Integrand size = 51, antiderivative size = 32 \[ \int \frac {\left (-4-e^3+2 x^2\right ) \log (x)+(-16 x-32 x \log (x)) \log ^3\left (\frac {1}{16} x^4 \log ^2(x)\right )}{2 x^2 \log (x)} \, dx=-\frac {-4-e^3}{2 x}+x-\log ^4\left (\frac {1}{16} x^4 \log ^2(x)\right ) \]
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Time = 0.16 (sec) , antiderivative size = 30, normalized size of antiderivative = 0.94, number of steps used = 6, number of rules used = 4, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.078, Rules used = {12, 6874, 14, 6818} \[ \int \frac {\left (-4-e^3+2 x^2\right ) \log (x)+(-16 x-32 x \log (x)) \log ^3\left (\frac {1}{16} x^4 \log ^2(x)\right )}{2 x^2 \log (x)} \, dx=-\log ^4\left (\frac {1}{16} x^4 \log ^2(x)\right )+x+\frac {4+e^3}{2 x} \]
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Rule 12
Rule 14
Rule 6818
Rule 6874
Rubi steps \begin{align*} \text {integral}& = \frac {1}{2} \int \frac {\left (-4-e^3+2 x^2\right ) \log (x)+(-16 x-32 x \log (x)) \log ^3\left (\frac {1}{16} x^4 \log ^2(x)\right )}{x^2 \log (x)} \, dx \\ & = \frac {1}{2} \int \left (\frac {-4-e^3+2 x^2}{x^2}-\frac {16 (1+2 \log (x)) \log ^3\left (\frac {1}{16} x^4 \log ^2(x)\right )}{x \log (x)}\right ) \, dx \\ & = \frac {1}{2} \int \frac {-4-e^3+2 x^2}{x^2} \, dx-8 \int \frac {(1+2 \log (x)) \log ^3\left (\frac {1}{16} x^4 \log ^2(x)\right )}{x \log (x)} \, dx \\ & = -\log ^4\left (\frac {1}{16} x^4 \log ^2(x)\right )+\frac {1}{2} \int \left (2+\frac {-4-e^3}{x^2}\right ) \, dx \\ & = \frac {4+e^3}{2 x}+x-\log ^4\left (\frac {1}{16} x^4 \log ^2(x)\right ) \\ \end{align*}
Time = 0.13 (sec) , antiderivative size = 33, normalized size of antiderivative = 1.03 \[ \int \frac {\left (-4-e^3+2 x^2\right ) \log (x)+(-16 x-32 x \log (x)) \log ^3\left (\frac {1}{16} x^4 \log ^2(x)\right )}{2 x^2 \log (x)} \, dx=\frac {2}{x}+\frac {e^3}{2 x}+x-\log ^4\left (\frac {1}{16} x^4 \log ^2(x)\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. \(597\) vs. \(2(27)=54\).
Time = 11.23 (sec) , antiderivative size = 598, normalized size of antiderivative = 18.69
method | result | size |
default | \(\text {Expression too large to display}\) | \(598\) |
parts | \(\text {Expression too large to display}\) | \(663\) |
risch | \(\text {Expression too large to display}\) | \(106036\) |
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Time = 0.24 (sec) , antiderivative size = 31, normalized size of antiderivative = 0.97 \[ \int \frac {\left (-4-e^3+2 x^2\right ) \log (x)+(-16 x-32 x \log (x)) \log ^3\left (\frac {1}{16} x^4 \log ^2(x)\right )}{2 x^2 \log (x)} \, dx=-\frac {2 \, x \log \left (\frac {1}{16} \, x^{4} \log \left (x\right )^{2}\right )^{4} - 2 \, x^{2} - e^{3} - 4}{2 \, x} \]
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Time = 0.12 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.69 \[ \int \frac {\left (-4-e^3+2 x^2\right ) \log (x)+(-16 x-32 x \log (x)) \log ^3\left (\frac {1}{16} x^4 \log ^2(x)\right )}{2 x^2 \log (x)} \, dx=x - \log {\left (\frac {x^{4} \log {\left (x \right )}^{2}}{16} \right )}^{4} + \frac {4 + e^{3}}{2 x} \]
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Leaf count of result is larger than twice the leaf count of optimal. 188 vs. \(2 (25) = 50\).
Time = 0.27 (sec) , antiderivative size = 188, normalized size of antiderivative = 5.88 \[ \int \frac {\left (-4-e^3+2 x^2\right ) \log (x)+(-16 x-32 x \log (x)) \log ^3\left (\frac {1}{16} x^4 \log ^2(x)\right )}{2 x^2 \log (x)} \, dx=-16 \, \log \left (\frac {1}{16} \, x^{4} \log \left (x\right )^{2}\right )^{3} \log \left (x\right ) + 256 \, \log \left (x\right )^{4} + 128 \, \log \left (2\right ) \log \left (\log \left (x\right )\right )^{3} - 16 \, \log \left (\log \left (x\right )\right )^{4} + 96 \, {\left (\log \left (x\right )^{2} + \log \left (x\right )\right )} \log \left (\frac {1}{16} \, x^{4} \log \left (x\right )^{2}\right )^{2} + 192 \, {\left (4 \, \log \left (2\right ) + 1\right )} \log \left (x\right )^{2} + 768 \, \log \left (x\right )^{3} - 384 \, {\left (\log \left (2\right )^{2} + \log \left (x\right )\right )} \log \left (\log \left (x\right )\right )^{2} - 64 \, {\left (4 \, \log \left (x\right )^{3} + 9 \, \log \left (x\right )^{2} + 6 \, \log \left (x\right )\right )} \log \left (\frac {1}{16} \, x^{4} \log \left (x\right )^{2}\right ) - 768 \, {\left (2 \, \log \left (2\right )^{2} + 2 \, \log \left (2\right ) + 1\right )} \log \left (x\right ) + 1344 \, \log \left (x\right )^{2} + 128 \, {\left (4 \, \log \left (2\right )^{3} + 6 \, {\left (2 \, \log \left (2\right ) + 1\right )} \log \left (x\right ) - 3 \, \log \left (x\right )^{2}\right )} \log \left (\log \left (x\right )\right ) + x + \frac {e^{3}}{2 \, x} + \frac {2}{x} + 768 \, \log \left (x\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. 178 vs. \(2 (25) = 50\).
Time = 0.41 (sec) , antiderivative size = 178, normalized size of antiderivative = 5.56 \[ \int \frac {\left (-4-e^3+2 x^2\right ) \log (x)+(-16 x-32 x \log (x)) \log ^3\left (\frac {1}{16} x^4 \log ^2(x)\right )}{2 x^2 \log (x)} \, dx=-\frac {1536 \, x \log \left (2\right )^{2} \log \left (x\right ) \log \left (\log \left (x\right )^{2}\right ) - 1536 \, x \log \left (2\right ) \log \left (x\right )^{2} \log \left (\log \left (x\right )^{2}\right ) + 512 \, x \log \left (x\right )^{3} \log \left (\log \left (x\right )^{2}\right ) + 192 \, x \log \left (2\right )^{2} \log \left (\log \left (x\right )^{2}\right )^{2} - 384 \, x \log \left (2\right ) \log \left (x\right ) \log \left (\log \left (x\right )^{2}\right )^{2} + 192 \, x \log \left (x\right )^{2} \log \left (\log \left (x\right )^{2}\right )^{2} - 32 \, x \log \left (2\right ) \log \left (\log \left (x\right )^{2}\right )^{3} + 32 \, x \log \left (x\right ) \log \left (\log \left (x\right )^{2}\right )^{3} + 2 \, x \log \left (\log \left (x\right )^{2}\right )^{4} - 2048 \, x \log \left (2\right )^{3} \log \left (x\right ) + 3072 \, x \log \left (2\right )^{2} \log \left (x\right )^{2} - 2048 \, x \log \left (2\right ) \log \left (x\right )^{3} + 512 \, x \log \left (x\right )^{4} - 1024 \, x \log \left (2\right )^{3} \log \left (\log \left (x\right )\right ) - 2 \, x^{2} - e^{3} - 4}{2 \, x} \]
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Time = 12.20 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.81 \[ \int \frac {\left (-4-e^3+2 x^2\right ) \log (x)+(-16 x-32 x \log (x)) \log ^3\left (\frac {1}{16} x^4 \log ^2(x)\right )}{2 x^2 \log (x)} \, dx=x-{\ln \left (\frac {x^4\,{\ln \left (x\right )}^2}{16}\right )}^4+\frac {\frac {{\mathrm {e}}^3}{2}+2}{x} \]
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