Integrand size = 55, antiderivative size = 17 \[ \int \left ((-512 x-512 x \log (2)) \log (x)+(768 x+768 x \log (2)) \log ^2(x)+(-384 x-384 x \log (2)) \log ^3(x)+(64 x+64 x \log (2)) \log ^4(x)\right ) \, dx=2 x^2 (1+\log (2)) (-4+2 \log (x))^4 \]
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Leaf count is larger than twice the leaf count of optimal. \(60\) vs. \(2(17)=34\).
Time = 0.06 (sec) , antiderivative size = 60, normalized size of antiderivative = 3.53, number of steps used = 19, number of rules used = 4, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.073, Rules used = {6, 12, 2341, 2342} \[ \int \left ((-512 x-512 x \log (2)) \log (x)+(768 x+768 x \log (2)) \log ^2(x)+(-384 x-384 x \log (2)) \log ^3(x)+(64 x+64 x \log (2)) \log ^4(x)\right ) \, dx=32 x^2 (1+\log (2)) \log ^4(x)-256 x^2 (1+\log (2)) \log ^3(x)+768 x^2 (1+\log (2)) \log ^2(x)-1024 x^2 (1+\log (2)) \log (x)+512 x^2 (1+\log (2)) \]
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Rule 6
Rule 12
Rule 2341
Rule 2342
Rubi steps \begin{align*} \text {integral}& = \int (-512 x-512 x \log (2)) \log (x) \, dx+\int (768 x+768 x \log (2)) \log ^2(x) \, dx+\int (-384 x-384 x \log (2)) \log ^3(x) \, dx+\int (64 x+64 x \log (2)) \log ^4(x) \, dx \\ & = \int x (-512-512 \log (2)) \log (x) \, dx+\int x (768+768 \log (2)) \log ^2(x) \, dx+\int x (-384-384 \log (2)) \log ^3(x) \, dx+\int x (64+64 \log (2)) \log ^4(x) \, dx \\ & = (64 (1+\log (2))) \int x \log ^4(x) \, dx-(384 (1+\log (2))) \int x \log ^3(x) \, dx-(512 (1+\log (2))) \int x \log (x) \, dx+(768 (1+\log (2))) \int x \log ^2(x) \, dx \\ & = 128 x^2 (1+\log (2))-256 x^2 (1+\log (2)) \log (x)+384 x^2 (1+\log (2)) \log ^2(x)-192 x^2 (1+\log (2)) \log ^3(x)+32 x^2 (1+\log (2)) \log ^4(x)-(128 (1+\log (2))) \int x \log ^3(x) \, dx+(576 (1+\log (2))) \int x \log ^2(x) \, dx-(768 (1+\log (2))) \int x \log (x) \, dx \\ & = 320 x^2 (1+\log (2))-640 x^2 (1+\log (2)) \log (x)+672 x^2 (1+\log (2)) \log ^2(x)-256 x^2 (1+\log (2)) \log ^3(x)+32 x^2 (1+\log (2)) \log ^4(x)+(192 (1+\log (2))) \int x \log ^2(x) \, dx-(576 (1+\log (2))) \int x \log (x) \, dx \\ & = 464 x^2 (1+\log (2))-928 x^2 (1+\log (2)) \log (x)+768 x^2 (1+\log (2)) \log ^2(x)-256 x^2 (1+\log (2)) \log ^3(x)+32 x^2 (1+\log (2)) \log ^4(x)-(192 (1+\log (2))) \int x \log (x) \, dx \\ & = 512 x^2 (1+\log (2))-1024 x^2 (1+\log (2)) \log (x)+768 x^2 (1+\log (2)) \log ^2(x)-256 x^2 (1+\log (2)) \log ^3(x)+32 x^2 (1+\log (2)) \log ^4(x) \\ \end{align*}
Leaf count is larger than twice the leaf count of optimal. \(48\) vs. \(2(17)=34\).
Time = 0.03 (sec) , antiderivative size = 48, normalized size of antiderivative = 2.82 \[ \int \left ((-512 x-512 x \log (2)) \log (x)+(768 x+768 x \log (2)) \log ^2(x)+(-384 x-384 x \log (2)) \log ^3(x)+(64 x+64 x \log (2)) \log ^4(x)\right ) \, dx=64 (1+\log (2)) \left (8 x^2-16 x^2 \log (x)+12 x^2 \log ^2(x)-4 x^2 \log ^3(x)+\frac {1}{2} x^2 \log ^4(x)\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. \(63\) vs. \(2(17)=34\).
Time = 0.06 (sec) , antiderivative size = 64, normalized size of antiderivative = 3.76
method | result | size |
risch | \(32 x^{2} \left (1+\ln \left (2\right )\right ) \ln \left (x \right )^{4}-256 x^{2} \left (1+\ln \left (2\right )\right ) \ln \left (x \right )^{3}+768 x^{2} \left (1+\ln \left (2\right )\right ) \ln \left (x \right )^{2}-1024 x^{2} \left (1+\ln \left (2\right )\right ) \ln \left (x \right )+512 x^{2} \ln \left (2\right )+512 x^{2}\) | \(64\) |
norman | \(\left (512 \ln \left (2\right )+512\right ) x^{2}+\left (-1024-1024 \ln \left (2\right )\right ) x^{2} \ln \left (x \right )+\left (-256 \ln \left (2\right )-256\right ) x^{2} \ln \left (x \right )^{3}+\left (32 \ln \left (2\right )+32\right ) x^{2} \ln \left (x \right )^{4}+\left (768 \ln \left (2\right )+768\right ) x^{2} \ln \left (x \right )^{2}\) | \(66\) |
parallelrisch | \(32 x^{2} \ln \left (x \right )^{4} \ln \left (2\right )+32 x^{2} \ln \left (x \right )^{4}-256 x^{2} \ln \left (x \right )^{3} \ln \left (2\right )-256 x^{2} \ln \left (x \right )^{3}+768 x^{2} \ln \left (2\right ) \ln \left (x \right )^{2}+768 x^{2} \ln \left (x \right )^{2}-1024 x^{2} \ln \left (2\right ) \ln \left (x \right )-1024 x^{2} \ln \left (x \right )+512 x^{2} \ln \left (2\right )+512 x^{2}\) | \(90\) |
default | \(-1024 x^{2} \ln \left (x \right )+512 x^{2}-256 x^{2} \ln \left (2\right ) \ln \left (x \right )+128 x^{2} \ln \left (2\right )-256 x^{2} \ln \left (x \right )^{3}+768 x^{2} \ln \left (x \right )^{2}-384 \ln \left (2\right ) \left (\frac {x^{2} \ln \left (x \right )^{3}}{2}-\frac {3 x^{2} \ln \left (x \right )^{2}}{4}+\frac {3 x^{2} \ln \left (x \right )}{4}-\frac {3 x^{2}}{8}\right )+32 x^{2} \ln \left (x \right )^{4}+64 \ln \left (2\right ) \left (\frac {x^{2} \ln \left (x \right )^{4}}{2}-x^{2} \ln \left (x \right )^{3}+\frac {3 x^{2} \ln \left (x \right )^{2}}{2}-\frac {3 x^{2} \ln \left (x \right )}{2}+\frac {3 x^{2}}{4}\right )+768 \ln \left (2\right ) \left (\frac {x^{2} \ln \left (x \right )^{2}}{2}-\frac {x^{2} \ln \left (x \right )}{2}+\frac {x^{2}}{4}\right )\) | \(162\) |
parts | \(-1024 x^{2} \ln \left (x \right )+512 x^{2}-256 x^{2} \ln \left (2\right ) \ln \left (x \right )+128 x^{2} \ln \left (2\right )-256 x^{2} \ln \left (x \right )^{3}+768 x^{2} \ln \left (x \right )^{2}-384 \ln \left (2\right ) \left (\frac {x^{2} \ln \left (x \right )^{3}}{2}-\frac {3 x^{2} \ln \left (x \right )^{2}}{4}+\frac {3 x^{2} \ln \left (x \right )}{4}-\frac {3 x^{2}}{8}\right )+32 x^{2} \ln \left (x \right )^{4}+64 \ln \left (2\right ) \left (\frac {x^{2} \ln \left (x \right )^{4}}{2}-x^{2} \ln \left (x \right )^{3}+\frac {3 x^{2} \ln \left (x \right )^{2}}{2}-\frac {3 x^{2} \ln \left (x \right )}{2}+\frac {3 x^{2}}{4}\right )+768 \ln \left (2\right ) \left (\frac {x^{2} \ln \left (x \right )^{2}}{2}-\frac {x^{2} \ln \left (x \right )}{2}+\frac {x^{2}}{4}\right )\) | \(162\) |
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Leaf count of result is larger than twice the leaf count of optimal. 75 vs. \(2 (15) = 30\).
Time = 0.27 (sec) , antiderivative size = 75, normalized size of antiderivative = 4.41 \[ \int \left ((-512 x-512 x \log (2)) \log (x)+(768 x+768 x \log (2)) \log ^2(x)+(-384 x-384 x \log (2)) \log ^3(x)+(64 x+64 x \log (2)) \log ^4(x)\right ) \, dx=32 \, {\left (x^{2} \log \left (2\right ) + x^{2}\right )} \log \left (x\right )^{4} - 256 \, {\left (x^{2} \log \left (2\right ) + x^{2}\right )} \log \left (x\right )^{3} + 512 \, x^{2} \log \left (2\right ) + 768 \, {\left (x^{2} \log \left (2\right ) + x^{2}\right )} \log \left (x\right )^{2} + 512 \, x^{2} - 1024 \, {\left (x^{2} \log \left (2\right ) + x^{2}\right )} \log \left (x\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. 85 vs. \(2 (17) = 34\).
Time = 0.14 (sec) , antiderivative size = 85, normalized size of antiderivative = 5.00 \[ \int \left ((-512 x-512 x \log (2)) \log (x)+(768 x+768 x \log (2)) \log ^2(x)+(-384 x-384 x \log (2)) \log ^3(x)+(64 x+64 x \log (2)) \log ^4(x)\right ) \, dx=x^{2} \cdot \left (512 \log {\left (2 \right )} + 512\right ) + \left (- 1024 x^{2} - 1024 x^{2} \log {\left (2 \right )}\right ) \log {\left (x \right )} + \left (- 256 x^{2} - 256 x^{2} \log {\left (2 \right )}\right ) \log {\left (x \right )}^{3} + \left (32 x^{2} \log {\left (2 \right )} + 32 x^{2}\right ) \log {\left (x \right )}^{4} + \left (768 x^{2} \log {\left (2 \right )} + 768 x^{2}\right ) \log {\left (x \right )}^{2} \]
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Leaf count of result is larger than twice the leaf count of optimal. 139 vs. \(2 (15) = 30\).
Time = 0.29 (sec) , antiderivative size = 139, normalized size of antiderivative = 8.18 \[ \int \left ((-512 x-512 x \log (2)) \log (x)+(768 x+768 x \log (2)) \log ^2(x)+(-384 x-384 x \log (2)) \log ^3(x)+(64 x+64 x \log (2)) \log ^4(x)\right ) \, dx=16 \, {\left (2 \, {\left (\log \left (2\right ) + 1\right )} \log \left (x\right )^{4} - 4 \, {\left (\log \left (2\right ) + 1\right )} \log \left (x\right )^{3} + 6 \, {\left (\log \left (2\right ) + 1\right )} \log \left (x\right )^{2} - 6 \, {\left (\log \left (2\right ) + 1\right )} \log \left (x\right ) + 3 \, \log \left (2\right ) + 3\right )} x^{2} - 48 \, {\left (4 \, {\left (\log \left (2\right ) + 1\right )} \log \left (x\right )^{3} - 6 \, {\left (\log \left (2\right ) + 1\right )} \log \left (x\right )^{2} + 6 \, {\left (\log \left (2\right ) + 1\right )} \log \left (x\right ) - 3 \, \log \left (2\right ) - 3\right )} x^{2} + 192 \, {\left (2 \, {\left (\log \left (2\right ) + 1\right )} \log \left (x\right )^{2} - 2 \, {\left (\log \left (2\right ) + 1\right )} \log \left (x\right ) + \log \left (2\right ) + 1\right )} x^{2} + 128 \, x^{2} {\left (\log \left (2\right ) + 1\right )} - 256 \, {\left (x^{2} \log \left (2\right ) + x^{2}\right )} \log \left (x\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. 89 vs. \(2 (15) = 30\).
Time = 0.28 (sec) , antiderivative size = 89, normalized size of antiderivative = 5.24 \[ \int \left ((-512 x-512 x \log (2)) \log (x)+(768 x+768 x \log (2)) \log ^2(x)+(-384 x-384 x \log (2)) \log ^3(x)+(64 x+64 x \log (2)) \log ^4(x)\right ) \, dx=32 \, x^{2} \log \left (2\right ) \log \left (x\right )^{4} - 256 \, x^{2} \log \left (2\right ) \log \left (x\right )^{3} + 32 \, x^{2} \log \left (x\right )^{4} + 768 \, x^{2} \log \left (2\right ) \log \left (x\right )^{2} - 256 \, x^{2} \log \left (x\right )^{3} - 1024 \, x^{2} \log \left (2\right ) \log \left (x\right ) + 768 \, x^{2} \log \left (x\right )^{2} + 512 \, x^{2} \log \left (2\right ) - 1024 \, x^{2} \log \left (x\right ) + 512 \, x^{2} \]
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Time = 12.74 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.88 \[ \int \left ((-512 x-512 x \log (2)) \log (x)+(768 x+768 x \log (2)) \log ^2(x)+(-384 x-384 x \log (2)) \log ^3(x)+(64 x+64 x \log (2)) \log ^4(x)\right ) \, dx=32\,x^2\,{\left (\ln \left (x\right )-2\right )}^4\,\left (\ln \left (2\right )+1\right ) \]
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