Integrand size = 315, antiderivative size = 20 \[ \int \left (1-3 x+2 x^2+2 x^3-3 x^4+x^5+\left (8-16 x+16 x^3-8 x^4\right ) \log (25)+\left (28-32 x-24 x^2+32 x^3-4 x^4\right ) \log ^2(25)+\left (56-24 x-56 x^2+24 x^3\right ) \log ^3(25)+\left (70+10 x-54 x^2+6 x^3\right ) \log ^4(25)+\left (56+32 x-24 x^2\right ) \log ^5(25)+\left (28+24 x-4 x^2\right ) \log ^6(25)+(8+8 x) \log ^7(25)+(1+x) \log ^8(25)+\left (1-6 x+6 x^2+8 x^3-15 x^4+6 x^5+\left (8-32 x+64 x^3-40 x^4\right ) \log (25)+\left (28-64 x-72 x^2+128 x^3-20 x^4\right ) \log ^2(25)+\left (56-48 x-168 x^2+96 x^3\right ) \log ^3(25)+\left (70+20 x-162 x^2+24 x^3\right ) \log ^4(25)+\left (56+64 x-72 x^2\right ) \log ^5(25)+\left (28+48 x-12 x^2\right ) \log ^6(25)+(8+16 x) \log ^7(25)+(1+2 x) \log ^8(25)\right ) \log (x)\right ) \, dx=\left (x+x^2\right ) \left (x-(1+\log (25))^2\right )^4 \log (x) \]
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Leaf count is larger than twice the leaf count of optimal. \(464\) vs. \(2(20)=40\).
Time = 0.20 (sec) , antiderivative size = 464, normalized size of antiderivative = 23.20, number of steps used = 15, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.010, Rules used = {2403, 2341, 2332} \[ \int \left (1-3 x+2 x^2+2 x^3-3 x^4+x^5+\left (8-16 x+16 x^3-8 x^4\right ) \log (25)+\left (28-32 x-24 x^2+32 x^3-4 x^4\right ) \log ^2(25)+\left (56-24 x-56 x^2+24 x^3\right ) \log ^3(25)+\left (70+10 x-54 x^2+6 x^3\right ) \log ^4(25)+\left (56+32 x-24 x^2\right ) \log ^5(25)+\left (28+24 x-4 x^2\right ) \log ^6(25)+(8+8 x) \log ^7(25)+(1+x) \log ^8(25)+\left (1-6 x+6 x^2+8 x^3-15 x^4+6 x^5+\left (8-32 x+64 x^3-40 x^4\right ) \log (25)+\left (28-64 x-72 x^2+128 x^3-20 x^4\right ) \log ^2(25)+\left (56-48 x-168 x^2+96 x^3\right ) \log ^3(25)+\left (70+20 x-162 x^2+24 x^3\right ) \log ^4(25)+\left (56+64 x-72 x^2\right ) \log ^5(25)+\left (28+48 x-12 x^2\right ) \log ^6(25)+(8+16 x) \log ^7(25)+(1+2 x) \log ^8(25)\right ) \log (x)\right ) \, dx=x^6 \log (x)-\frac {3 x^5}{5}-x^5 \left (3+4 \log ^2(25)+8 \log (25)\right ) \log (x)+\frac {1}{5} x^5 \left (3+4 \log ^2(25)+8 \log (25)\right )-\frac {4}{5} x^5 \log ^2(25)-\frac {8}{5} x^5 \log (25)+\frac {x^4}{2}+\frac {3}{2} x^4 \log ^4(25)+6 x^4 \log ^3(25)+2 x^4 (1+\log (25))^2 \left (1+3 \log ^2(25)+6 \log (25)\right ) \log (x)-\frac {1}{2} x^4 (1+\log (25))^2 \left (1+3 \log ^2(25)+6 \log (25)\right )+8 x^4 \log ^2(25)+4 x^4 \log (25)+\frac {2 x^3}{3}-\frac {4}{3} x^3 \log ^6(25)-8 x^3 \log ^5(25)-18 x^3 \log ^4(25)-\frac {56}{3} x^3 \log ^3(25)+2 x^3 (1+\log (25))^4 \left (1-2 \log ^2(25)-4 \log (25)\right ) \log (x)-\frac {2}{3} x^3 (1+\log (25))^4 \left (1-2 \log ^2(25)-4 \log (25)\right )-8 x^3 \log ^2(25)-\frac {3 x^2}{2}+12 x^2 \log ^6(25)+16 x^2 \log ^5(25)+5 x^2 \log ^4(25)-12 x^2 \log ^3(25)-x^2 (1+\log (25))^6 \left (3-\log ^2(25)-\log (625)\right ) \log (x)+\frac {1}{2} x^2 (1+\log (25))^6 \left (3-\log ^2(25)-\log (625)\right )-16 x^2 \log ^2(25)-8 x^2 \log (25)+x+\frac {1}{2} (x+1)^2 \log ^8(25)+4 (x+1)^2 \log ^7(25)+28 x \log ^6(25)+56 x \log ^5(25)+70 x \log ^4(25)+56 x \log ^3(25)+28 x \log ^2(25)+x (1+\log (25))^8 \log (x)-x (1+\log (25))^8+8 x \log (25) \]
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Rule 2332
Rule 2341
Rule 2403
Rubi steps \begin{align*} \text {integral}& = x-\frac {3 x^2}{2}+\frac {2 x^3}{3}+\frac {x^4}{2}-\frac {3 x^5}{5}+\frac {x^6}{6}+4 (1+x)^2 \log ^7(25)+\frac {1}{2} (1+x)^2 \log ^8(25)+\log (25) \int \left (8-16 x+16 x^3-8 x^4\right ) \, dx+\log ^2(25) \int \left (28-32 x-24 x^2+32 x^3-4 x^4\right ) \, dx+\log ^3(25) \int \left (56-24 x-56 x^2+24 x^3\right ) \, dx+\log ^4(25) \int \left (70+10 x-54 x^2+6 x^3\right ) \, dx+\log ^5(25) \int \left (56+32 x-24 x^2\right ) \, dx+\log ^6(25) \int \left (28+24 x-4 x^2\right ) \, dx+\int \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) \, dx \\ & = x-\frac {3 x^2}{2}+\frac {2 x^3}{3}+\frac {x^4}{2}-\frac {3 x^5}{5}+\frac {x^6}{6}+8 x \log (25)-8 x^2 \log (25)+4 x^4 \log (25)-\frac {8}{5} x^5 \log (25)+28 x \log ^2(25)-16 x^2 \log ^2(25)-8 x^3 \log ^2(25)+8 x^4 \log ^2(25)-\frac {4}{5} x^5 \log ^2(25)+56 x \log ^3(25)-12 x^2 \log ^3(25)-\frac {56}{3} x^3 \log ^3(25)+6 x^4 \log ^3(25)+70 x \log ^4(25)+5 x^2 \log ^4(25)-18 x^3 \log ^4(25)+\frac {3}{2} x^4 \log ^4(25)+56 x \log ^5(25)+16 x^2 \log ^5(25)-8 x^3 \log ^5(25)+28 x \log ^6(25)+12 x^2 \log ^6(25)-\frac {4}{3} x^3 \log ^6(25)+4 (1+x)^2 \log ^7(25)+\frac {1}{2} (1+x)^2 \log ^8(25)+\int \left (6 x^5 \log (x)+(1+\log (25))^8 \log (x)-6 x^2 (1+\log (25))^4 \left (-1+4 \log (25)+2 \log ^2(25)\right ) \log (x)+8 x^3 (1+\log (25))^2 \left (1+6 \log (25)+3 \log ^2(25)\right ) \log (x)-5 x^4 \left (3+8 \log (25)+4 \log ^2(25)\right ) \log (x)+2 x (1+\log (25))^6 \left (-3+\log ^2(25)+\log (625)\right ) \log (x)\right ) \, dx \\ & = x-\frac {3 x^2}{2}+\frac {2 x^3}{3}+\frac {x^4}{2}-\frac {3 x^5}{5}+\frac {x^6}{6}+8 x \log (25)-8 x^2 \log (25)+4 x^4 \log (25)-\frac {8}{5} x^5 \log (25)+28 x \log ^2(25)-16 x^2 \log ^2(25)-8 x^3 \log ^2(25)+8 x^4 \log ^2(25)-\frac {4}{5} x^5 \log ^2(25)+56 x \log ^3(25)-12 x^2 \log ^3(25)-\frac {56}{3} x^3 \log ^3(25)+6 x^4 \log ^3(25)+70 x \log ^4(25)+5 x^2 \log ^4(25)-18 x^3 \log ^4(25)+\frac {3}{2} x^4 \log ^4(25)+56 x \log ^5(25)+16 x^2 \log ^5(25)-8 x^3 \log ^5(25)+28 x \log ^6(25)+12 x^2 \log ^6(25)-\frac {4}{3} x^3 \log ^6(25)+4 (1+x)^2 \log ^7(25)+\frac {1}{2} (1+x)^2 \log ^8(25)+6 \int x^5 \log (x) \, dx+(1+\log (25))^8 \int \log (x) \, dx+\left (6 (1+\log (25))^4 \left (1-4 \log (25)-2 \log ^2(25)\right )\right ) \int x^2 \log (x) \, dx+\left (8 (1+\log (25))^2 \left (1+6 \log (25)+3 \log ^2(25)\right )\right ) \int x^3 \log (x) \, dx-\left (5 \left (3+8 \log (25)+4 \log ^2(25)\right )\right ) \int x^4 \log (x) \, dx-\left (2 (1+\log (25))^6 \left (3-\log ^2(25)-\log (625)\right )\right ) \int x \log (x) \, dx \\ & = x-\frac {3 x^2}{2}+\frac {2 x^3}{3}+\frac {x^4}{2}-\frac {3 x^5}{5}+8 x \log (25)-8 x^2 \log (25)+4 x^4 \log (25)-\frac {8}{5} x^5 \log (25)+28 x \log ^2(25)-16 x^2 \log ^2(25)-8 x^3 \log ^2(25)+8 x^4 \log ^2(25)-\frac {4}{5} x^5 \log ^2(25)+56 x \log ^3(25)-12 x^2 \log ^3(25)-\frac {56}{3} x^3 \log ^3(25)+6 x^4 \log ^3(25)+70 x \log ^4(25)+5 x^2 \log ^4(25)-18 x^3 \log ^4(25)+\frac {3}{2} x^4 \log ^4(25)+56 x \log ^5(25)+16 x^2 \log ^5(25)-8 x^3 \log ^5(25)+28 x \log ^6(25)+12 x^2 \log ^6(25)-\frac {4}{3} x^3 \log ^6(25)+4 (1+x)^2 \log ^7(25)+\frac {1}{2} (1+x)^2 \log ^8(25)-x (1+\log (25))^8-\frac {2}{3} x^3 (1+\log (25))^4 \left (1-4 \log (25)-2 \log ^2(25)\right )-\frac {1}{2} x^4 (1+\log (25))^2 \left (1+6 \log (25)+3 \log ^2(25)\right )+\frac {1}{5} x^5 \left (3+8 \log (25)+4 \log ^2(25)\right )+\frac {1}{2} x^2 (1+\log (25))^6 \left (3-\log ^2(25)-\log (625)\right )+x^6 \log (x)+x (1+\log (25))^8 \log (x)+2 x^3 (1+\log (25))^4 \left (1-4 \log (25)-2 \log ^2(25)\right ) \log (x)+2 x^4 (1+\log (25))^2 \left (1+6 \log (25)+3 \log ^2(25)\right ) \log (x)-x^5 \left (3+8 \log (25)+4 \log ^2(25)\right ) \log (x)-x^2 (1+\log (25))^6 \left (3-\log ^2(25)-\log (625)\right ) \log (x) \\ \end{align*}
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 \[ \int \left (1-3 x+2 x^2+2 x^3-3 x^4+x^5+\left (8-16 x+16 x^3-8 x^4\right ) \log (25)+\left (28-32 x-24 x^2+32 x^3-4 x^4\right ) \log ^2(25)+\left (56-24 x-56 x^2+24 x^3\right ) \log ^3(25)+\left (70+10 x-54 x^2+6 x^3\right ) \log ^4(25)+\left (56+32 x-24 x^2\right ) \log ^5(25)+\left (28+24 x-4 x^2\right ) \log ^6(25)+(8+8 x) \log ^7(25)+(1+x) \log ^8(25)+\left (1-6 x+6 x^2+8 x^3-15 x^4+6 x^5+\left (8-32 x+64 x^3-40 x^4\right ) \log (25)+\left (28-64 x-72 x^2+128 x^3-20 x^4\right ) \log ^2(25)+\left (56-48 x-168 x^2+96 x^3\right ) \log ^3(25)+\left (70+20 x-162 x^2+24 x^3\right ) \log ^4(25)+\left (56+64 x-72 x^2\right ) \log ^5(25)+\left (28+48 x-12 x^2\right ) \log ^6(25)+(8+16 x) \log ^7(25)+(1+2 x) \log ^8(25)\right ) \log (x)\right ) \, dx=x \left (x^5+(1+\log (25))^8-2 x^2 (1+\log (25))^4 \left (-1+4 \log (25)+2 \log ^2(25)\right )+2 x^3 (1+\log (25))^2 \left (1+6 \log (25)+3 \log ^2(25)\right )-x^4 \left (3+8 \log (25)+4 \log ^2(25)\right )+x (1+\log (25))^6 \left (-3+\log ^2(25)+\log (625)\right )\right ) \log (x) \]
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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 | \(\text {Expression too large to display}\) | \(724\) |
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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 \[ \int \left (1-3 x+2 x^2+2 x^3-3 x^4+x^5+\left (8-16 x+16 x^3-8 x^4\right ) \log (25)+\left (28-32 x-24 x^2+32 x^3-4 x^4\right ) \log ^2(25)+\left (56-24 x-56 x^2+24 x^3\right ) \log ^3(25)+\left (70+10 x-54 x^2+6 x^3\right ) \log ^4(25)+\left (56+32 x-24 x^2\right ) \log ^5(25)+\left (28+24 x-4 x^2\right ) \log ^6(25)+(8+8 x) \log ^7(25)+(1+x) \log ^8(25)+\left (1-6 x+6 x^2+8 x^3-15 x^4+6 x^5+\left (8-32 x+64 x^3-40 x^4\right ) \log (25)+\left (28-64 x-72 x^2+128 x^3-20 x^4\right ) \log ^2(25)+\left (56-48 x-168 x^2+96 x^3\right ) \log ^3(25)+\left (70+20 x-162 x^2+24 x^3\right ) \log ^4(25)+\left (56+64 x-72 x^2\right ) \log ^5(25)+\left (28+48 x-12 x^2\right ) \log ^6(25)+(8+16 x) \log ^7(25)+(1+2 x) \log ^8(25)\right ) \log (x)\right ) \, dx={\left (256 \, {\left (x^{2} + x\right )} \log \left (5\right )^{8} + 1024 \, {\left (x^{2} + x\right )} \log \left (5\right )^{7} - 256 \, {\left (x^{3} - 6 \, x^{2} - 7 \, x\right )} \log \left (5\right )^{6} + x^{6} - 256 \, {\left (3 \, x^{3} - 4 \, x^{2} - 7 \, x\right )} \log \left (5\right )^{5} - 3 \, x^{5} + 32 \, {\left (3 \, x^{4} - 27 \, x^{3} + 5 \, x^{2} + 35 \, x\right )} \log \left (5\right )^{4} + 2 \, x^{4} + 64 \, {\left (3 \, x^{4} - 7 \, x^{3} - 3 \, x^{2} + 7 \, x\right )} \log \left (5\right )^{3} + 2 \, x^{3} - 16 \, {\left (x^{5} - 8 \, x^{4} + 6 \, x^{3} + 8 \, x^{2} - 7 \, x\right )} \log \left (5\right )^{2} - 3 \, x^{2} - 16 \, {\left (x^{5} - 2 \, x^{4} + 2 \, x^{2} - x\right )} \log \left (5\right ) + x\right )} \log \left (x\right ) \]
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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 \[ \int \left (1-3 x+2 x^2+2 x^3-3 x^4+x^5+\left (8-16 x+16 x^3-8 x^4\right ) \log (25)+\left (28-32 x-24 x^2+32 x^3-4 x^4\right ) \log ^2(25)+\left (56-24 x-56 x^2+24 x^3\right ) \log ^3(25)+\left (70+10 x-54 x^2+6 x^3\right ) \log ^4(25)+\left (56+32 x-24 x^2\right ) \log ^5(25)+\left (28+24 x-4 x^2\right ) \log ^6(25)+(8+8 x) \log ^7(25)+(1+x) \log ^8(25)+\left (1-6 x+6 x^2+8 x^3-15 x^4+6 x^5+\left (8-32 x+64 x^3-40 x^4\right ) \log (25)+\left (28-64 x-72 x^2+128 x^3-20 x^4\right ) \log ^2(25)+\left (56-48 x-168 x^2+96 x^3\right ) \log ^3(25)+\left (70+20 x-162 x^2+24 x^3\right ) \log ^4(25)+\left (56+64 x-72 x^2\right ) \log ^5(25)+\left (28+48 x-12 x^2\right ) \log ^6(25)+(8+16 x) \log ^7(25)+(1+2 x) \log ^8(25)\right ) \log (x)\right ) \, dx=\left (x^{6} - 16 x^{5} \log {\left (5 \right )}^{2} - 16 x^{5} \log {\left (5 \right )} - 3 x^{5} + 2 x^{4} + 32 x^{4} \log {\left (5 \right )} + 128 x^{4} \log {\left (5 \right )}^{2} + 96 x^{4} \log {\left (5 \right )}^{4} + 192 x^{4} \log {\left (5 \right )}^{3} - 768 x^{3} \log {\left (5 \right )}^{5} - 864 x^{3} \log {\left (5 \right )}^{4} - 256 x^{3} \log {\left (5 \right )}^{6} - 448 x^{3} \log {\left (5 \right )}^{3} - 96 x^{3} \log {\left (5 \right )}^{2} + 2 x^{3} - 192 x^{2} \log {\left (5 \right )}^{3} - 128 x^{2} \log {\left (5 \right )}^{2} - 32 x^{2} \log {\left (5 \right )} - 3 x^{2} + 160 x^{2} \log {\left (5 \right )}^{4} + 1024 x^{2} \log {\left (5 \right )}^{5} + 256 x^{2} \log {\left (5 \right )}^{8} + 1536 x^{2} \log {\left (5 \right )}^{6} + 1024 x^{2} \log {\left (5 \right )}^{7} + x + 16 x \log {\left (5 \right )} + 112 x \log {\left (5 \right )}^{2} + 448 x \log {\left (5 \right )}^{3} + 1120 x \log {\left (5 \right )}^{4} + 256 x \log {\left (5 \right )}^{8} + 1792 x \log {\left (5 \right )}^{5} + 1024 x \log {\left (5 \right )}^{7} + 1792 x \log {\left (5 \right )}^{6}\right ) \log {\left (x \right )} \]
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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=128 \, {\left (x^{2} + 2 \, x\right )} \log \left (5\right )^{8} + 512 \, {\left (x^{2} + 2 \, x\right )} \log \left (5\right )^{7} - \frac {256}{3} \, {\left (x^{3} - 9 \, x^{2} - 21 \, x\right )} \log \left (5\right )^{6} + \frac {1}{5} \, {\left (16 \, \log \left (5\right )^{2} + 16 \, \log \left (5\right ) + 3\right )} x^{5} - 256 \, {\left (x^{3} - 2 \, x^{2} - 7 \, x\right )} \log \left (5\right )^{5} - \frac {1}{2} \, {\left (48 \, \log \left (5\right )^{4} + 96 \, \log \left (5\right )^{3} + 64 \, \log \left (5\right )^{2} + 16 \, \log \left (5\right ) + 1\right )} x^{4} - \frac {3}{5} \, x^{5} + 8 \, {\left (3 \, x^{4} - 36 \, x^{3} + 10 \, x^{2} + 140 \, x\right )} \log \left (5\right )^{4} + \frac {2}{3} \, {\left (128 \, \log \left (5\right )^{6} + 384 \, \log \left (5\right )^{5} + 432 \, \log \left (5\right )^{4} + 224 \, \log \left (5\right )^{3} + 48 \, \log \left (5\right )^{2} - 1\right )} x^{3} + \frac {1}{2} \, x^{4} + \frac {16}{3} \, {\left (9 \, x^{4} - 28 \, x^{3} - 18 \, x^{2} + 84 \, x\right )} \log \left (5\right )^{3} - \frac {1}{2} \, {\left (256 \, \log \left (5\right )^{8} + 1024 \, \log \left (5\right )^{7} + 1536 \, \log \left (5\right )^{6} + 1024 \, \log \left (5\right )^{5} + 160 \, \log \left (5\right )^{4} - 192 \, \log \left (5\right )^{3} - 128 \, \log \left (5\right )^{2} - 32 \, \log \left (5\right ) - 3\right )} x^{2} + \frac {2}{3} \, x^{3} - \frac {16}{5} \, {\left (x^{5} - 10 \, x^{4} + 10 \, x^{3} + 20 \, x^{2} - 35 \, x\right )} \log \left (5\right )^{2} - {\left (256 \, \log \left (5\right )^{8} + 1024 \, \log \left (5\right )^{7} + 1792 \, \log \left (5\right )^{6} + 1792 \, \log \left (5\right )^{5} + 1120 \, \log \left (5\right )^{4} + 448 \, \log \left (5\right )^{3} + 112 \, \log \left (5\right )^{2} + 16 \, \log \left (5\right ) + 1\right )} x - \frac {3}{2} \, x^{2} - \frac {8}{5} \, {\left (2 \, x^{5} - 5 \, x^{4} + 10 \, x^{2} - 10 \, x\right )} \log \left (5\right ) + {\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 ) + x \]
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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 \[ \int \left (1-3 x+2 x^2+2 x^3-3 x^4+x^5+\left (8-16 x+16 x^3-8 x^4\right ) \log (25)+\left (28-32 x-24 x^2+32 x^3-4 x^4\right ) \log ^2(25)+\left (56-24 x-56 x^2+24 x^3\right ) \log ^3(25)+\left (70+10 x-54 x^2+6 x^3\right ) \log ^4(25)+\left (56+32 x-24 x^2\right ) \log ^5(25)+\left (28+24 x-4 x^2\right ) \log ^6(25)+(8+8 x) \log ^7(25)+(1+x) \log ^8(25)+\left (1-6 x+6 x^2+8 x^3-15 x^4+6 x^5+\left (8-32 x+64 x^3-40 x^4\right ) \log (25)+\left (28-64 x-72 x^2+128 x^3-20 x^4\right ) \log ^2(25)+\left (56-48 x-168 x^2+96 x^3\right ) \log ^3(25)+\left (70+20 x-162 x^2+24 x^3\right ) \log ^4(25)+\left (56+64 x-72 x^2\right ) \log ^5(25)+\left (28+48 x-12 x^2\right ) \log ^6(25)+(8+16 x) \log ^7(25)+(1+2 x) \log ^8(25)\right ) \log (x)\right ) \, dx=\text {Too large to display} \]
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Time = 10.35 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int \left (1-3 x+2 x^2+2 x^3-3 x^4+x^5+\left (8-16 x+16 x^3-8 x^4\right ) \log (25)+\left (28-32 x-24 x^2+32 x^3-4 x^4\right ) \log ^2(25)+\left (56-24 x-56 x^2+24 x^3\right ) \log ^3(25)+\left (70+10 x-54 x^2+6 x^3\right ) \log ^4(25)+\left (56+32 x-24 x^2\right ) \log ^5(25)+\left (28+24 x-4 x^2\right ) \log ^6(25)+(8+8 x) \log ^7(25)+(1+x) \log ^8(25)+\left (1-6 x+6 x^2+8 x^3-15 x^4+6 x^5+\left (8-32 x+64 x^3-40 x^4\right ) \log (25)+\left (28-64 x-72 x^2+128 x^3-20 x^4\right ) \log ^2(25)+\left (56-48 x-168 x^2+96 x^3\right ) \log ^3(25)+\left (70+20 x-162 x^2+24 x^3\right ) \log ^4(25)+\left (56+64 x-72 x^2\right ) \log ^5(25)+\left (28+48 x-12 x^2\right ) \log ^6(25)+(8+16 x) \log ^7(25)+(1+2 x) \log ^8(25)\right ) \log (x)\right ) \, dx=x\,\ln \left (x\right )\,\left (x+1\right )\,{\left (\ln \left (625\right )-x+4\,{\ln \left (5\right )}^2+1\right )}^4 \]
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