Integrand size = 40, antiderivative size = 24 \[ \int \frac {\left (-12 x^3+24 x^4+\left (-12 x^3+24 x^4\right ) \log (3)\right ) \log (4)}{9-48 x+64 x^2} \, dx=\frac {x^3 (1+\log (3)) \log (4)}{2 \left (4-\frac {3}{2 x}\right )} \]
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Time = 0.01 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.75, number of steps used = 3, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.075, Rules used = {12, 27, 1602} \[ \int \frac {\left (-12 x^3+24 x^4+\left (-12 x^3+24 x^4\right ) \log (3)\right ) \log (4)}{9-48 x+64 x^2} \, dx=-\frac {x^4 (1+\log (3)) \log (4)}{3-8 x} \]
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Rule 12
Rule 27
Rule 1602
Rubi steps \begin{align*} \text {integral}& = \log (4) \int \frac {-12 x^3+24 x^4+\left (-12 x^3+24 x^4\right ) \log (3)}{9-48 x+64 x^2} \, dx \\ & = \log (4) \int \frac {-12 x^3+24 x^4+\left (-12 x^3+24 x^4\right ) \log (3)}{(-3+8 x)^2} \, dx \\ & = -\frac {x^4 (1+\log (3)) \log (4)}{3-8 x} \\ \end{align*}
Time = 0.02 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.12 \[ \int \frac {\left (-12 x^3+24 x^4+\left (-12 x^3+24 x^4\right ) \log (3)\right ) \log (4)}{9-48 x+64 x^2} \, dx=\frac {\left (81-216 x+1024 x^4\right ) (1+\log (3)) \log (4)}{1024 (-3+8 x)} \]
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Time = 0.31 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.79
method | result | size |
gosper | \(\frac {2 x^{4} \left (\ln \left (3\right )+1\right ) \ln \left (2\right )}{8 x -3}\) | \(19\) |
norman | \(\frac {\left (2 \ln \left (2\right ) \ln \left (3\right )+2 \ln \left (2\right )\right ) x^{4}}{8 x -3}\) | \(23\) |
parallelrisch | \(\frac {\ln \left (2\right ) \left (8 x^{4} \ln \left (3\right )+8 x^{4}\right )}{32 x -12}\) | \(25\) |
default | \(2 \ln \left (2\right ) \left (12 \ln \left (3\right )+12\right ) \left (\frac {x^{3}}{96}+\frac {x^{2}}{256}+\frac {3 x}{2048}+\frac {27}{16384 \left (8 x -3\right )}\right )\) | \(34\) |
risch | \(\frac {x^{3} \ln \left (3\right ) \ln \left (2\right )}{4}+\frac {3 \ln \left (2\right ) \ln \left (3\right ) x^{2}}{32}+\frac {9 x \ln \left (2\right ) \ln \left (3\right )}{256}+\frac {x^{3} \ln \left (2\right )}{4}+\frac {3 x^{2} \ln \left (2\right )}{32}+\frac {9 x \ln \left (2\right )}{256}+\frac {81 \ln \left (2\right )}{16384 \left (x -\frac {3}{8}\right )}+\frac {81 \ln \left (2\right ) \ln \left (3\right )}{16384 \left (x -\frac {3}{8}\right )}\) | \(66\) |
meijerg | \(-\frac {243 \left (\frac {16 \ln \left (3\right )}{3}+\frac {16}{3}\right ) \ln \left (2\right ) \left (-\frac {8 x \left (-\frac {2560}{27} x^{3}-\frac {640}{9} x^{2}-80 x +60\right )}{45 \left (1-\frac {8 x}{3}\right )}-4 \ln \left (1-\frac {8 x}{3}\right )\right )}{32768}+\frac {81 \left (-\frac {8 \ln \left (3\right )}{3}-\frac {8}{3}\right ) \ln \left (2\right ) \left (\frac {2 x \left (-\frac {128}{9} x^{2}-16 x +12\right )}{3 \left (1-\frac {8 x}{3}\right )}+3 \ln \left (1-\frac {8 x}{3}\right )\right )}{4096}\) | \(85\) |
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Time = 0.24 (sec) , antiderivative size = 38, normalized size of antiderivative = 1.58 \[ \int \frac {\left (-12 x^3+24 x^4+\left (-12 x^3+24 x^4\right ) \log (3)\right ) \log (4)}{9-48 x+64 x^2} \, dx=\frac {{\left (4096 \, x^{4} - 216 \, x + 81\right )} \log \left (3\right ) \log \left (2\right ) + {\left (4096 \, x^{4} - 216 \, x + 81\right )} \log \left (2\right )}{2048 \, {\left (8 \, x - 3\right )}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 73 vs. \(2 (17) = 34\).
Time = 0.13 (sec) , antiderivative size = 73, normalized size of antiderivative = 3.04 \[ \int \frac {\left (-12 x^3+24 x^4+\left (-12 x^3+24 x^4\right ) \log (3)\right ) \log (4)}{9-48 x+64 x^2} \, dx=x^{3} \left (\frac {\log {\left (2 \right )}}{4} + \frac {\log {\left (2 \right )} \log {\left (3 \right )}}{4}\right ) + x^{2} \cdot \left (\frac {3 \log {\left (2 \right )}}{32} + \frac {3 \log {\left (2 \right )} \log {\left (3 \right )}}{32}\right ) + x \left (\frac {9 \log {\left (2 \right )}}{256} + \frac {9 \log {\left (2 \right )} \log {\left (3 \right )}}{256}\right ) + \frac {81 \log {\left (2 \right )} + 81 \log {\left (2 \right )} \log {\left (3 \right )}}{16384 x - 6144} \]
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Leaf count of result is larger than twice the leaf count of optimal. 43 vs. \(2 (20) = 40\).
Time = 0.19 (sec) , antiderivative size = 43, normalized size of antiderivative = 1.79 \[ \int \frac {\left (-12 x^3+24 x^4+\left (-12 x^3+24 x^4\right ) \log (3)\right ) \log (4)}{9-48 x+64 x^2} \, dx=\frac {1}{2048} \, {\left (512 \, x^{3} {\left (\log \left (3\right ) + 1\right )} + 192 \, x^{2} {\left (\log \left (3\right ) + 1\right )} + 72 \, x {\left (\log \left (3\right ) + 1\right )} + \frac {81 \, {\left (\log \left (3\right ) + 1\right )}}{8 \, x - 3}\right )} \log \left (2\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. 50 vs. \(2 (20) = 40\).
Time = 0.29 (sec) , antiderivative size = 50, normalized size of antiderivative = 2.08 \[ \int \frac {\left (-12 x^3+24 x^4+\left (-12 x^3+24 x^4\right ) \log (3)\right ) \log (4)}{9-48 x+64 x^2} \, dx=\frac {1}{2048} \, {\left (512 \, x^{3} \log \left (3\right ) + 512 \, x^{3} + 192 \, x^{2} \log \left (3\right ) + 192 \, x^{2} + 72 \, x \log \left (3\right ) + 72 \, x + \frac {81 \, {\left (\log \left (3\right ) + 1\right )}}{8 \, x - 3}\right )} \log \left (2\right ) \]
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Time = 13.02 (sec) , antiderivative size = 51, normalized size of antiderivative = 2.12 \[ \int \frac {\left (-12 x^3+24 x^4+\left (-12 x^3+24 x^4\right ) \log (3)\right ) \log (4)}{9-48 x+64 x^2} \, dx=\frac {\frac {81\,\ln \left (2\right )}{8}+\frac {81\,\ln \left (2\right )\,\ln \left (3\right )}{8}}{2048\,x-768}+\frac {9\,x\,\ln \left (2\right )\,\left (\ln \left (3\right )+1\right )}{256}+\frac {3\,x^2\,\ln \left (2\right )\,\left (\ln \left (3\right )+1\right )}{32}+\frac {x^3\,\ln \left (2\right )\,\left (\ln \left (3\right )+1\right )}{4} \]
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