Integrand size = 87, antiderivative size = 21 \[ \int \left (-36 x+12 e^3 x^2-e^6 x^3+\left (-12 x+2 e^3 x^2\right ) \log (4)-x \log ^2(4)+\left (-72 x+36 e^3 x^2-4 e^6 x^3+\left (-24 x+6 e^3 x^2\right ) \log (4)-2 x \log ^2(4)\right ) \log (x)\right ) \, dx=5-x^2 \left (6-e^3 x+\log (4)\right )^2 \log (x) \]
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Leaf count is larger than twice the leaf count of optimal. \(105\) vs. \(2(21)=42\).
Time = 0.06 (sec) , antiderivative size = 105, normalized size of antiderivative = 5.00, number of steps used = 9, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.034, Rules used = {6, 2403, 2341} \[ \int \left (-36 x+12 e^3 x^2-e^6 x^3+\left (-12 x+2 e^3 x^2\right ) \log (4)-x \log ^2(4)+\left (-72 x+36 e^3 x^2-4 e^6 x^3+\left (-24 x+6 e^3 x^2\right ) \log (4)-2 x \log ^2(4)\right ) \log (x)\right ) \, dx=-e^6 x^4 \log (x)+4 e^3 x^3+2 e^3 x^3 (6+\log (4)) \log (x)-\frac {2}{3} e^3 x^3 (6+\log (4))+\frac {2}{3} e^3 x^3 \log (4)-\frac {1}{2} x^2 \left (36+\log ^2(4)\right )-x^2 (6+\log (4))^2 \log (x)+\frac {1}{2} x^2 (6+\log (4))^2-6 x^2 \log (4) \]
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Rule 6
Rule 2341
Rule 2403
Rubi steps \begin{align*} \text {integral}& = \int \left (12 e^3 x^2-e^6 x^3+\left (-12 x+2 e^3 x^2\right ) \log (4)+x \left (-36-\log ^2(4)\right )+\left (-72 x+36 e^3 x^2-4 e^6 x^3+\left (-24 x+6 e^3 x^2\right ) \log (4)-2 x \log ^2(4)\right ) \log (x)\right ) \, dx \\ & = 4 e^3 x^3-\frac {e^6 x^4}{4}-\frac {1}{2} x^2 \left (36+\log ^2(4)\right )+\log (4) \int \left (-12 x+2 e^3 x^2\right ) \, dx+\int \left (-72 x+36 e^3 x^2-4 e^6 x^3+\left (-24 x+6 e^3 x^2\right ) \log (4)-2 x \log ^2(4)\right ) \log (x) \, dx \\ & = 4 e^3 x^3-\frac {e^6 x^4}{4}-6 x^2 \log (4)+\frac {2}{3} e^3 x^3 \log (4)-\frac {1}{2} x^2 \left (36+\log ^2(4)\right )+\int \left (36 e^3 x^2-4 e^6 x^3+\left (-24 x+6 e^3 x^2\right ) \log (4)+x \left (-72-2 \log ^2(4)\right )\right ) \log (x) \, dx \\ & = 4 e^3 x^3-\frac {e^6 x^4}{4}-6 x^2 \log (4)+\frac {2}{3} e^3 x^3 \log (4)-\frac {1}{2} x^2 \left (36+\log ^2(4)\right )+\int \left (-4 e^6 x^3 \log (x)+6 e^3 x^2 (6+\log (4)) \log (x)-2 x (6+\log (4))^2 \log (x)\right ) \, dx \\ & = 4 e^3 x^3-\frac {e^6 x^4}{4}-6 x^2 \log (4)+\frac {2}{3} e^3 x^3 \log (4)-\frac {1}{2} x^2 \left (36+\log ^2(4)\right )-\left (4 e^6\right ) \int x^3 \log (x) \, dx+\left (6 e^3 (6+\log (4))\right ) \int x^2 \log (x) \, dx-\left (2 (6+\log (4))^2\right ) \int x \log (x) \, dx \\ & = 4 e^3 x^3-6 x^2 \log (4)+\frac {2}{3} e^3 x^3 \log (4)-\frac {2}{3} e^3 x^3 (6+\log (4))+\frac {1}{2} x^2 (6+\log (4))^2-\frac {1}{2} x^2 \left (36+\log ^2(4)\right )-e^6 x^4 \log (x)+2 e^3 x^3 (6+\log (4)) \log (x)-x^2 (6+\log (4))^2 \log (x) \\ \end{align*}
Time = 0.05 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.90 \[ \int \left (-36 x+12 e^3 x^2-e^6 x^3+\left (-12 x+2 e^3 x^2\right ) \log (4)-x \log ^2(4)+\left (-72 x+36 e^3 x^2-4 e^6 x^3+\left (-24 x+6 e^3 x^2\right ) \log (4)-2 x \log ^2(4)\right ) \log (x)\right ) \, dx=-x^2 \left (6-e^3 x+\log (4)\right )^2 \log (x) \]
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Time = 0.31 (sec) , antiderivative size = 38, normalized size of antiderivative = 1.81
method | result | size |
risch | \(-x^{2} \left (x^{2} {\mathrm e}^{6}-4 \,{\mathrm e}^{3} \ln \left (2\right ) x -12 x \,{\mathrm e}^{3}+4 \ln \left (2\right )^{2}+24 \ln \left (2\right )+36\right ) \ln \left (x \right )\) | \(38\) |
norman | \(\left (4 \,{\mathrm e}^{3} \ln \left (2\right )+12 \,{\mathrm e}^{3}\right ) x^{3} \ln \left (x \right )+\left (-4 \ln \left (2\right )^{2}-24 \ln \left (2\right )-36\right ) x^{2} \ln \left (x \right )-{\mathrm e}^{6} x^{4} \ln \left (x \right )\) | \(48\) |
parallelrisch | \(-{\mathrm e}^{6} x^{4} \ln \left (x \right )+4 \,{\mathrm e}^{3} \ln \left (2\right ) \ln \left (x \right ) x^{3}+12 \,{\mathrm e}^{3} \ln \left (x \right ) x^{3}-4 \ln \left (2\right )^{2} x^{2} \ln \left (x \right )-24 x^{2} \ln \left (2\right ) \ln \left (x \right )-36 x^{2} \ln \left (x \right )\) | \(60\) |
parts | \(-{\mathrm e}^{6} x^{4} \ln \left (x \right )+4 \,{\mathrm e}^{3} \ln \left (2\right ) \ln \left (x \right ) x^{3}+12 \,{\mathrm e}^{3} \ln \left (x \right ) x^{3}-4 \ln \left (2\right )^{2} x^{2} \ln \left (x \right )-24 x^{2} \ln \left (2\right ) \ln \left (x \right )-36 x^{2} \ln \left (x \right )\) | \(60\) |
default | \(-{\mathrm e}^{6} x^{4} \ln \left (x \right )+4 \,{\mathrm e}^{3} \ln \left (2\right ) \ln \left (x \right ) x^{3}-\frac {4 \,{\mathrm e}^{3} \ln \left (2\right ) x^{3}}{3}+12 \,{\mathrm e}^{3} \ln \left (x \right ) x^{3}-4 \ln \left (2\right )^{2} x^{2} \ln \left (x \right )-24 x^{2} \ln \left (2\right ) \ln \left (x \right )+12 x^{2} \ln \left (2\right )-36 x^{2} \ln \left (x \right )+4 \ln \left (2\right ) \left (\frac {x^{3} {\mathrm e}^{3}}{3}-3 x^{2}\right )\) | \(93\) |
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Leaf count of result is larger than twice the leaf count of optimal. 48 vs. \(2 (21) = 42\).
Time = 0.25 (sec) , antiderivative size = 48, normalized size of antiderivative = 2.29 \[ \int \left (-36 x+12 e^3 x^2-e^6 x^3+\left (-12 x+2 e^3 x^2\right ) \log (4)-x \log ^2(4)+\left (-72 x+36 e^3 x^2-4 e^6 x^3+\left (-24 x+6 e^3 x^2\right ) \log (4)-2 x \log ^2(4)\right ) \log (x)\right ) \, dx=-{\left (x^{4} e^{6} - 12 \, x^{3} e^{3} + 4 \, x^{2} \log \left (2\right )^{2} + 36 \, x^{2} - 4 \, {\left (x^{3} e^{3} - 6 \, x^{2}\right )} \log \left (2\right )\right )} \log \left (x\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. 53 vs. \(2 (20) = 40\).
Time = 0.10 (sec) , antiderivative size = 53, normalized size of antiderivative = 2.52 \[ \int \left (-36 x+12 e^3 x^2-e^6 x^3+\left (-12 x+2 e^3 x^2\right ) \log (4)-x \log ^2(4)+\left (-72 x+36 e^3 x^2-4 e^6 x^3+\left (-24 x+6 e^3 x^2\right ) \log (4)-2 x \log ^2(4)\right ) \log (x)\right ) \, dx=\left (- x^{4} e^{6} + 4 x^{3} e^{3} \log {\left (2 \right )} + 12 x^{3} e^{3} - 36 x^{2} - 24 x^{2} \log {\left (2 \right )} - 4 x^{2} \log {\left (2 \right )}^{2}\right ) \log {\left (x \right )} \]
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Leaf count of result is larger than twice the leaf count of optimal. 116 vs. \(2 (21) = 42\).
Time = 0.19 (sec) , antiderivative size = 116, normalized size of antiderivative = 5.52 \[ \int \left (-36 x+12 e^3 x^2-e^6 x^3+\left (-12 x+2 e^3 x^2\right ) \log (4)-x \log ^2(4)+\left (-72 x+36 e^3 x^2-4 e^6 x^3+\left (-24 x+6 e^3 x^2\right ) \log (4)-2 x \log ^2(4)\right ) \log (x)\right ) \, dx=-\frac {4}{3} \, {\left (e^{3} \log \left (2\right ) + 3 \, e^{3}\right )} x^{3} + 4 \, x^{3} e^{3} - 2 \, x^{2} \log \left (2\right )^{2} + 2 \, {\left (\log \left (2\right )^{2} + 6 \, \log \left (2\right ) + 9\right )} x^{2} - 18 \, x^{2} + \frac {4}{3} \, {\left (x^{3} e^{3} - 9 \, x^{2}\right )} \log \left (2\right ) - {\left (x^{4} e^{6} - 12 \, x^{3} e^{3} + 4 \, x^{2} \log \left (2\right )^{2} + 36 \, x^{2} - 4 \, {\left (x^{3} e^{3} - 6 \, x^{2}\right )} \log \left (2\right )\right )} \log \left (x\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. 89 vs. \(2 (21) = 42\).
Time = 0.29 (sec) , antiderivative size = 89, normalized size of antiderivative = 4.24 \[ \int \left (-36 x+12 e^3 x^2-e^6 x^3+\left (-12 x+2 e^3 x^2\right ) \log (4)-x \log ^2(4)+\left (-72 x+36 e^3 x^2-4 e^6 x^3+\left (-24 x+6 e^3 x^2\right ) \log (4)-2 x \log ^2(4)\right ) \log (x)\right ) \, dx=-x^{4} e^{6} \log \left (x\right ) + 4 \, x^{3} e^{3} \log \left (2\right ) \log \left (x\right ) - \frac {4}{3} \, x^{3} e^{3} \log \left (2\right ) + 12 \, x^{3} e^{3} \log \left (x\right ) - 4 \, x^{2} \log \left (2\right )^{2} \log \left (x\right ) - 24 \, x^{2} \log \left (2\right ) \log \left (x\right ) + 12 \, x^{2} \log \left (2\right ) - 36 \, x^{2} \log \left (x\right ) + \frac {4}{3} \, {\left (x^{3} e^{3} - 9 \, x^{2}\right )} \log \left (2\right ) \]
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Time = 11.55 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.86 \[ \int \left (-36 x+12 e^3 x^2-e^6 x^3+\left (-12 x+2 e^3 x^2\right ) \log (4)-x \log ^2(4)+\left (-72 x+36 e^3 x^2-4 e^6 x^3+\left (-24 x+6 e^3 x^2\right ) \log (4)-2 x \log ^2(4)\right ) \log (x)\right ) \, dx=-x^2\,\ln \left (x\right )\,{\left (\ln \left (4\right )-x\,{\mathrm {e}}^3+6\right )}^2 \]
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