Integrand size = 315, antiderivative size = 20 \[ \int \left (1-3 x+2 x^2+2 x^3-3 x^4+x^5+\left (8-16 x+16 x^3-8 x^4\right ) \log (25)+\left (28-32 x-24 x^2+32 x^3-4 x^4\right ) \log ^2(25)+\left (56-24 x-56 x^2+24 x^3\right ) \log ^3(25)+\left (70+10 x-54 x^2+6 x^3\right ) \log ^4(25)+\left (56+32 x-24 x^2\right ) \log ^5(25)+\left (28+24 x-4 x^2\right ) \log ^6(25)+(8+8 x) \log ^7(25)+(1+x) \log ^8(25)+\left (1-6 x+6 x^2+8 x^3-15 x^4+6 x^5+\left (8-32 x+64 x^3-40 x^4\right ) \log (25)+\left (28-64 x-72 x^2+128 x^3-20 x^4\right ) \log ^2(25)+\left (56-48 x-168 x^2+96 x^3\right ) \log ^3(25)+\left (70+20 x-162 x^2+24 x^3\right ) \log ^4(25)+\left (56+64 x-72 x^2\right ) \log ^5(25)+\left (28+48 x-12 x^2\right ) \log ^6(25)+(8+16 x) \log ^7(25)+(1+2 x) \log ^8(25)\right ) \log (x)\right ) \, dx=\left (x+x^2\right ) \left (x-(1+\log (25))^2\right )^4 \log (x) \]
Leaf count is larger than twice the leaf count of optimal. \(93\) vs. \(2(20)=40\).
Time = 0.18 (sec) , antiderivative size = 93, normalized size of antiderivative = 4.65 \[ \int \left (1-3 x+2 x^2+2 x^3-3 x^4+x^5+\left (8-16 x+16 x^3-8 x^4\right ) \log (25)+\left (28-32 x-24 x^2+32 x^3-4 x^4\right ) \log ^2(25)+\left (56-24 x-56 x^2+24 x^3\right ) \log ^3(25)+\left (70+10 x-54 x^2+6 x^3\right ) \log ^4(25)+\left (56+32 x-24 x^2\right ) \log ^5(25)+\left (28+24 x-4 x^2\right ) \log ^6(25)+(8+8 x) \log ^7(25)+(1+x) \log ^8(25)+\left (1-6 x+6 x^2+8 x^3-15 x^4+6 x^5+\left (8-32 x+64 x^3-40 x^4\right ) \log (25)+\left (28-64 x-72 x^2+128 x^3-20 x^4\right ) \log ^2(25)+\left (56-48 x-168 x^2+96 x^3\right ) \log ^3(25)+\left (70+20 x-162 x^2+24 x^3\right ) \log ^4(25)+\left (56+64 x-72 x^2\right ) \log ^5(25)+\left (28+48 x-12 x^2\right ) \log ^6(25)+(8+16 x) \log ^7(25)+(1+2 x) \log ^8(25)\right ) \log (x)\right ) \, dx=x \left (x^5+(1+\log (25))^8-2 x^2 (1+\log (25))^4 \left (-1+4 \log (25)+2 \log ^2(25)\right )+2 x^3 (1+\log (25))^2 \left (1+6 \log (25)+3 \log ^2(25)\right )-x^4 \left (3+8 \log (25)+4 \log ^2(25)\right )+x (1+\log (25))^6 \left (-3+\log ^2(25)+\log (625)\right )\right ) \log (x) \]
Integrate[1 - 3*x + 2*x^2 + 2*x^3 - 3*x^4 + x^5 + (8 - 16*x + 16*x^3 - 8*x ^4)*Log[25] + (28 - 32*x - 24*x^2 + 32*x^3 - 4*x^4)*Log[25]^2 + (56 - 24*x - 56*x^2 + 24*x^3)*Log[25]^3 + (70 + 10*x - 54*x^2 + 6*x^3)*Log[25]^4 + ( 56 + 32*x - 24*x^2)*Log[25]^5 + (28 + 24*x - 4*x^2)*Log[25]^6 + (8 + 8*x)* Log[25]^7 + (1 + x)*Log[25]^8 + (1 - 6*x + 6*x^2 + 8*x^3 - 15*x^4 + 6*x^5 + (8 - 32*x + 64*x^3 - 40*x^4)*Log[25] + (28 - 64*x - 72*x^2 + 128*x^3 - 2 0*x^4)*Log[25]^2 + (56 - 48*x - 168*x^2 + 96*x^3)*Log[25]^3 + (70 + 20*x - 162*x^2 + 24*x^3)*Log[25]^4 + (56 + 64*x - 72*x^2)*Log[25]^5 + (28 + 48*x - 12*x^2)*Log[25]^6 + (8 + 16*x)*Log[25]^7 + (1 + 2*x)*Log[25]^8)*Log[x], x]
x*(x^5 + (1 + Log[25])^8 - 2*x^2*(1 + Log[25])^4*(-1 + 4*Log[25] + 2*Log[2 5]^2) + 2*x^3*(1 + Log[25])^2*(1 + 6*Log[25] + 3*Log[25]^2) - x^4*(3 + 8*L og[25] + 4*Log[25]^2) + x*(1 + Log[25])^6*(-3 + Log[25]^2 + Log[625]))*Log [x]
Leaf count is larger than twice the leaf count of optimal. \(464\) vs. \(2(20)=40\).
Time = 0.67 (sec) , antiderivative size = 464, normalized size of antiderivative = 23.20, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.003, Rules used = {2009}
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.
| \(\displaystyle \int \left (x^5-3 x^4+2 x^3+2 x^2+\left (-4 x^2+24 x+28\right ) \log ^6(25)+\left (-24 x^2+32 x+56\right ) \log ^5(25)+\left (-8 x^4+16 x^3-16 x+8\right ) \log (25)+\left (6 x^3-54 x^2+10 x+70\right ) \log ^4(25)+\left (24 x^3-56 x^2-24 x+56\right ) \log ^3(25)+\left (-4 x^4+32 x^3-24 x^2-32 x+28\right ) \log ^2(25)+\left (6 x^5-15 x^4+8 x^3+6 x^2+\left (-12 x^2+48 x+28\right ) \log ^6(25)+\left (-72 x^2+64 x+56\right ) \log ^5(25)+\left (-40 x^4+64 x^3-32 x+8\right ) \log (25)+\left (24 x^3-162 x^2+20 x+70\right ) \log ^4(25)+\left (96 x^3-168 x^2-48 x+56\right ) \log ^3(25)+\left (-20 x^4+128 x^3-72 x^2-64 x+28\right ) \log ^2(25)-6 x+(2 x+1) \log ^8(25)+(16 x+8) \log ^7(25)+1\right ) \log (x)-3 x+(x+1) \log ^8(25)+(8 x+8) \log ^7(25)+1\right ) \, dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle x^6 \log (x)-\frac {3 x^5}{5}-x^5 \left (3+4 \log ^2(25)+8 \log (25)\right ) \log (x)+\frac {1}{5} x^5 \left (3+4 \log ^2(25)+8 \log (25)\right )-\frac {4}{5} x^5 \log ^2(25)-\frac {8}{5} x^5 \log (25)+\frac {x^4}{2}+\frac {3}{2} x^4 \log ^4(25)+6 x^4 \log ^3(25)+2 x^4 (1+\log (25))^2 \left (1+3 \log ^2(25)+6 \log (25)\right ) \log (x)-\frac {1}{2} x^4 (1+\log (25))^2 \left (1+3 \log ^2(25)+6 \log (25)\right )+8 x^4 \log ^2(25)+4 x^4 \log (25)+\frac {2 x^3}{3}-\frac {4}{3} x^3 \log ^6(25)-8 x^3 \log ^5(25)-18 x^3 \log ^4(25)-\frac {56}{3} x^3 \log ^3(25)+2 x^3 (1+\log (25))^4 \left (1-2 \log ^2(25)-4 \log (25)\right ) \log (x)-\frac {2}{3} x^3 (1+\log (25))^4 \left (1-2 \log ^2(25)-4 \log (25)\right )-8 x^3 \log ^2(25)-\frac {3 x^2}{2}+12 x^2 \log ^6(25)+16 x^2 \log ^5(25)+5 x^2 \log ^4(25)-12 x^2 \log ^3(25)-x^2 (1+\log (25))^6 \left (3-\log ^2(25)-\log (625)\right ) \log (x)+\frac {1}{2} x^2 (1+\log (25))^6 \left (3-\log ^2(25)-\log (625)\right )-16 x^2 \log ^2(25)-8 x^2 \log (25)+x+\frac {1}{2} (x+1)^2 \log ^8(25)+4 (x+1)^2 \log ^7(25)+28 x \log ^6(25)+56 x \log ^5(25)+70 x \log ^4(25)+56 x \log ^3(25)+28 x \log ^2(25)+x (1+\log (25))^8 \log (x)-x (1+\log (25))^8+8 x \log (25)\) |
Int[1 - 3*x + 2*x^2 + 2*x^3 - 3*x^4 + x^5 + (8 - 16*x + 16*x^3 - 8*x^4)*Lo g[25] + (28 - 32*x - 24*x^2 + 32*x^3 - 4*x^4)*Log[25]^2 + (56 - 24*x - 56* x^2 + 24*x^3)*Log[25]^3 + (70 + 10*x - 54*x^2 + 6*x^3)*Log[25]^4 + (56 + 3 2*x - 24*x^2)*Log[25]^5 + (28 + 24*x - 4*x^2)*Log[25]^6 + (8 + 8*x)*Log[25 ]^7 + (1 + x)*Log[25]^8 + (1 - 6*x + 6*x^2 + 8*x^3 - 15*x^4 + 6*x^5 + (8 - 32*x + 64*x^3 - 40*x^4)*Log[25] + (28 - 64*x - 72*x^2 + 128*x^3 - 20*x^4) *Log[25]^2 + (56 - 48*x - 168*x^2 + 96*x^3)*Log[25]^3 + (70 + 20*x - 162*x ^2 + 24*x^3)*Log[25]^4 + (56 + 64*x - 72*x^2)*Log[25]^5 + (28 + 48*x - 12* x^2)*Log[25]^6 + (8 + 16*x)*Log[25]^7 + (1 + 2*x)*Log[25]^8)*Log[x],x]
x - (3*x^2)/2 + (2*x^3)/3 + x^4/2 - (3*x^5)/5 + 8*x*Log[25] - 8*x^2*Log[25 ] + 4*x^4*Log[25] - (8*x^5*Log[25])/5 + 28*x*Log[25]^2 - 16*x^2*Log[25]^2 - 8*x^3*Log[25]^2 + 8*x^4*Log[25]^2 - (4*x^5*Log[25]^2)/5 + 56*x*Log[25]^3 - 12*x^2*Log[25]^3 - (56*x^3*Log[25]^3)/3 + 6*x^4*Log[25]^3 + 70*x*Log[25 ]^4 + 5*x^2*Log[25]^4 - 18*x^3*Log[25]^4 + (3*x^4*Log[25]^4)/2 + 56*x*Log[ 25]^5 + 16*x^2*Log[25]^5 - 8*x^3*Log[25]^5 + 28*x*Log[25]^6 + 12*x^2*Log[2 5]^6 - (4*x^3*Log[25]^6)/3 + 4*(1 + x)^2*Log[25]^7 + ((1 + x)^2*Log[25]^8) /2 - x*(1 + Log[25])^8 - (2*x^3*(1 + Log[25])^4*(1 - 4*Log[25] - 2*Log[25] ^2))/3 - (x^4*(1 + Log[25])^2*(1 + 6*Log[25] + 3*Log[25]^2))/2 + (x^5*(3 + 8*Log[25] + 4*Log[25]^2))/5 + (x^2*(1 + Log[25])^6*(3 - Log[25]^2 - Log[6 25]))/2 + x^6*Log[x] + x*(1 + Log[25])^8*Log[x] + 2*x^3*(1 + Log[25])^4*(1 - 4*Log[25] - 2*Log[25]^2)*Log[x] + 2*x^4*(1 + Log[25])^2*(1 + 6*Log[25] + 3*Log[25]^2)*Log[x] - x^5*(3 + 8*Log[25] + 4*Log[25]^2)*Log[x] - x^2*(1 + Log[25])^6*(3 - Log[25]^2 - Log[625])*Log[x]
3.10.51.3.1 Defintions of rubi rules used
Leaf count of result is larger than twice the leaf count of optimal. \(199\) vs. \(2(22)=44\).
Time = 1.30 (sec) , antiderivative size = 200, normalized size of antiderivative = 10.00
| method | result | size |
| norman | \(x^{6} \ln \left (x \right )+\left (-16 \ln \left (5\right )-3-16 \ln \left (5\right )^{2}\right ) x^{5} \ln \left (x \right )+\left (2+128 \ln \left (5\right )^{2}+96 \ln \left (5\right )^{4}+192 \ln \left (5\right )^{3}+32 \ln \left (5\right )\right ) x^{4} \ln \left (x \right )+\left (-768 \ln \left (5\right )^{5}+2-864 \ln \left (5\right )^{4}-448 \ln \left (5\right )^{3}-256 \ln \left (5\right )^{6}-96 \ln \left (5\right )^{2}\right ) x^{3} \ln \left (x \right )+\left (-3-128 \ln \left (5\right )^{2}-192 \ln \left (5\right )^{3}+160 \ln \left (5\right )^{4}+1536 \ln \left (5\right )^{6}+1024 \ln \left (5\right )^{7}-32 \ln \left (5\right )+256 \ln \left (5\right )^{8}+1024 \ln \left (5\right )^{5}\right ) x^{2} \ln \left (x \right )+\left (256 \ln \left (5\right )^{8}+1024 \ln \left (5\right )^{7}+1792 \ln \left (5\right )^{6}+1792 \ln \left (5\right )^{5}+1120 \ln \left (5\right )^{4}+448 \ln \left (5\right )^{3}+112 \ln \left (5\right )^{2}+16 \ln \left (5\right )+1\right ) x \ln \left (x \right )\) | \(200\) |
| risch | \(x \left (1-3 x +1536 x \ln \left (5\right )^{6}+128 x^{3} \ln \left (5\right )^{2}+192 x^{3} \ln \left (5\right )^{3}+160 x \ln \left (5\right )^{4}-32 x \ln \left (5\right )-96 x^{2} \ln \left (5\right )^{2}+32 x^{3} \ln \left (5\right )+96 x^{3} \ln \left (5\right )^{4}-16 x^{4} \ln \left (5\right )^{2}-128 x \ln \left (5\right )^{2}+256 \ln \left (5\right )^{8}+1024 \ln \left (5\right )^{7}+1792 \ln \left (5\right )^{6}+1792 \ln \left (5\right )^{5}-16 x^{4} \ln \left (5\right )+1120 \ln \left (5\right )^{4}+448 \ln \left (5\right )^{3}-448 x^{2} \ln \left (5\right )^{3}-768 x^{2} \ln \left (5\right )^{5}+16 \ln \left (5\right )+112 \ln \left (5\right )^{2}-3 x^{4}+2 x^{3}+2 x^{2}+x^{5}-192 \ln \left (5\right )^{3} x -864 \ln \left (5\right )^{4} x^{2}-256 \ln \left (5\right )^{6} x^{2}+1024 \ln \left (5\right )^{5} x +256 \ln \left (5\right )^{8} x +1024 \ln \left (5\right )^{7} x \right ) \ln \left (x \right )\) | \(223\) |
| parallelrisch | \(-96 x^{3} \ln \left (5\right )^{2} \ln \left (x \right )+x^{6} \ln \left (x \right )-3 x^{5} \ln \left (x \right )+2 x^{4} \ln \left (x \right )+x \ln \left (x \right )+256 x \ln \left (5\right )^{8} \ln \left (x \right )+16 x \ln \left (5\right ) \ln \left (x \right )-32 x^{2} \ln \left (5\right ) \ln \left (x \right )+2 x^{3} \ln \left (x \right )-3 x^{2} \ln \left (x \right )-128 \ln \left (x \right ) \ln \left (5\right )^{2} x^{2}+96 \ln \left (5\right )^{4} x^{4} \ln \left (x \right )-16 \ln \left (5\right ) x^{5} \ln \left (x \right )-16 \ln \left (5\right )^{2} x^{5} \ln \left (x \right )+192 \ln \left (5\right )^{3} x^{4} \ln \left (x \right )+256 \ln \left (5\right )^{8} x^{2} \ln \left (x \right )+1024 \ln \left (5\right )^{7} x^{2} \ln \left (x \right )+448 \ln \left (x \right ) \ln \left (5\right )^{3} x +112 \ln \left (x \right ) \ln \left (5\right )^{2} x +1120 \ln \left (x \right ) \ln \left (5\right )^{4} x +1024 \ln \left (x \right ) \ln \left (5\right )^{7} x +1536 \ln \left (x \right ) \ln \left (5\right )^{6} x^{2}+1792 \ln \left (x \right ) \ln \left (5\right )^{6} x +1024 \ln \left (x \right ) \ln \left (5\right )^{5} x^{2}-864 \ln \left (x \right ) \ln \left (5\right )^{4} x^{3}+1792 \ln \left (x \right ) \ln \left (5\right )^{5} x +160 \ln \left (x \right ) \ln \left (5\right )^{4} x^{2}-448 \ln \left (x \right ) \ln \left (5\right )^{3} x^{3}+128 \ln \left (x \right ) \ln \left (5\right )^{2} x^{4}-192 \ln \left (x \right ) \ln \left (5\right )^{3} x^{2}+32 \ln \left (x \right ) \ln \left (5\right ) x^{4}-256 \ln \left (5\right )^{6} x^{3} \ln \left (x \right )-768 \ln \left (5\right )^{5} x^{3} \ln \left (x \right )\) | \(313\) |
| default | \(\text {Expression too large to display}\) | \(672\) |
| parts | \(\text {Expression too large to display}\) | \(724\) |
int((256*(1+2*x)*ln(5)^8+128*(16*x+8)*ln(5)^7+64*(-12*x^2+48*x+28)*ln(5)^6 +32*(-72*x^2+64*x+56)*ln(5)^5+16*(24*x^3-162*x^2+20*x+70)*ln(5)^4+8*(96*x^ 3-168*x^2-48*x+56)*ln(5)^3+4*(-20*x^4+128*x^3-72*x^2-64*x+28)*ln(5)^2+2*(- 40*x^4+64*x^3-32*x+8)*ln(5)+6*x^5-15*x^4+8*x^3+6*x^2-6*x+1)*ln(x)+256*(1+x )*ln(5)^8+128*(8*x+8)*ln(5)^7+64*(-4*x^2+24*x+28)*ln(5)^6+32*(-24*x^2+32*x +56)*ln(5)^5+16*(6*x^3-54*x^2+10*x+70)*ln(5)^4+8*(24*x^3-56*x^2-24*x+56)*l n(5)^3+4*(-4*x^4+32*x^3-24*x^2-32*x+28)*ln(5)^2+2*(-8*x^4+16*x^3-16*x+8)*l n(5)+x^5-3*x^4+2*x^3+2*x^2-3*x+1,x,method=_RETURNVERBOSE)
x^6*ln(x)+(-16*ln(5)-3-16*ln(5)^2)*x^5*ln(x)+(2+128*ln(5)^2+96*ln(5)^4+192 *ln(5)^3+32*ln(5))*x^4*ln(x)+(-768*ln(5)^5+2-864*ln(5)^4-448*ln(5)^3-256*l n(5)^6-96*ln(5)^2)*x^3*ln(x)+(-3-128*ln(5)^2-192*ln(5)^3+160*ln(5)^4+1536* ln(5)^6+1024*ln(5)^7-32*ln(5)+256*ln(5)^8+1024*ln(5)^5)*x^2*ln(x)+(256*ln( 5)^8+1024*ln(5)^7+1792*ln(5)^6+1792*ln(5)^5+1120*ln(5)^4+448*ln(5)^3+112*l n(5)^2+16*ln(5)+1)*x*ln(x)
Leaf count of result is larger than twice the leaf count of optimal. 187 vs. \(2 (22) = 44\).
Time = 0.25 (sec) , antiderivative size = 187, normalized size of antiderivative = 9.35 \[ \int \left (1-3 x+2 x^2+2 x^3-3 x^4+x^5+\left (8-16 x+16 x^3-8 x^4\right ) \log (25)+\left (28-32 x-24 x^2+32 x^3-4 x^4\right ) \log ^2(25)+\left (56-24 x-56 x^2+24 x^3\right ) \log ^3(25)+\left (70+10 x-54 x^2+6 x^3\right ) \log ^4(25)+\left (56+32 x-24 x^2\right ) \log ^5(25)+\left (28+24 x-4 x^2\right ) \log ^6(25)+(8+8 x) \log ^7(25)+(1+x) \log ^8(25)+\left (1-6 x+6 x^2+8 x^3-15 x^4+6 x^5+\left (8-32 x+64 x^3-40 x^4\right ) \log (25)+\left (28-64 x-72 x^2+128 x^3-20 x^4\right ) \log ^2(25)+\left (56-48 x-168 x^2+96 x^3\right ) \log ^3(25)+\left (70+20 x-162 x^2+24 x^3\right ) \log ^4(25)+\left (56+64 x-72 x^2\right ) \log ^5(25)+\left (28+48 x-12 x^2\right ) \log ^6(25)+(8+16 x) \log ^7(25)+(1+2 x) \log ^8(25)\right ) \log (x)\right ) \, dx={\left (256 \, {\left (x^{2} + x\right )} \log \left (5\right )^{8} + 1024 \, {\left (x^{2} + x\right )} \log \left (5\right )^{7} - 256 \, {\left (x^{3} - 6 \, x^{2} - 7 \, x\right )} \log \left (5\right )^{6} + x^{6} - 256 \, {\left (3 \, x^{3} - 4 \, x^{2} - 7 \, x\right )} \log \left (5\right )^{5} - 3 \, x^{5} + 32 \, {\left (3 \, x^{4} - 27 \, x^{3} + 5 \, x^{2} + 35 \, x\right )} \log \left (5\right )^{4} + 2 \, x^{4} + 64 \, {\left (3 \, x^{4} - 7 \, x^{3} - 3 \, x^{2} + 7 \, x\right )} \log \left (5\right )^{3} + 2 \, x^{3} - 16 \, {\left (x^{5} - 8 \, x^{4} + 6 \, x^{3} + 8 \, x^{2} - 7 \, x\right )} \log \left (5\right )^{2} - 3 \, x^{2} - 16 \, {\left (x^{5} - 2 \, x^{4} + 2 \, x^{2} - x\right )} \log \left (5\right ) + x\right )} \log \left (x\right ) \]
integrate((256*(1+2*x)*log(5)^8+128*(16*x+8)*log(5)^7+64*(-12*x^2+48*x+28) *log(5)^6+32*(-72*x^2+64*x+56)*log(5)^5+16*(24*x^3-162*x^2+20*x+70)*log(5) ^4+8*(96*x^3-168*x^2-48*x+56)*log(5)^3+4*(-20*x^4+128*x^3-72*x^2-64*x+28)* log(5)^2+2*(-40*x^4+64*x^3-32*x+8)*log(5)+6*x^5-15*x^4+8*x^3+6*x^2-6*x+1)* log(x)+256*(1+x)*log(5)^8+128*(8*x+8)*log(5)^7+64*(-4*x^2+24*x+28)*log(5)^ 6+32*(-24*x^2+32*x+56)*log(5)^5+16*(6*x^3-54*x^2+10*x+70)*log(5)^4+8*(24*x ^3-56*x^2-24*x+56)*log(5)^3+4*(-4*x^4+32*x^3-24*x^2-32*x+28)*log(5)^2+2*(- 8*x^4+16*x^3-16*x+8)*log(5)+x^5-3*x^4+2*x^3+2*x^2-3*x+1,x, algorithm=\
(256*(x^2 + x)*log(5)^8 + 1024*(x^2 + x)*log(5)^7 - 256*(x^3 - 6*x^2 - 7*x )*log(5)^6 + x^6 - 256*(3*x^3 - 4*x^2 - 7*x)*log(5)^5 - 3*x^5 + 32*(3*x^4 - 27*x^3 + 5*x^2 + 35*x)*log(5)^4 + 2*x^4 + 64*(3*x^4 - 7*x^3 - 3*x^2 + 7* x)*log(5)^3 + 2*x^3 - 16*(x^5 - 8*x^4 + 6*x^3 + 8*x^2 - 7*x)*log(5)^2 - 3* x^2 - 16*(x^5 - 2*x^4 + 2*x^2 - x)*log(5) + x)*log(x)
Leaf count of result is larger than twice the leaf count of optimal. 282 vs. \(2 (19) = 38\).
Time = 0.29 (sec) , antiderivative size = 282, normalized size of antiderivative = 14.10 \[ \int \left (1-3 x+2 x^2+2 x^3-3 x^4+x^5+\left (8-16 x+16 x^3-8 x^4\right ) \log (25)+\left (28-32 x-24 x^2+32 x^3-4 x^4\right ) \log ^2(25)+\left (56-24 x-56 x^2+24 x^3\right ) \log ^3(25)+\left (70+10 x-54 x^2+6 x^3\right ) \log ^4(25)+\left (56+32 x-24 x^2\right ) \log ^5(25)+\left (28+24 x-4 x^2\right ) \log ^6(25)+(8+8 x) \log ^7(25)+(1+x) \log ^8(25)+\left (1-6 x+6 x^2+8 x^3-15 x^4+6 x^5+\left (8-32 x+64 x^3-40 x^4\right ) \log (25)+\left (28-64 x-72 x^2+128 x^3-20 x^4\right ) \log ^2(25)+\left (56-48 x-168 x^2+96 x^3\right ) \log ^3(25)+\left (70+20 x-162 x^2+24 x^3\right ) \log ^4(25)+\left (56+64 x-72 x^2\right ) \log ^5(25)+\left (28+48 x-12 x^2\right ) \log ^6(25)+(8+16 x) \log ^7(25)+(1+2 x) \log ^8(25)\right ) \log (x)\right ) \, dx=\left (x^{6} - 16 x^{5} \log {\left (5 \right )}^{2} - 16 x^{5} \log {\left (5 \right )} - 3 x^{5} + 2 x^{4} + 32 x^{4} \log {\left (5 \right )} + 128 x^{4} \log {\left (5 \right )}^{2} + 96 x^{4} \log {\left (5 \right )}^{4} + 192 x^{4} \log {\left (5 \right )}^{3} - 768 x^{3} \log {\left (5 \right )}^{5} - 864 x^{3} \log {\left (5 \right )}^{4} - 256 x^{3} \log {\left (5 \right )}^{6} - 448 x^{3} \log {\left (5 \right )}^{3} - 96 x^{3} \log {\left (5 \right )}^{2} + 2 x^{3} - 192 x^{2} \log {\left (5 \right )}^{3} - 128 x^{2} \log {\left (5 \right )}^{2} - 32 x^{2} \log {\left (5 \right )} - 3 x^{2} + 160 x^{2} \log {\left (5 \right )}^{4} + 1024 x^{2} \log {\left (5 \right )}^{5} + 256 x^{2} \log {\left (5 \right )}^{8} + 1536 x^{2} \log {\left (5 \right )}^{6} + 1024 x^{2} \log {\left (5 \right )}^{7} + x + 16 x \log {\left (5 \right )} + 112 x \log {\left (5 \right )}^{2} + 448 x \log {\left (5 \right )}^{3} + 1120 x \log {\left (5 \right )}^{4} + 256 x \log {\left (5 \right )}^{8} + 1792 x \log {\left (5 \right )}^{5} + 1024 x \log {\left (5 \right )}^{7} + 1792 x \log {\left (5 \right )}^{6}\right ) \log {\left (x \right )} \]
integrate((256*(1+2*x)*ln(5)**8+128*(16*x+8)*ln(5)**7+64*(-12*x**2+48*x+28 )*ln(5)**6+32*(-72*x**2+64*x+56)*ln(5)**5+16*(24*x**3-162*x**2+20*x+70)*ln (5)**4+8*(96*x**3-168*x**2-48*x+56)*ln(5)**3+4*(-20*x**4+128*x**3-72*x**2- 64*x+28)*ln(5)**2+2*(-40*x**4+64*x**3-32*x+8)*ln(5)+6*x**5-15*x**4+8*x**3+ 6*x**2-6*x+1)*ln(x)+256*(1+x)*ln(5)**8+128*(8*x+8)*ln(5)**7+64*(-4*x**2+24 *x+28)*ln(5)**6+32*(-24*x**2+32*x+56)*ln(5)**5+16*(6*x**3-54*x**2+10*x+70) *ln(5)**4+8*(24*x**3-56*x**2-24*x+56)*ln(5)**3+4*(-4*x**4+32*x**3-24*x**2- 32*x+28)*ln(5)**2+2*(-8*x**4+16*x**3-16*x+8)*ln(5)+x**5-3*x**4+2*x**3+2*x* *2-3*x+1,x)
(x**6 - 16*x**5*log(5)**2 - 16*x**5*log(5) - 3*x**5 + 2*x**4 + 32*x**4*log (5) + 128*x**4*log(5)**2 + 96*x**4*log(5)**4 + 192*x**4*log(5)**3 - 768*x* *3*log(5)**5 - 864*x**3*log(5)**4 - 256*x**3*log(5)**6 - 448*x**3*log(5)** 3 - 96*x**3*log(5)**2 + 2*x**3 - 192*x**2*log(5)**3 - 128*x**2*log(5)**2 - 32*x**2*log(5) - 3*x**2 + 160*x**2*log(5)**4 + 1024*x**2*log(5)**5 + 256* x**2*log(5)**8 + 1536*x**2*log(5)**6 + 1024*x**2*log(5)**7 + x + 16*x*log( 5) + 112*x*log(5)**2 + 448*x*log(5)**3 + 1120*x*log(5)**4 + 256*x*log(5)** 8 + 1792*x*log(5)**5 + 1024*x*log(5)**7 + 1792*x*log(5)**6)*log(x)
Leaf count of result is larger than twice the leaf count of optimal. 559 vs. \(2 (22) = 44\).
Time = 0.19 (sec) , antiderivative size = 559, normalized size of antiderivative = 27.95 \[ \int \left (1-3 x+2 x^2+2 x^3-3 x^4+x^5+\left (8-16 x+16 x^3-8 x^4\right ) \log (25)+\left (28-32 x-24 x^2+32 x^3-4 x^4\right ) \log ^2(25)+\left (56-24 x-56 x^2+24 x^3\right ) \log ^3(25)+\left (70+10 x-54 x^2+6 x^3\right ) \log ^4(25)+\left (56+32 x-24 x^2\right ) \log ^5(25)+\left (28+24 x-4 x^2\right ) \log ^6(25)+(8+8 x) \log ^7(25)+(1+x) \log ^8(25)+\left (1-6 x+6 x^2+8 x^3-15 x^4+6 x^5+\left (8-32 x+64 x^3-40 x^4\right ) \log (25)+\left (28-64 x-72 x^2+128 x^3-20 x^4\right ) \log ^2(25)+\left (56-48 x-168 x^2+96 x^3\right ) \log ^3(25)+\left (70+20 x-162 x^2+24 x^3\right ) \log ^4(25)+\left (56+64 x-72 x^2\right ) \log ^5(25)+\left (28+48 x-12 x^2\right ) \log ^6(25)+(8+16 x) \log ^7(25)+(1+2 x) \log ^8(25)\right ) \log (x)\right ) \, dx =\text {Too large to display} \]
integrate((256*(1+2*x)*log(5)^8+128*(16*x+8)*log(5)^7+64*(-12*x^2+48*x+28) *log(5)^6+32*(-72*x^2+64*x+56)*log(5)^5+16*(24*x^3-162*x^2+20*x+70)*log(5) ^4+8*(96*x^3-168*x^2-48*x+56)*log(5)^3+4*(-20*x^4+128*x^3-72*x^2-64*x+28)* log(5)^2+2*(-40*x^4+64*x^3-32*x+8)*log(5)+6*x^5-15*x^4+8*x^3+6*x^2-6*x+1)* log(x)+256*(1+x)*log(5)^8+128*(8*x+8)*log(5)^7+64*(-4*x^2+24*x+28)*log(5)^ 6+32*(-24*x^2+32*x+56)*log(5)^5+16*(6*x^3-54*x^2+10*x+70)*log(5)^4+8*(24*x ^3-56*x^2-24*x+56)*log(5)^3+4*(-4*x^4+32*x^3-24*x^2-32*x+28)*log(5)^2+2*(- 8*x^4+16*x^3-16*x+8)*log(5)+x^5-3*x^4+2*x^3+2*x^2-3*x+1,x, algorithm=\
128*(x^2 + 2*x)*log(5)^8 + 512*(x^2 + 2*x)*log(5)^7 - 256/3*(x^3 - 9*x^2 - 21*x)*log(5)^6 + 1/5*(16*log(5)^2 + 16*log(5) + 3)*x^5 - 256*(x^3 - 2*x^2 - 7*x)*log(5)^5 - 1/2*(48*log(5)^4 + 96*log(5)^3 + 64*log(5)^2 + 16*log(5 ) + 1)*x^4 - 3/5*x^5 + 8*(3*x^4 - 36*x^3 + 10*x^2 + 140*x)*log(5)^4 + 2/3* (128*log(5)^6 + 384*log(5)^5 + 432*log(5)^4 + 224*log(5)^3 + 48*log(5)^2 - 1)*x^3 + 1/2*x^4 + 16/3*(9*x^4 - 28*x^3 - 18*x^2 + 84*x)*log(5)^3 - 1/2*( 256*log(5)^8 + 1024*log(5)^7 + 1536*log(5)^6 + 1024*log(5)^5 + 160*log(5)^ 4 - 192*log(5)^3 - 128*log(5)^2 - 32*log(5) - 3)*x^2 + 2/3*x^3 - 16/5*(x^5 - 10*x^4 + 10*x^3 + 20*x^2 - 35*x)*log(5)^2 - (256*log(5)^8 + 1024*log(5) ^7 + 1792*log(5)^6 + 1792*log(5)^5 + 1120*log(5)^4 + 448*log(5)^3 + 112*lo g(5)^2 + 16*log(5) + 1)*x - 3/2*x^2 - 8/5*(2*x^5 - 5*x^4 + 10*x^2 - 10*x)* log(5) + (256*(x^2 + x)*log(5)^8 + 1024*(x^2 + x)*log(5)^7 - 256*(x^3 - 6* x^2 - 7*x)*log(5)^6 + x^6 - 256*(3*x^3 - 4*x^2 - 7*x)*log(5)^5 - 3*x^5 + 3 2*(3*x^4 - 27*x^3 + 5*x^2 + 35*x)*log(5)^4 + 2*x^4 + 64*(3*x^4 - 7*x^3 - 3 *x^2 + 7*x)*log(5)^3 + 2*x^3 - 16*(x^5 - 8*x^4 + 6*x^3 + 8*x^2 - 7*x)*log( 5)^2 - 3*x^2 - 16*(x^5 - 2*x^4 + 2*x^2 - x)*log(5) + x)*log(x) + x
Leaf count of result is larger than twice the leaf count of optimal. 694 vs. \(2 (22) = 44\).
Time = 0.27 (sec) , antiderivative size = 694, normalized size of antiderivative = 34.70 \[ \int \left (1-3 x+2 x^2+2 x^3-3 x^4+x^5+\left (8-16 x+16 x^3-8 x^4\right ) \log (25)+\left (28-32 x-24 x^2+32 x^3-4 x^4\right ) \log ^2(25)+\left (56-24 x-56 x^2+24 x^3\right ) \log ^3(25)+\left (70+10 x-54 x^2+6 x^3\right ) \log ^4(25)+\left (56+32 x-24 x^2\right ) \log ^5(25)+\left (28+24 x-4 x^2\right ) \log ^6(25)+(8+8 x) \log ^7(25)+(1+x) \log ^8(25)+\left (1-6 x+6 x^2+8 x^3-15 x^4+6 x^5+\left (8-32 x+64 x^3-40 x^4\right ) \log (25)+\left (28-64 x-72 x^2+128 x^3-20 x^4\right ) \log ^2(25)+\left (56-48 x-168 x^2+96 x^3\right ) \log ^3(25)+\left (70+20 x-162 x^2+24 x^3\right ) \log ^4(25)+\left (56+64 x-72 x^2\right ) \log ^5(25)+\left (28+48 x-12 x^2\right ) \log ^6(25)+(8+16 x) \log ^7(25)+(1+2 x) \log ^8(25)\right ) \log (x)\right ) \, dx=\text {Too large to display} \]
integrate((256*(1+2*x)*log(5)^8+128*(16*x+8)*log(5)^7+64*(-12*x^2+48*x+28) *log(5)^6+32*(-72*x^2+64*x+56)*log(5)^5+16*(24*x^3-162*x^2+20*x+70)*log(5) ^4+8*(96*x^3-168*x^2-48*x+56)*log(5)^3+4*(-20*x^4+128*x^3-72*x^2-64*x+28)* log(5)^2+2*(-40*x^4+64*x^3-32*x+8)*log(5)+6*x^5-15*x^4+8*x^3+6*x^2-6*x+1)* log(x)+256*(1+x)*log(5)^8+128*(8*x+8)*log(5)^7+64*(-4*x^2+24*x+28)*log(5)^ 6+32*(-24*x^2+32*x+56)*log(5)^5+16*(6*x^3-54*x^2+10*x+70)*log(5)^4+8*(24*x ^3-56*x^2-24*x+56)*log(5)^3+4*(-4*x^4+32*x^3-24*x^2-32*x+28)*log(5)^2+2*(- 8*x^4+16*x^3-16*x+8)*log(5)+x^5-3*x^4+2*x^3+2*x^2-3*x+1,x, algorithm=\
256*x^2*log(5)^8*log(x) - 128*x^2*log(5)^8 - 256*x^3*log(5)^6*log(x) + 102 4*x^2*log(5)^7*log(x) + 256*x*log(5)^8*log(x) + 256/3*x^3*log(5)^6 - 512*x ^2*log(5)^7 + 128*(x^2 + 2*x)*log(5)^8 - 256*x*log(5)^8 + 96*x^4*log(5)^4* log(x) - 768*x^3*log(5)^5*log(x) + 1536*x^2*log(5)^6*log(x) + 1024*x*log(5 )^7*log(x) - 24*x^4*log(5)^4 + 256*x^3*log(5)^5 - 768*x^2*log(5)^6 + 512*( x^2 + 2*x)*log(5)^7 - 1024*x*log(5)^7 - 16*x^5*log(5)^2*log(x) + 192*x^4*l og(5)^3*log(x) - 864*x^3*log(5)^4*log(x) + 1024*x^2*log(5)^5*log(x) + 1792 *x*log(5)^6*log(x) + 16/5*x^5*log(5)^2 - 48*x^4*log(5)^3 + 288*x^3*log(5)^ 4 - 512*x^2*log(5)^5 - 256/3*(x^3 - 9*x^2 - 21*x)*log(5)^6 - 1792*x*log(5) ^6 + x^6*log(x) - 16*x^5*log(5)*log(x) + 128*x^4*log(5)^2*log(x) - 448*x^3 *log(5)^3*log(x) + 160*x^2*log(5)^4*log(x) + 1792*x*log(5)^5*log(x) + 16/5 *x^5*log(5) - 32*x^4*log(5)^2 + 448/3*x^3*log(5)^3 - 80*x^2*log(5)^4 - 256 *(x^3 - 2*x^2 - 7*x)*log(5)^5 - 1792*x*log(5)^5 - 3*x^5*log(x) + 32*x^4*lo g(5)*log(x) - 96*x^3*log(5)^2*log(x) - 192*x^2*log(5)^3*log(x) + 1120*x*lo g(5)^4*log(x) - 8*x^4*log(5) + 32*x^3*log(5)^2 + 96*x^2*log(5)^3 + 8*(3*x^ 4 - 36*x^3 + 10*x^2 + 140*x)*log(5)^4 - 1120*x*log(5)^4 + 2*x^4*log(x) - 1 28*x^2*log(5)^2*log(x) + 448*x*log(5)^3*log(x) + 64*x^2*log(5)^2 + 16/3*(9 *x^4 - 28*x^3 - 18*x^2 + 84*x)*log(5)^3 - 448*x*log(5)^3 + 2*x^3*log(x) - 32*x^2*log(5)*log(x) + 112*x*log(5)^2*log(x) + 16*x^2*log(5) - 16/5*(x^5 - 10*x^4 + 10*x^3 + 20*x^2 - 35*x)*log(5)^2 - 112*x*log(5)^2 - 3*x^2*log...
Time = 10.35 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int \left (1-3 x+2 x^2+2 x^3-3 x^4+x^5+\left (8-16 x+16 x^3-8 x^4\right ) \log (25)+\left (28-32 x-24 x^2+32 x^3-4 x^4\right ) \log ^2(25)+\left (56-24 x-56 x^2+24 x^3\right ) \log ^3(25)+\left (70+10 x-54 x^2+6 x^3\right ) \log ^4(25)+\left (56+32 x-24 x^2\right ) \log ^5(25)+\left (28+24 x-4 x^2\right ) \log ^6(25)+(8+8 x) \log ^7(25)+(1+x) \log ^8(25)+\left (1-6 x+6 x^2+8 x^3-15 x^4+6 x^5+\left (8-32 x+64 x^3-40 x^4\right ) \log (25)+\left (28-64 x-72 x^2+128 x^3-20 x^4\right ) \log ^2(25)+\left (56-48 x-168 x^2+96 x^3\right ) \log ^3(25)+\left (70+20 x-162 x^2+24 x^3\right ) \log ^4(25)+\left (56+64 x-72 x^2\right ) \log ^5(25)+\left (28+48 x-12 x^2\right ) \log ^6(25)+(8+16 x) \log ^7(25)+(1+2 x) \log ^8(25)\right ) \log (x)\right ) \, dx=x\,\ln \left (x\right )\,\left (x+1\right )\,{\left (\ln \left (625\right )-x+4\,{\ln \left (5\right )}^2+1\right )}^4 \]
int(256*log(5)^8*(x + 1) - 3*x - 4*log(5)^2*(32*x + 24*x^2 - 32*x^3 + 4*x^ 4 - 28) + 128*log(5)^7*(8*x + 8) + log(x)*(256*log(5)^8*(2*x + 1) - 4*log( 5)^2*(64*x + 72*x^2 - 128*x^3 + 20*x^4 - 28) - 6*x + 128*log(5)^7*(16*x + 8) - 2*log(5)*(32*x - 64*x^3 + 40*x^4 - 8) + 64*log(5)^6*(48*x - 12*x^2 + 28) + 32*log(5)^5*(64*x - 72*x^2 + 56) + 16*log(5)^4*(20*x - 162*x^2 + 24* x^3 + 70) - 8*log(5)^3*(48*x + 168*x^2 - 96*x^3 - 56) + 6*x^2 + 8*x^3 - 15 *x^4 + 6*x^5 + 1) - 2*log(5)*(16*x - 16*x^3 + 8*x^4 - 8) + 64*log(5)^6*(24 *x - 4*x^2 + 28) + 32*log(5)^5*(32*x - 24*x^2 + 56) + 16*log(5)^4*(10*x - 54*x^2 + 6*x^3 + 70) - 8*log(5)^3*(24*x + 56*x^2 - 24*x^3 - 56) + 2*x^2 + 2*x^3 - 3*x^4 + x^5 + 1,x)