972 x^5+216 x^6+612 x^7+144 x^8+\left (324 x^5+252 x^6+48 x^7\right ) \log (5)\right ) \log ^4\left (\frac {1}{2} (3-3 x-\log (5))\right )+\left (216 x^8+72 x^9\right ) \log ^5\left (\frac {1}{2} (3-3 x-\log (5))\right )+\left (-288 x^7+180 x^8+108 x^9+\left (96 x^7+36 x^8\right ) \log (5)\right ) \log ^6\left (\frac {1}{2} (3-3 x-\log (5))\right )+24 x^{10} \log ^7\left (\frac {1}{2} (3-3 x-\log (5))\right )+\left (-30 x^9+30 x^{10}+10 x^9 \log (5)\right ) \log ^8\left (\frac {1}{2} (3-3 x-\log (5))\right )}{-3+3 x+\log (5)} \, dx=x^2 \left (3+x+x^2 \log ^2\left (-x+\frac {1}{2} (3-x-\log (5))\right )\right )^4 \] Output:

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

Mathematica [B] (verified)

Leaf count is larger than twice the leaf count of optimal. \(14593\) vs. \(2(33)=66\).

Time = 26.95 (sec) , antiderivative size = 14593, normalized size of antiderivative = 442.21 \[ \int \frac {-486 x-486 x^2+324 x^3+468 x^4+162 x^5+18 x^6+\left (162 x+324 x^2+216 x^3+60 x^4+6 x^5\right ) \log (5)+\left (648 x^4+648 x^5+216 x^6+24 x^7\right ) \log \left (\frac {1}{2} (3-3 x-\log (5))\right )+\left (-1296 x^3-324 x^4+972 x^5+564 x^6+84 x^7+\left (432 x^3+540 x^4+216 x^5+28 x^6\right ) \log (5)\right ) \log ^2\left (\frac {1}{2} (3-3 x-\log (5))\right )+\left (648 x^6+432 x^7+72 x^8\right ) \log ^3\left (\frac {1}{2} (3-3 x-\log (5))\right )+\left (-972 x^5+216 x^6+612 x^7+144 x^8+\left (324 x^5+252 x^6+48 x^7\right ) \log (5)\right ) \log ^4\left (\frac {1}{2} (3-3 x-\log (5))\right )+\left (216 x^8+72 x^9\right ) \log ^5\left (\frac {1}{2} (3-3 x-\log (5))\right )+\left (-288 x^7+180 x^8+108 x^9+\left (96 x^7+36 x^8\right ) \log (5)\right ) \log ^6\left (\frac {1}{2} (3-3 x-\log (5))\right )+24 x^{10} \log ^7\left (\frac {1}{2} (3-3 x-\log (5))\right )+\left (-30 x^9+30 x^{10}+10 x^9 \log (5)\right ) \log ^8\left (\frac {1}{2} (3-3 x-\log (5))\right )}{-3+3 x+\log (5)} \, dx=\text {Result too large to show} \] Input:

Integrate[(-486*x - 486*x^2 + 324*x^3 + 468*x^4 + 162*x^5 + 18*x^6 + (162* 
x + 324*x^2 + 216*x^3 + 60*x^4 + 6*x^5)*Log[5] + (648*x^4 + 648*x^5 + 216* 
x^6 + 24*x^7)*Log[(3 - 3*x - Log[5])/2] + (-1296*x^3 - 324*x^4 + 972*x^5 + 
 564*x^6 + 84*x^7 + (432*x^3 + 540*x^4 + 216*x^5 + 28*x^6)*Log[5])*Log[(3 
- 3*x - Log[5])/2]^2 + (648*x^6 + 432*x^7 + 72*x^8)*Log[(3 - 3*x - Log[5]) 
/2]^3 + (-972*x^5 + 216*x^6 + 612*x^7 + 144*x^8 + (324*x^5 + 252*x^6 + 48* 
x^7)*Log[5])*Log[(3 - 3*x - Log[5])/2]^4 + (216*x^8 + 72*x^9)*Log[(3 - 3*x 
 - Log[5])/2]^5 + (-288*x^7 + 180*x^8 + 108*x^9 + (96*x^7 + 36*x^8)*Log[5] 
)*Log[(3 - 3*x - Log[5])/2]^6 + 24*x^10*Log[(3 - 3*x - Log[5])/2]^7 + (-30 
*x^9 + 30*x^10 + 10*x^9*Log[5])*Log[(3 - 3*x - Log[5])/2]^8)/(-3 + 3*x + L 
og[5]),x]
 

Output:

Result too large to show
 

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.

\(\displaystyle \int \frac {24 x^{10} \log ^7\left (\frac {1}{2} (-3 x+3-\log (5))\right )+18 x^6+162 x^5+468 x^4+324 x^3-486 x^2+\left (30 x^{10}-30 x^9+10 x^9 \log (5)\right ) \log ^8\left (\frac {1}{2} (-3 x+3-\log (5))\right )+\left (72 x^9+216 x^8\right ) \log ^5\left (\frac {1}{2} (-3 x+3-\log (5))\right )+\left (108 x^9+180 x^8-288 x^7+\left (36 x^8+96 x^7\right ) \log (5)\right ) \log ^6\left (\frac {1}{2} (-3 x+3-\log (5))\right )+\left (72 x^8+432 x^7+648 x^6\right ) \log ^3\left (\frac {1}{2} (-3 x+3-\log (5))\right )+\left (144 x^8+612 x^7+216 x^6-972 x^5+\left (48 x^7+252 x^6+324 x^5\right ) \log (5)\right ) \log ^4\left (\frac {1}{2} (-3 x+3-\log (5))\right )+\left (24 x^7+216 x^6+648 x^5+648 x^4\right ) \log \left (\frac {1}{2} (-3 x+3-\log (5))\right )+\left (6 x^5+60 x^4+216 x^3+324 x^2+162 x\right ) \log (5)+\left (84 x^7+564 x^6+972 x^5-324 x^4-1296 x^3+\left (28 x^6+216 x^5+540 x^4+432 x^3\right ) \log (5)\right ) \log ^2\left (\frac {1}{2} (-3 x+3-\log (5))\right )-486 x}{3 x-3+\log (5)} \, dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {2 x \left (x^2 \log ^2\left (\frac {1}{2} (-3 x+3-\log (5))\right )+x+3\right )^3 \left (-12 x^3 \log \left (\frac {1}{2} (-3 x+3-\log (5))\right )-5 x^2 (3 x-3+\log (5)) \log ^2\left (\frac {1}{2} (-3 x+3-\log (5))\right )-3 (x+1) (3 x-3+\log (5))\right )}{-3 x+3-\log (5)}dx\)

\(\Big \downarrow \) 27

\(\displaystyle 2 \int \frac {x \left (x^2 \log ^2\left (\frac {1}{2} (-3 x-\log (5)+3)\right )+x+3\right )^3 \left (-12 \log \left (\frac {1}{2} (-3 x-\log (5)+3)\right ) x^3+5 (-3 x-\log (5)+3) \log ^2\left (\frac {1}{2} (-3 x-\log (5)+3)\right ) x^2+3 (x+1) (-3 x-\log (5)+3)\right )}{-3 x-\log (5)+3}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle 2 \int \left (\frac {12 \log ^7\left (\frac {1}{2} (3-\log (5))-\frac {3 x}{2}\right ) x^{10}}{3 x+\log (5)-3}+5 \log ^8\left (\frac {1}{2} (3-\log (5))-\frac {3 x}{2}\right ) x^9+\frac {36 (-x-3) \log ^5\left (\frac {1}{2} (3-\log (5))-\frac {3 x}{2}\right ) x^8}{-3 x-\log (5)+3}+6 (3 x+8) \log ^6\left (\frac {1}{2} (3-\log (5))-\frac {3 x}{2}\right ) x^7+\frac {36 (x+3)^2 \log ^3\left (\frac {1}{2} (3-\log (5))-\frac {3 x}{2}\right ) x^6}{3 x+\log (5)-3}+6 \left (4 x^2+21 x+27\right ) \log ^4\left (\frac {1}{2} (3-\log (5))-\frac {3 x}{2}\right ) x^5+\frac {12 (-x-3)^3 \log \left (\frac {1}{2} (3-\log (5))-\frac {3 x}{2}\right ) x^4}{-3 x-\log (5)+3}+2 (x+3)^2 (7 x+12) \log ^2\left (\frac {1}{2} (3-\log (5))-\frac {3 x}{2}\right ) x^3+3 (x+1) (x+3)^3 x\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle 2 \int \frac {x \left (x^2 \log ^2\left (\frac {1}{2} (-3 x-\log (5)+3)\right )+x+3\right )^3 \left (-12 \log \left (\frac {1}{2} (-3 x-\log (5)+3)\right ) x^3-5 (3 x+\log (5)-3) \log ^2\left (\frac {1}{2} (-3 x-\log (5)+3)\right ) x^2-9 x^2-3 \log (5) x+9 \left (1-\frac {\log (5)}{3}\right )\right )}{-3 x-\log (5)+3}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle 2 \int \left (\frac {12 \log ^7\left (\frac {1}{2} (3-\log (5))-\frac {3 x}{2}\right ) x^{10}}{3 x+\log (5)-3}+5 \log ^8\left (\frac {1}{2} (3-\log (5))-\frac {3 x}{2}\right ) x^9+\frac {36 (-x-3) \log ^5\left (\frac {1}{2} (3-\log (5))-\frac {3 x}{2}\right ) x^8}{-3 x-\log (5)+3}+6 (3 x+8) \log ^6\left (\frac {1}{2} (3-\log (5))-\frac {3 x}{2}\right ) x^7+\frac {36 (x+3)^2 \log ^3\left (\frac {1}{2} (3-\log (5))-\frac {3 x}{2}\right ) x^6}{3 x+\log (5)-3}+\frac {9 x^6}{3 x+\log (5)-3}+6 \left (4 x^2+21 x+27\right ) \log ^4\left (\frac {1}{2} (3-\log (5))-\frac {3 x}{2}\right ) x^5+\frac {81 \left (1+\frac {\log (5)}{27}\right ) x^5}{3 x+\log (5)-3}+\frac {12 (-x-3)^3 \log \left (\frac {1}{2} (3-\log (5))-\frac {3 x}{2}\right ) x^4}{-3 x-\log (5)+3}+\frac {243 \left (1+\frac {1}{81} (-3+10 \log (5))\right ) x^4}{3 x+\log (5)-3}+2 (x+3)^2 (7 x+12) \log ^2\left (\frac {1}{2} (3-\log (5))-\frac {3 x}{2}\right ) x^3+\frac {243 \left (1+\frac {1}{9} (-3+\log (625))\right ) x^3}{3 x+\log (5)-3}+\frac {81 (-3+\log (5)) \left (1+\frac {\log (5)}{-3+\log (5)}\right ) x^2}{3 x+\log (5)-3}+\frac {81 (-3+\log (5)) x}{3 x+\log (5)-3}\right )dx\)

\(\Big \downarrow \) 7292

\(\displaystyle 2 \int \left (\frac {12 \log ^7\left (\frac {1}{2} (3-\log (5))-\frac {3 x}{2}\right ) x^{10}}{3 x+\log (5)-3}+5 \log ^8\left (\frac {1}{2} (3-\log (5))-\frac {3 x}{2}\right ) x^9+\frac {36 (-x-3) \log ^5\left (\frac {1}{2} (3-\log (5))-\frac {3 x}{2}\right ) x^8}{-3 x-\log (5)+3}+6 (3 x+8) \log ^6\left (\frac {1}{2} (3-\log (5))-\frac {3 x}{2}\right ) x^7+\frac {36 (x+3)^2 \log ^3\left (\frac {1}{2} (3-\log (5))-\frac {3 x}{2}\right ) x^6}{3 x+\log (5)-3}+\frac {9 x^6}{3 x+\log (5)-3}+6 \left (4 x^2+21 x+27\right ) \log ^4\left (\frac {1}{2} (3-\log (5))-\frac {3 x}{2}\right ) x^5+\frac {3 (27+\log (5)) x^5}{3 x+\log (5)-3}+\frac {12 (-x-3)^3 \log \left (\frac {1}{2} (3-\log (5))-\frac {3 x}{2}\right ) x^4}{-3 x-\log (5)+3}+\frac {6 (39+5 \log (5)) x^4}{3 x+\log (5)-3}+2 (x+3)^2 (7 x+12) \log ^2\left (\frac {1}{2} (3-\log (5))-\frac {3 x}{2}\right ) x^3+\frac {54 (3+\log (25)) x^3}{3 x+\log (5)-3}+\frac {81 (-3+\log (5)) \left (1-\frac {\log (5)}{3-\log (5)}\right ) x^2}{3 x+\log (5)-3}+\frac {81 (-3+\log (5)) x}{3 x+\log (5)-3}\right )dx\)

\(\Big \downarrow \) 7292

\(\displaystyle 2 \int \left (\frac {12 \log ^7\left (\frac {1}{2} (3-\log (5))-\frac {3 x}{2}\right ) x^{10}}{3 x+\log (5)-3}+5 \log ^8\left (\frac {1}{2} (3-\log (5))-\frac {3 x}{2}\right ) x^9+\frac {36 (-x-3) \log ^5\left (\frac {1}{2} (3-\log (5))-\frac {3 x}{2}\right ) x^8}{-3 x-\log (5)+3}+6 (3 x+8) \log ^6\left (\frac {1}{2} (3-\log (5))-\frac {3 x}{2}\right ) x^7+\frac {36 (x+3)^2 \log ^3\left (\frac {1}{2} (3-\log (5))-\frac {3 x}{2}\right ) x^6}{3 x+\log (5)-3}+\frac {9 x^6}{3 x+\log (5)-3}+6 \left (4 x^2+21 x+27\right ) \log ^4\left (\frac {1}{2} (3-\log (5))-\frac {3 x}{2}\right ) x^5+\frac {3 (27+\log (5)) x^5}{3 x+\log (5)-3}+\frac {12 (-x-3)^3 \log \left (\frac {1}{2} (3-\log (5))-\frac {3 x}{2}\right ) x^4}{-3 x-\log (5)+3}+\frac {6 (39+5 \log (5)) x^4}{3 x+\log (5)-3}+2 (x+3)^2 (7 x+12) \log ^2\left (\frac {1}{2} (3-\log (5))-\frac {3 x}{2}\right ) x^3+\frac {54 (3+\log (25)) x^3}{3 x+\log (5)-3}+\frac {81 (-3+\log (5)) (3-\log (25)) x^2}{(3-\log (5)) (3 x+\log (5)-3)}+\frac {81 (-3+\log (5)) x}{3 x+\log (5)-3}\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle 2 \int \left (\frac {12 \log ^7\left (\frac {1}{2} (3-\log (5))-\frac {3 x}{2}\right ) x^{10}}{3 x+\log (5)-3}+5 \log ^8\left (\frac {1}{2} (3-\log (5))-\frac {3 x}{2}\right ) x^9+\frac {36 (-x-3) \log ^5\left (\frac {1}{2} (3-\log (5))-\frac {3 x}{2}\right ) x^8}{-3 x-\log (5)+3}+6 (3 x+8) \log ^6\left (\frac {1}{2} (3-\log (5))-\frac {3 x}{2}\right ) x^7+\frac {36 (x+3)^2 \log ^3\left (\frac {1}{2} (3-\log (5))-\frac {3 x}{2}\right ) x^6}{3 x+\log (5)-3}+\frac {9 x^6}{3 x+\log (5)-3}+6 \left (4 x^2+21 x+27\right ) \log ^4\left (\frac {1}{2} (3-\log (5))-\frac {3 x}{2}\right ) x^5+\frac {3 (27+\log (5)) x^5}{3 x+\log (5)-3}+\frac {12 (-x-3)^3 \log \left (\frac {1}{2} (3-\log (5))-\frac {3 x}{2}\right ) x^4}{-3 x-\log (5)+3}+\frac {6 (39+5 \log (5)) x^4}{3 x+\log (5)-3}+2 (x+3)^2 (7 x+12) \log ^2\left (\frac {1}{2} (3-\log (5))-\frac {3 x}{2}\right ) x^3+\frac {54 (3+\log (25)) x^3}{3 x+\log (5)-3}+\frac {81 (-3+\log (25)) x^2}{3 x+\log (5)-3}+\frac {81 (-3+\log (5)) x}{3 x+\log (5)-3}\right )dx\)

\(\Big \downarrow \) 7299

\(\displaystyle 2 \int \left (\frac {12 \log ^7\left (\frac {1}{2} (3-\log (5))-\frac {3 x}{2}\right ) x^{10}}{3 x+\log (5)-3}+5 \log ^8\left (\frac {1}{2} (3-\log (5))-\frac {3 x}{2}\right ) x^9+\frac {36 (-x-3) \log ^5\left (\frac {1}{2} (3-\log (5))-\frac {3 x}{2}\right ) x^8}{-3 x-\log (5)+3}+6 (3 x+8) \log ^6\left (\frac {1}{2} (3-\log (5))-\frac {3 x}{2}\right ) x^7+\frac {36 (x+3)^2 \log ^3\left (\frac {1}{2} (3-\log (5))-\frac {3 x}{2}\right ) x^6}{3 x+\log (5)-3}+\frac {9 x^6}{3 x+\log (5)-3}+6 \left (4 x^2+21 x+27\right ) \log ^4\left (\frac {1}{2} (3-\log (5))-\frac {3 x}{2}\right ) x^5+\frac {3 (27+\log (5)) x^5}{3 x+\log (5)-3}+\frac {12 (-x-3)^3 \log \left (\frac {1}{2} (3-\log (5))-\frac {3 x}{2}\right ) x^4}{-3 x-\log (5)+3}+\frac {6 (39+5 \log (5)) x^4}{3 x+\log (5)-3}+2 (x+3)^2 (7 x+12) \log ^2\left (\frac {1}{2} (3-\log (5))-\frac {3 x}{2}\right ) x^3+\frac {54 (3+\log (25)) x^3}{3 x+\log (5)-3}+\frac {81 (-3+\log (25)) x^2}{3 x+\log (5)-3}+\frac {81 (-3+\log (5)) x}{3 x+\log (5)-3}\right )dx\)

Input:

Int[(-486*x - 486*x^2 + 324*x^3 + 468*x^4 + 162*x^5 + 18*x^6 + (162*x + 32 
4*x^2 + 216*x^3 + 60*x^4 + 6*x^5)*Log[5] + (648*x^4 + 648*x^5 + 216*x^6 + 
24*x^7)*Log[(3 - 3*x - Log[5])/2] + (-1296*x^3 - 324*x^4 + 972*x^5 + 564*x 
^6 + 84*x^7 + (432*x^3 + 540*x^4 + 216*x^5 + 28*x^6)*Log[5])*Log[(3 - 3*x 
- Log[5])/2]^2 + (648*x^6 + 432*x^7 + 72*x^8)*Log[(3 - 3*x - Log[5])/2]^3 
+ (-972*x^5 + 216*x^6 + 612*x^7 + 144*x^8 + (324*x^5 + 252*x^6 + 48*x^7)*L 
og[5])*Log[(3 - 3*x - Log[5])/2]^4 + (216*x^8 + 72*x^9)*Log[(3 - 3*x - Log 
[5])/2]^5 + (-288*x^7 + 180*x^8 + 108*x^9 + (96*x^7 + 36*x^8)*Log[5])*Log[ 
(3 - 3*x - Log[5])/2]^6 + 24*x^10*Log[(3 - 3*x - Log[5])/2]^7 + (-30*x^9 + 
 30*x^10 + 10*x^9*Log[5])*Log[(3 - 3*x - Log[5])/2]^8)/(-3 + 3*x + Log[5]) 
,x]
 

Output:

$Aborted
 

Maple [B] (verified)

Leaf count of result is larger than twice the leaf count of optimal. \(2355\) vs. \(2(25)=50\).

Time = 0.07 (sec) , antiderivative size = 2356, normalized size of antiderivative = 71.39

\[\text {Expression too large to display}\]

Input:

int(((10*x^9*ln(5)+30*x^10-30*x^9)*ln(-1/2*ln(5)-3/2*x+3/2)^8+24*x^10*ln(- 
1/2*ln(5)-3/2*x+3/2)^7+((36*x^8+96*x^7)*ln(5)+108*x^9+180*x^8-288*x^7)*ln( 
-1/2*ln(5)-3/2*x+3/2)^6+(72*x^9+216*x^8)*ln(-1/2*ln(5)-3/2*x+3/2)^5+((48*x 
^7+252*x^6+324*x^5)*ln(5)+144*x^8+612*x^7+216*x^6-972*x^5)*ln(-1/2*ln(5)-3 
/2*x+3/2)^4+(72*x^8+432*x^7+648*x^6)*ln(-1/2*ln(5)-3/2*x+3/2)^3+((28*x^6+2 
16*x^5+540*x^4+432*x^3)*ln(5)+84*x^7+564*x^6+972*x^5-324*x^4-1296*x^3)*ln( 
-1/2*ln(5)-3/2*x+3/2)^2+(24*x^7+216*x^6+648*x^5+648*x^4)*ln(-1/2*ln(5)-3/2 
*x+3/2)+(6*x^5+60*x^4+216*x^3+324*x^2+162*x)*ln(5)+18*x^6+162*x^5+468*x^4+ 
324*x^3-486*x^2-486*x)/(ln(5)+3*x-3),x)
 

Output:

-256+2/27*ln(5)^5-32*ln(5)*ln(-1/2*ln(5)-3/2*x+3/2)^6*x^7-84*ln(5)*ln(-1/2 
*ln(5)-3/2*x+3/2)^4*x^6-72*ln(5)*ln(-1/2*ln(5)-3/2*x+3/2)^2*x^5-1/729*ln(5 
)^6+464/27*ln(5)^3-43/27*ln(5)^4-96*ln(5)^2+256*ln(5)+12*x^5+x^6+81*x^2+10 
8*x^3+54*x^4-144*ln(5)*ln(-1/2*ln(5)-3/2*x+3/2)^2*x^3-108*ln(5)*ln(-1/2*ln 
(5)-3/2*x+3/2)^4*x^5-72*ln(5)^2*ln(-1/2*ln(5)-3/2*x+3/2)^2*x^2-120*ln(5)^2 
*ln(-1/2*ln(5)-3/2*x+3/2)^2*x^3-180*ln(5)*ln(-1/2*ln(5)-3/2*x+3/2)^2*x^4-9 
0*ln(5)^2*ln(-1/2*ln(5)-3/2*x+3/2)^4*x^4+ln(-1/2*ln(5)-3/2*x+3/2)^8+16*ln( 
-1/2*ln(5)-3/2*x+3/2)^6+96*ln(-1/2*ln(5)-3/2*x+3/2)^4+256*ln(-1/2*ln(5)-3/ 
2*x+3/2)^2-4/3*ln(-1/2*ln(5)-3/2*x+3/2)^2*ln(5)^4-4/81*ln(-1/2*ln(5)-3/2*x 
+3/2)^2*ln(5)^6-4/9*ln(-1/2*ln(5)-3/2*x+3/2)^2*ln(5)^5-2/27*ln(-1/2*ln(5)- 
3/2*x+3/2)^4*ln(5)^6-4/243*ln(-1/2*ln(5)-3/2*x+3/2)^4*ln(5)^7-4/2187*ln(-1 
/2*ln(5)-3/2*x+3/2)^6*ln(5)^8+4480/243*ln(-1/2*ln(5)-3/2*x+3/2)^8*(-1/2*ln 
(5)-3/2*x+3/2)^6+4096/2187*ln(-1/2*ln(5)-3/2*x+3/2)^6*(-1/2*ln(5)-3/2*x+3/ 
2)^8-896/27*ln(-1/2*ln(5)-3/2*x+3/2)^8*(-1/2*ln(5)-3/2*x+3/2)^5-10240/729* 
ln(-1/2*ln(5)-3/2*x+3/2)^6*(-1/2*ln(5)-3/2*x+3/2)^7+1120/27*ln(-1/2*ln(5)- 
3/2*x+3/2)^8*(-1/2*ln(5)-3/2*x+3/2)^4+1024/59049*ln(-1/2*ln(5)-3/2*x+3/2)^ 
8*(-1/2*ln(5)-3/2*x+3/2)^10-5120/19683*ln(-1/2*ln(5)-3/2*x+3/2)^8*(-1/2*ln 
(5)-3/2*x+3/2)^9-1/59049*ln(5)^10*ln(-1/2*ln(5)-3/2*x+3/2)^8-4/19683*ln(5) 
^9*ln(-1/2*ln(5)-3/2*x+3/2)^6-4/2187*ln(5)^7*ln(-1/2*ln(5)-3/2*x+3/2)^2-2/ 
2187*ln(5)^8*ln(-1/2*ln(5)-3/2*x+3/2)^4+512/2187*ln(-1/2*ln(5)-3/2*x+3/...
 

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 124 vs. \(2 (25) = 50\).

Time = 0.10 (sec) , antiderivative size = 124, normalized size of antiderivative = 3.76 \[ \int \frac {-486 x-486 x^2+324 x^3+468 x^4+162 x^5+18 x^6+\left (162 x+324 x^2+216 x^3+60 x^4+6 x^5\right ) \log (5)+\left (648 x^4+648 x^5+216 x^6+24 x^7\right ) \log \left (\frac {1}{2} (3-3 x-\log (5))\right )+\left (-1296 x^3-324 x^4+972 x^5+564 x^6+84 x^7+\left (432 x^3+540 x^4+216 x^5+28 x^6\right ) \log (5)\right ) \log ^2\left (\frac {1}{2} (3-3 x-\log (5))\right )+\left (648 x^6+432 x^7+72 x^8\right ) \log ^3\left (\frac {1}{2} (3-3 x-\log (5))\right )+\left (-972 x^5+216 x^6+612 x^7+144 x^8+\left (324 x^5+252 x^6+48 x^7\right ) \log (5)\right ) \log ^4\left (\frac {1}{2} (3-3 x-\log (5))\right )+\left (216 x^8+72 x^9\right ) \log ^5\left (\frac {1}{2} (3-3 x-\log (5))\right )+\left (-288 x^7+180 x^8+108 x^9+\left (96 x^7+36 x^8\right ) \log (5)\right ) \log ^6\left (\frac {1}{2} (3-3 x-\log (5))\right )+24 x^{10} \log ^7\left (\frac {1}{2} (3-3 x-\log (5))\right )+\left (-30 x^9+30 x^{10}+10 x^9 \log (5)\right ) \log ^8\left (\frac {1}{2} (3-3 x-\log (5))\right )}{-3+3 x+\log (5)} \, dx=x^{10} \log \left (-\frac {3}{2} \, x - \frac {1}{2} \, \log \left (5\right ) + \frac {3}{2}\right )^{8} + 4 \, {\left (x^{9} + 3 \, x^{8}\right )} \log \left (-\frac {3}{2} \, x - \frac {1}{2} \, \log \left (5\right ) + \frac {3}{2}\right )^{6} + x^{6} + 12 \, x^{5} + 6 \, {\left (x^{8} + 6 \, x^{7} + 9 \, x^{6}\right )} \log \left (-\frac {3}{2} \, x - \frac {1}{2} \, \log \left (5\right ) + \frac {3}{2}\right )^{4} + 54 \, x^{4} + 108 \, x^{3} + 4 \, {\left (x^{7} + 9 \, x^{6} + 27 \, x^{5} + 27 \, x^{4}\right )} \log \left (-\frac {3}{2} \, x - \frac {1}{2} \, \log \left (5\right ) + \frac {3}{2}\right )^{2} + 81 \, x^{2} \] Input:

integrate(((10*x^9*log(5)+30*x^10-30*x^9)*log(-1/2*log(5)-3/2*x+3/2)^8+24* 
x^10*log(-1/2*log(5)-3/2*x+3/2)^7+((36*x^8+96*x^7)*log(5)+108*x^9+180*x^8- 
288*x^7)*log(-1/2*log(5)-3/2*x+3/2)^6+(72*x^9+216*x^8)*log(-1/2*log(5)-3/2 
*x+3/2)^5+((48*x^7+252*x^6+324*x^5)*log(5)+144*x^8+612*x^7+216*x^6-972*x^5 
)*log(-1/2*log(5)-3/2*x+3/2)^4+(72*x^8+432*x^7+648*x^6)*log(-1/2*log(5)-3/ 
2*x+3/2)^3+((28*x^6+216*x^5+540*x^4+432*x^3)*log(5)+84*x^7+564*x^6+972*x^5 
-324*x^4-1296*x^3)*log(-1/2*log(5)-3/2*x+3/2)^2+(24*x^7+216*x^6+648*x^5+64 
8*x^4)*log(-1/2*log(5)-3/2*x+3/2)+(6*x^5+60*x^4+216*x^3+324*x^2+162*x)*log 
(5)+18*x^6+162*x^5+468*x^4+324*x^3-486*x^2-486*x)/(log(5)+3*x-3),x, algori 
thm="fricas")
 

Output:

x^10*log(-3/2*x - 1/2*log(5) + 3/2)^8 + 4*(x^9 + 3*x^8)*log(-3/2*x - 1/2*l 
og(5) + 3/2)^6 + x^6 + 12*x^5 + 6*(x^8 + 6*x^7 + 9*x^6)*log(-3/2*x - 1/2*l 
og(5) + 3/2)^4 + 54*x^4 + 108*x^3 + 4*(x^7 + 9*x^6 + 27*x^5 + 27*x^4)*log( 
-3/2*x - 1/2*log(5) + 3/2)^2 + 81*x^2
 

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 139 vs. \(2 (27) = 54\).

Time = 0.24 (sec) , antiderivative size = 139, normalized size of antiderivative = 4.21 \[ \int \frac {-486 x-486 x^2+324 x^3+468 x^4+162 x^5+18 x^6+\left (162 x+324 x^2+216 x^3+60 x^4+6 x^5\right ) \log (5)+\left (648 x^4+648 x^5+216 x^6+24 x^7\right ) \log \left (\frac {1}{2} (3-3 x-\log (5))\right )+\left (-1296 x^3-324 x^4+972 x^5+564 x^6+84 x^7+\left (432 x^3+540 x^4+216 x^5+28 x^6\right ) \log (5)\right ) \log ^2\left (\frac {1}{2} (3-3 x-\log (5))\right )+\left (648 x^6+432 x^7+72 x^8\right ) \log ^3\left (\frac {1}{2} (3-3 x-\log (5))\right )+\left (-972 x^5+216 x^6+612 x^7+144 x^8+\left (324 x^5+252 x^6+48 x^7\right ) \log (5)\right ) \log ^4\left (\frac {1}{2} (3-3 x-\log (5))\right )+\left (216 x^8+72 x^9\right ) \log ^5\left (\frac {1}{2} (3-3 x-\log (5))\right )+\left (-288 x^7+180 x^8+108 x^9+\left (96 x^7+36 x^8\right ) \log (5)\right ) \log ^6\left (\frac {1}{2} (3-3 x-\log (5))\right )+24 x^{10} \log ^7\left (\frac {1}{2} (3-3 x-\log (5))\right )+\left (-30 x^9+30 x^{10}+10 x^9 \log (5)\right ) \log ^8\left (\frac {1}{2} (3-3 x-\log (5))\right )}{-3+3 x+\log (5)} \, dx=x^{10} \log {\left (- \frac {3 x}{2} - \frac {\log {\left (5 \right )}}{2} + \frac {3}{2} \right )}^{8} + x^{6} + 12 x^{5} + 54 x^{4} + 108 x^{3} + 81 x^{2} + \left (4 x^{9} + 12 x^{8}\right ) \log {\left (- \frac {3 x}{2} - \frac {\log {\left (5 \right )}}{2} + \frac {3}{2} \right )}^{6} + \left (6 x^{8} + 36 x^{7} + 54 x^{6}\right ) \log {\left (- \frac {3 x}{2} - \frac {\log {\left (5 \right )}}{2} + \frac {3}{2} \right )}^{4} + \left (4 x^{7} + 36 x^{6} + 108 x^{5} + 108 x^{4}\right ) \log {\left (- \frac {3 x}{2} - \frac {\log {\left (5 \right )}}{2} + \frac {3}{2} \right )}^{2} \] Input:

integrate(((10*x**9*ln(5)+30*x**10-30*x**9)*ln(-1/2*ln(5)-3/2*x+3/2)**8+24 
*x**10*ln(-1/2*ln(5)-3/2*x+3/2)**7+((36*x**8+96*x**7)*ln(5)+108*x**9+180*x 
**8-288*x**7)*ln(-1/2*ln(5)-3/2*x+3/2)**6+(72*x**9+216*x**8)*ln(-1/2*ln(5) 
-3/2*x+3/2)**5+((48*x**7+252*x**6+324*x**5)*ln(5)+144*x**8+612*x**7+216*x* 
*6-972*x**5)*ln(-1/2*ln(5)-3/2*x+3/2)**4+(72*x**8+432*x**7+648*x**6)*ln(-1 
/2*ln(5)-3/2*x+3/2)**3+((28*x**6+216*x**5+540*x**4+432*x**3)*ln(5)+84*x**7 
+564*x**6+972*x**5-324*x**4-1296*x**3)*ln(-1/2*ln(5)-3/2*x+3/2)**2+(24*x** 
7+216*x**6+648*x**5+648*x**4)*ln(-1/2*ln(5)-3/2*x+3/2)+(6*x**5+60*x**4+216 
*x**3+324*x**2+162*x)*ln(5)+18*x**6+162*x**5+468*x**4+324*x**3-486*x**2-48 
6*x)/(ln(5)+3*x-3),x)
 

Output:

x**10*log(-3*x/2 - log(5)/2 + 3/2)**8 + x**6 + 12*x**5 + 54*x**4 + 108*x** 
3 + 81*x**2 + (4*x**9 + 12*x**8)*log(-3*x/2 - log(5)/2 + 3/2)**6 + (6*x**8 
 + 36*x**7 + 54*x**6)*log(-3*x/2 - log(5)/2 + 3/2)**4 + (4*x**7 + 36*x**6 
+ 108*x**5 + 108*x**4)*log(-3*x/2 - log(5)/2 + 3/2)**2
 

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 39766 vs. \(2 (25) = 50\).

Time = 0.52 (sec) , antiderivative size = 39766, normalized size of antiderivative = 1205.03 \[ \int \frac {-486 x-486 x^2+324 x^3+468 x^4+162 x^5+18 x^6+\left (162 x+324 x^2+216 x^3+60 x^4+6 x^5\right ) \log (5)+\left (648 x^4+648 x^5+216 x^6+24 x^7\right ) \log \left (\frac {1}{2} (3-3 x-\log (5))\right )+\left (-1296 x^3-324 x^4+972 x^5+564 x^6+84 x^7+\left (432 x^3+540 x^4+216 x^5+28 x^6\right ) \log (5)\right ) \log ^2\left (\frac {1}{2} (3-3 x-\log (5))\right )+\left (648 x^6+432 x^7+72 x^8\right ) \log ^3\left (\frac {1}{2} (3-3 x-\log (5))\right )+\left (-972 x^5+216 x^6+612 x^7+144 x^8+\left (324 x^5+252 x^6+48 x^7\right ) \log (5)\right ) \log ^4\left (\frac {1}{2} (3-3 x-\log (5))\right )+\left (216 x^8+72 x^9\right ) \log ^5\left (\frac {1}{2} (3-3 x-\log (5))\right )+\left (-288 x^7+180 x^8+108 x^9+\left (96 x^7+36 x^8\right ) \log (5)\right ) \log ^6\left (\frac {1}{2} (3-3 x-\log (5))\right )+24 x^{10} \log ^7\left (\frac {1}{2} (3-3 x-\log (5))\right )+\left (-30 x^9+30 x^{10}+10 x^9 \log (5)\right ) \log ^8\left (\frac {1}{2} (3-3 x-\log (5))\right )}{-3+3 x+\log (5)} \, dx=\text {Too large to display} \] Input:

integrate(((10*x^9*log(5)+30*x^10-30*x^9)*log(-1/2*log(5)-3/2*x+3/2)^8+24* 
x^10*log(-1/2*log(5)-3/2*x+3/2)^7+((36*x^8+96*x^7)*log(5)+108*x^9+180*x^8- 
288*x^7)*log(-1/2*log(5)-3/2*x+3/2)^6+(72*x^9+216*x^8)*log(-1/2*log(5)-3/2 
*x+3/2)^5+((48*x^7+252*x^6+324*x^5)*log(5)+144*x^8+612*x^7+216*x^6-972*x^5 
)*log(-1/2*log(5)-3/2*x+3/2)^4+(72*x^8+432*x^7+648*x^6)*log(-1/2*log(5)-3/ 
2*x+3/2)^3+((28*x^6+216*x^5+540*x^4+432*x^3)*log(5)+84*x^7+564*x^6+972*x^5 
-324*x^4-1296*x^3)*log(-1/2*log(5)-3/2*x+3/2)^2+(24*x^7+216*x^6+648*x^5+64 
8*x^4)*log(-1/2*log(5)-3/2*x+3/2)+(6*x^5+60*x^4+216*x^3+324*x^2+162*x)*log 
(5)+18*x^6+162*x^5+468*x^4+324*x^3-486*x^2-486*x)/(log(5)+3*x-3),x, algori 
thm="maxima")
 

Output:

1/9226406250*(156250*log(-3/2*x - 1/2*log(5) + 3/2)^8 - 125000*log(-3/2*x 
- 1/2*log(5) + 3/2)^7 + 87500*log(-3/2*x - 1/2*log(5) + 3/2)^6 - 52500*log 
(-3/2*x - 1/2*log(5) + 3/2)^5 + 26250*log(-3/2*x - 1/2*log(5) + 3/2)^4 - 1 
0500*log(-3/2*x - 1/2*log(5) + 3/2)^3 + 3150*log(-3/2*x - 1/2*log(5) + 3/2 
)^2 - 630*log(-3/2*x - 1/2*log(5) + 3/2) + 63)*(3*x + log(5) - 3)^10 + 1/9 
226406250*(125000*log(-3/2*x - 1/2*log(5) + 3/2)^7 - 87500*log(-3/2*x - 1/ 
2*log(5) + 3/2)^6 + 52500*log(-3/2*x - 1/2*log(5) + 3/2)^5 - 26250*log(-3/ 
2*x - 1/2*log(5) + 3/2)^4 + 10500*log(-3/2*x - 1/2*log(5) + 3/2)^3 - 3150* 
log(-3/2*x - 1/2*log(5) + 3/2)^2 + 630*log(-3/2*x - 1/2*log(5) + 3/2) - 63 
)*(3*x + log(5) - 3)^10 - 100/2541865828329*(4782969*(log(5) - 3)*log(-3/2 
*x - 1/2*log(5) + 3/2)^8 - 4251528*(log(5) - 3)*log(-3/2*x - 1/2*log(5) + 
3/2)^7 + 3306744*(log(5) - 3)*log(-3/2*x - 1/2*log(5) + 3/2)^6 - 2204496*( 
log(5) - 3)*log(-3/2*x - 1/2*log(5) + 3/2)^5 + 1224720*(log(5) - 3)*log(-3 
/2*x - 1/2*log(5) + 3/2)^4 - 544320*(log(5) - 3)*log(-3/2*x - 1/2*log(5) + 
 3/2)^3 + 181440*(log(5) - 3)*log(-3/2*x - 1/2*log(5) + 3/2)^2 - 40320*(lo 
g(5) - 3)*log(-3/2*x - 1/2*log(5) + 3/2) + 4480*log(5) - 13440)*(3*x + log 
(5) - 3)^9 - 80/282429536481*(531441*(log(5) - 3)*log(-3/2*x - 1/2*log(5) 
+ 3/2)^7 - 413343*(log(5) - 3)*log(-3/2*x - 1/2*log(5) + 3/2)^6 + 275562*( 
log(5) - 3)*log(-3/2*x - 1/2*log(5) + 3/2)^5 - 153090*(log(5) - 3)*log(-3/ 
2*x - 1/2*log(5) + 3/2)^4 + 68040*(log(5) - 3)*log(-3/2*x - 1/2*log(5) ...
 

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 497 vs. \(2 (25) = 50\).

Time = 1.03 (sec) , antiderivative size = 497, normalized size of antiderivative = 15.06 \[ \int \frac {-486 x-486 x^2+324 x^3+468 x^4+162 x^5+18 x^6+\left (162 x+324 x^2+216 x^3+60 x^4+6 x^5\right ) \log (5)+\left (648 x^4+648 x^5+216 x^6+24 x^7\right ) \log \left (\frac {1}{2} (3-3 x-\log (5))\right )+\left (-1296 x^3-324 x^4+972 x^5+564 x^6+84 x^7+\left (432 x^3+540 x^4+216 x^5+28 x^6\right ) \log (5)\right ) \log ^2\left (\frac {1}{2} (3-3 x-\log (5))\right )+\left (648 x^6+432 x^7+72 x^8\right ) \log ^3\left (\frac {1}{2} (3-3 x-\log (5))\right )+\left (-972 x^5+216 x^6+612 x^7+144 x^8+\left (324 x^5+252 x^6+48 x^7\right ) \log (5)\right ) \log ^4\left (\frac {1}{2} (3-3 x-\log (5))\right )+\left (216 x^8+72 x^9\right ) \log ^5\left (\frac {1}{2} (3-3 x-\log (5))\right )+\left (-288 x^7+180 x^8+108 x^9+\left (96 x^7+36 x^8\right ) \log (5)\right ) \log ^6\left (\frac {1}{2} (3-3 x-\log (5))\right )+24 x^{10} \log ^7\left (\frac {1}{2} (3-3 x-\log (5))\right )+\left (-30 x^9+30 x^{10}+10 x^9 \log (5)\right ) \log ^8\left (\frac {1}{2} (3-3 x-\log (5))\right )}{-3+3 x+\log (5)} \, dx =\text {Too large to display} \] Input:

integrate(((10*x^9*log(5)+30*x^10-30*x^9)*log(-1/2*log(5)-3/2*x+3/2)^8+24* 
x^10*log(-1/2*log(5)-3/2*x+3/2)^7+((36*x^8+96*x^7)*log(5)+108*x^9+180*x^8- 
288*x^7)*log(-1/2*log(5)-3/2*x+3/2)^6+(72*x^9+216*x^8)*log(-1/2*log(5)-3/2 
*x+3/2)^5+((48*x^7+252*x^6+324*x^5)*log(5)+144*x^8+612*x^7+216*x^6-972*x^5 
)*log(-1/2*log(5)-3/2*x+3/2)^4+(72*x^8+432*x^7+648*x^6)*log(-1/2*log(5)-3/ 
2*x+3/2)^3+((28*x^6+216*x^5+540*x^4+432*x^3)*log(5)+84*x^7+564*x^6+972*x^5 
-324*x^4-1296*x^3)*log(-1/2*log(5)-3/2*x+3/2)^2+(24*x^7+216*x^6+648*x^5+64 
8*x^4)*log(-1/2*log(5)-3/2*x+3/2)+(6*x^5+60*x^4+216*x^3+324*x^2+162*x)*log 
(5)+18*x^6+162*x^5+468*x^4+324*x^3-486*x^2-486*x)/(log(5)+3*x-3),x, algori 
thm="giac")
 

Output:

x^10*log(2)^8 - 8*x^10*log(2)*log(-3*x - log(5) + 3)^7 + x^10*log(-3*x - l 
og(5) + 3)^8 + 4*x^9*log(2)^6 + 6*(2*log(2)^6 + log(2)^4)*x^8 + 4*(9*log(2 
)^4 + log(2)^2)*x^7 + (54*log(2)^4 + 36*log(2)^2 + 1)*x^6 + 4*(7*x^10*log( 
2)^2 + x^9 + 3*x^8)*log(-3*x - log(5) + 3)^6 + 12*(9*log(2)^2 + 1)*x^5 - 8 
*(7*x^10*log(2)^3 + 3*x^9*log(2) + 9*x^8*log(2))*log(-3*x - log(5) + 3)^5 
+ 54*(2*log(2)^2 + 1)*x^4 + 2*(35*x^10*log(2)^4 + 30*x^9*log(2)^2 + 3*(30* 
log(2)^2 + 1)*x^8 + 18*x^7 + 27*x^6)*log(-3*x - log(5) + 3)^4 - 8*(7*x^10* 
log(2)^5 + 10*x^9*log(2)^3 + 3*(10*log(2)^3 + log(2))*x^8 + 18*x^7*log(2) 
+ 27*x^6*log(2))*log(-3*x - log(5) + 3)^3 + 108*x^3 + 4*(7*x^10*log(2)^6 + 
 15*x^9*log(2)^4 + 9*(5*log(2)^4 + log(2)^2)*x^8 + (54*log(2)^2 + 1)*x^7 + 
 9*(9*log(2)^2 + 1)*x^6 + 27*x^5 + 27*x^4)*log(-3*x - log(5) + 3)^2 + 81*x 
^2 - 8*(x^10*log(2)^7 + 3*x^9*log(2)^5 + 3*(3*log(2)^5 + log(2)^3)*x^8 + ( 
18*log(2)^3 + log(2))*x^7 + 9*(3*log(2)^3 + log(2))*x^6 + 27*x^5*log(2) + 
27*x^4*log(2))*log(-3*x - log(5) + 3)
 

Mupad [B] (verification not implemented)

Time = 2.76 (sec) , antiderivative size = 127, normalized size of antiderivative = 3.85 \[ \int \frac {-486 x-486 x^2+324 x^3+468 x^4+162 x^5+18 x^6+\left (162 x+324 x^2+216 x^3+60 x^4+6 x^5\right ) \log (5)+\left (648 x^4+648 x^5+216 x^6+24 x^7\right ) \log \left (\frac {1}{2} (3-3 x-\log (5))\right )+\left (-1296 x^3-324 x^4+972 x^5+564 x^6+84 x^7+\left (432 x^3+540 x^4+216 x^5+28 x^6\right ) \log (5)\right ) \log ^2\left (\frac {1}{2} (3-3 x-\log (5))\right )+\left (648 x^6+432 x^7+72 x^8\right ) \log ^3\left (\frac {1}{2} (3-3 x-\log (5))\right )+\left (-972 x^5+216 x^6+612 x^7+144 x^8+\left (324 x^5+252 x^6+48 x^7\right ) \log (5)\right ) \log ^4\left (\frac {1}{2} (3-3 x-\log (5))\right )+\left (216 x^8+72 x^9\right ) \log ^5\left (\frac {1}{2} (3-3 x-\log (5))\right )+\left (-288 x^7+180 x^8+108 x^9+\left (96 x^7+36 x^8\right ) \log (5)\right ) \log ^6\left (\frac {1}{2} (3-3 x-\log (5))\right )+24 x^{10} \log ^7\left (\frac {1}{2} (3-3 x-\log (5))\right )+\left (-30 x^9+30 x^{10}+10 x^9 \log (5)\right ) \log ^8\left (\frac {1}{2} (3-3 x-\log (5))\right )}{-3+3 x+\log (5)} \, dx=x^{10}\,{\ln \left (\frac {3}{2}-\frac {\ln \left (5\right )}{2}-\frac {3\,x}{2}\right )}^8+{\ln \left (\frac {3}{2}-\frac {\ln \left (5\right )}{2}-\frac {3\,x}{2}\right )}^4\,\left (6\,x^8+36\,x^7+54\,x^6\right )+{\ln \left (\frac {3}{2}-\frac {\ln \left (5\right )}{2}-\frac {3\,x}{2}\right )}^2\,\left (4\,x^7+36\,x^6+108\,x^5+108\,x^4\right )+81\,x^2+108\,x^3+54\,x^4+12\,x^5+x^6+{\ln \left (\frac {3}{2}-\frac {\ln \left (5\right )}{2}-\frac {3\,x}{2}\right )}^6\,\left (4\,x^9+12\,x^8\right ) \] Input:

int((24*x^10*log(3/2 - log(5)/2 - (3*x)/2)^7 - 486*x + log(3/2 - log(5)/2 
- (3*x)/2)*(648*x^4 + 648*x^5 + 216*x^6 + 24*x^7) + log(3/2 - log(5)/2 - ( 
3*x)/2)^3*(648*x^6 + 432*x^7 + 72*x^8) + log(3/2 - log(5)/2 - (3*x)/2)^4*( 
log(5)*(324*x^5 + 252*x^6 + 48*x^7) - 972*x^5 + 216*x^6 + 612*x^7 + 144*x^ 
8) + log(3/2 - log(5)/2 - (3*x)/2)^8*(10*x^9*log(5) - 30*x^9 + 30*x^10) + 
log(3/2 - log(5)/2 - (3*x)/2)^2*(log(5)*(432*x^3 + 540*x^4 + 216*x^5 + 28* 
x^6) - 1296*x^3 - 324*x^4 + 972*x^5 + 564*x^6 + 84*x^7) + log(3/2 - log(5) 
/2 - (3*x)/2)^6*(log(5)*(96*x^7 + 36*x^8) - 288*x^7 + 180*x^8 + 108*x^9) - 
 486*x^2 + 324*x^3 + 468*x^4 + 162*x^5 + 18*x^6 + log(5)*(162*x + 324*x^2 
+ 216*x^3 + 60*x^4 + 6*x^5) + log(3/2 - log(5)/2 - (3*x)/2)^5*(216*x^8 + 7 
2*x^9))/(3*x + log(5) - 3),x)
 

Output:

x^10*log(3/2 - log(5)/2 - (3*x)/2)^8 + log(3/2 - log(5)/2 - (3*x)/2)^4*(54 
*x^6 + 36*x^7 + 6*x^8) + log(3/2 - log(5)/2 - (3*x)/2)^2*(108*x^4 + 108*x^ 
5 + 36*x^6 + 4*x^7) + 81*x^2 + 108*x^3 + 54*x^4 + 12*x^5 + x^6 + log(3/2 - 
 log(5)/2 - (3*x)/2)^6*(12*x^8 + 4*x^9)
 

Reduce [B] (verification not implemented)

Time = 0.51 (sec) , antiderivative size = 191, normalized size of antiderivative = 5.79 \[ \int \frac {-486 x-486 x^2+324 x^3+468 x^4+162 x^5+18 x^6+\left (162 x+324 x^2+216 x^3+60 x^4+6 x^5\right ) \log (5)+\left (648 x^4+648 x^5+216 x^6+24 x^7\right ) \log \left (\frac {1}{2} (3-3 x-\log (5))\right )+\left (-1296 x^3-324 x^4+972 x^5+564 x^6+84 x^7+\left (432 x^3+540 x^4+216 x^5+28 x^6\right ) \log (5)\right ) \log ^2\left (\frac {1}{2} (3-3 x-\log (5))\right )+\left (648 x^6+432 x^7+72 x^8\right ) \log ^3\left (\frac {1}{2} (3-3 x-\log (5))\right )+\left (-972 x^5+216 x^6+612 x^7+144 x^8+\left (324 x^5+252 x^6+48 x^7\right ) \log (5)\right ) \log ^4\left (\frac {1}{2} (3-3 x-\log (5))\right )+\left (216 x^8+72 x^9\right ) \log ^5\left (\frac {1}{2} (3-3 x-\log (5))\right )+\left (-288 x^7+180 x^8+108 x^9+\left (96 x^7+36 x^8\right ) \log (5)\right ) \log ^6\left (\frac {1}{2} (3-3 x-\log (5))\right )+24 x^{10} \log ^7\left (\frac {1}{2} (3-3 x-\log (5))\right )+\left (-30 x^9+30 x^{10}+10 x^9 \log (5)\right ) \log ^8\left (\frac {1}{2} (3-3 x-\log (5))\right )}{-3+3 x+\log (5)} \, dx=x^{2} \left (\mathrm {log}\left (-\frac {\mathrm {log}\left (5\right )}{2}-\frac {3 x}{2}+\frac {3}{2}\right )^{8} x^{8}+4 \mathrm {log}\left (-\frac {\mathrm {log}\left (5\right )}{2}-\frac {3 x}{2}+\frac {3}{2}\right )^{6} x^{7}+12 \mathrm {log}\left (-\frac {\mathrm {log}\left (5\right )}{2}-\frac {3 x}{2}+\frac {3}{2}\right )^{6} x^{6}+6 \mathrm {log}\left (-\frac {\mathrm {log}\left (5\right )}{2}-\frac {3 x}{2}+\frac {3}{2}\right )^{4} x^{6}+36 \mathrm {log}\left (-\frac {\mathrm {log}\left (5\right )}{2}-\frac {3 x}{2}+\frac {3}{2}\right )^{4} x^{5}+54 \mathrm {log}\left (-\frac {\mathrm {log}\left (5\right )}{2}-\frac {3 x}{2}+\frac {3}{2}\right )^{4} x^{4}+4 \mathrm {log}\left (-\frac {\mathrm {log}\left (5\right )}{2}-\frac {3 x}{2}+\frac {3}{2}\right )^{2} x^{5}+36 \mathrm {log}\left (-\frac {\mathrm {log}\left (5\right )}{2}-\frac {3 x}{2}+\frac {3}{2}\right )^{2} x^{4}+108 \mathrm {log}\left (-\frac {\mathrm {log}\left (5\right )}{2}-\frac {3 x}{2}+\frac {3}{2}\right )^{2} x^{3}+108 \mathrm {log}\left (-\frac {\mathrm {log}\left (5\right )}{2}-\frac {3 x}{2}+\frac {3}{2}\right )^{2} x^{2}+x^{4}+12 x^{3}+54 x^{2}+108 x +81\right ) \] Input:

int(((10*x^9*log(5)+30*x^10-30*x^9)*log(-1/2*log(5)-3/2*x+3/2)^8+24*x^10*l 
og(-1/2*log(5)-3/2*x+3/2)^7+((36*x^8+96*x^7)*log(5)+108*x^9+180*x^8-288*x^ 
7)*log(-1/2*log(5)-3/2*x+3/2)^6+(72*x^9+216*x^8)*log(-1/2*log(5)-3/2*x+3/2 
)^5+((48*x^7+252*x^6+324*x^5)*log(5)+144*x^8+612*x^7+216*x^6-972*x^5)*log( 
-1/2*log(5)-3/2*x+3/2)^4+(72*x^8+432*x^7+648*x^6)*log(-1/2*log(5)-3/2*x+3/ 
2)^3+((28*x^6+216*x^5+540*x^4+432*x^3)*log(5)+84*x^7+564*x^6+972*x^5-324*x 
^4-1296*x^3)*log(-1/2*log(5)-3/2*x+3/2)^2+(24*x^7+216*x^6+648*x^5+648*x^4) 
*log(-1/2*log(5)-3/2*x+3/2)+(6*x^5+60*x^4+216*x^3+324*x^2+162*x)*log(5)+18 
*x^6+162*x^5+468*x^4+324*x^3-486*x^2-486*x)/(log(5)+3*x-3),x)
 

Output:

x**2*(log(( - log(5) - 3*x + 3)/2)**8*x**8 + 4*log(( - log(5) - 3*x + 3)/2 
)**6*x**7 + 12*log(( - log(5) - 3*x + 3)/2)**6*x**6 + 6*log(( - log(5) - 3 
*x + 3)/2)**4*x**6 + 36*log(( - log(5) - 3*x + 3)/2)**4*x**5 + 54*log(( - 
log(5) - 3*x + 3)/2)**4*x**4 + 4*log(( - log(5) - 3*x + 3)/2)**2*x**5 + 36 
*log(( - log(5) - 3*x + 3)/2)**2*x**4 + 108*log(( - log(5) - 3*x + 3)/2)** 
2*x**3 + 108*log(( - log(5) - 3*x + 3)/2)**2*x**2 + x**4 + 12*x**3 + 54*x* 
*2 + 108*x + 81)