Integrand size = 101, antiderivative size = 24 \[ \int \left (1250 x+4500 x^2+4200 x^3+900 x^4+54 x^5+\left (-300 x-990 x^2-792 x^3-90 x^4\right ) \log (2)+\left (18 x+54 x^2+36 x^3\right ) \log ^2(2)+\left (-300 x-540 x^2-72 x^3+\left (36 x+54 x^2\right ) \log (2)\right ) \log (4)+18 x \log ^2(4)\right ) \, dx=(2 x+3 x (-((1+x) (9+x-\log (2)))+\log (4)))^2 \]
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Leaf count is larger than twice the leaf count of optimal. \(127\) vs. \(2(24)=48\).
Time = 0.03 (sec) , antiderivative size = 127, normalized size of antiderivative = 5.29, number of steps used = 6, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.010, Rules used = {6} \[ \int \left (1250 x+4500 x^2+4200 x^3+900 x^4+54 x^5+\left (-300 x-990 x^2-792 x^3-90 x^4\right ) \log (2)+\left (18 x+54 x^2+36 x^3\right ) \log ^2(2)+\left (-300 x-540 x^2-72 x^3+\left (36 x+54 x^2\right ) \log (2)\right ) \log (4)+18 x \log ^2(4)\right ) \, dx=9 x^6+180 x^5-18 x^5 \log (2)+1050 x^4+9 x^4 \log ^2(2)-18 x^4 \log (4)-198 x^4 \log (2)+1500 x^3+18 x^3 \log ^2(2)+18 x^3 \log (2) \log (4)-180 x^3 \log (4)-330 x^3 \log (2)+x^2 \left (625+9 \log ^2(4)\right )+9 x^2 \log ^2(2)+18 x^2 \log (2) \log (4)-150 x^2 \log (4)-150 x^2 \log (2) \]
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Rule 6
Rubi steps \begin{align*} \text {integral}& = \int \left (4500 x^2+4200 x^3+900 x^4+54 x^5+\left (-300 x-990 x^2-792 x^3-90 x^4\right ) \log (2)+\left (18 x+54 x^2+36 x^3\right ) \log ^2(2)+\left (-300 x-540 x^2-72 x^3+\left (36 x+54 x^2\right ) \log (2)\right ) \log (4)+x \left (1250+18 \log ^2(4)\right )\right ) \, dx \\ & = 1500 x^3+1050 x^4+180 x^5+9 x^6+x^2 \left (625+9 \log ^2(4)\right )+\log (2) \int \left (-300 x-990 x^2-792 x^3-90 x^4\right ) \, dx+\log ^2(2) \int \left (18 x+54 x^2+36 x^3\right ) \, dx+\log (4) \int \left (-300 x-540 x^2-72 x^3+\left (36 x+54 x^2\right ) \log (2)\right ) \, dx \\ & = 1500 x^3+1050 x^4+180 x^5+9 x^6-150 x^2 \log (2)-330 x^3 \log (2)-198 x^4 \log (2)-18 x^5 \log (2)+9 x^2 \log ^2(2)+18 x^3 \log ^2(2)+9 x^4 \log ^2(2)-150 x^2 \log (4)-180 x^3 \log (4)-18 x^4 \log (4)+x^2 \left (625+9 \log ^2(4)\right )+(\log (2) \log (4)) \int \left (36 x+54 x^2\right ) \, dx \\ & = 1500 x^3+1050 x^4+180 x^5+9 x^6-150 x^2 \log (2)-330 x^3 \log (2)-198 x^4 \log (2)-18 x^5 \log (2)+9 x^2 \log ^2(2)+18 x^3 \log ^2(2)+9 x^4 \log ^2(2)-150 x^2 \log (4)-180 x^3 \log (4)-18 x^4 \log (4)+18 x^2 \log (2) \log (4)+18 x^3 \log (2) \log (4)+x^2 \left (625+9 \log ^2(4)\right ) \\ \end{align*}
Leaf count is larger than twice the leaf count of optimal. \(57\) vs. \(2(24)=48\).
Time = 0.03 (sec) , antiderivative size = 57, normalized size of antiderivative = 2.38 \[ \int \left (1250 x+4500 x^2+4200 x^3+900 x^4+54 x^5+\left (-300 x-990 x^2-792 x^3-90 x^4\right ) \log (2)+\left (18 x+54 x^2+36 x^3\right ) \log ^2(2)+\left (-300 x-540 x^2-72 x^3+\left (36 x+54 x^2\right ) \log (2)\right ) \log (4)+18 x \log ^2(4)\right ) \, dx=x^2 \left (9 x^4-18 x^3 (-10+\log (2))+3 x^2 \left (350-66 \log (2)+3 \log ^2(2)-6 \log (4)\right )+6 x (-10+\log (2)) (-25+\log (512))+(-25+\log (512))^2\right ) \]
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Time = 0.13 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.08
method | result | size |
gosper | \(x^{2} \left (3 x \ln \left (2\right )-3 x^{2}+9 \ln \left (2\right )-30 x -25\right )^{2}\) | \(26\) |
norman | \(\left (-18 \ln \left (2\right )+180\right ) x^{5}+\left (9 \ln \left (2\right )^{2}-234 \ln \left (2\right )+1050\right ) x^{4}+\left (54 \ln \left (2\right )^{2}-690 \ln \left (2\right )+1500\right ) x^{3}+\left (81 \ln \left (2\right )^{2}-450 \ln \left (2\right )+625\right ) x^{2}+9 x^{6}\) | \(65\) |
risch | \(9 x^{4} \ln \left (2\right )^{2}-18 x^{5} \ln \left (2\right )+9 x^{6}+54 x^{3} \ln \left (2\right )^{2}-234 x^{4} \ln \left (2\right )+180 x^{5}+81 x^{2} \ln \left (2\right )^{2}-690 x^{3} \ln \left (2\right )+1050 x^{4}-450 x^{2} \ln \left (2\right )+1500 x^{3}+625 x^{2}\) | \(82\) |
parallelrisch | \(9 x^{4} \ln \left (2\right )^{2}-18 x^{5} \ln \left (2\right )+9 x^{6}+54 x^{3} \ln \left (2\right )^{2}-234 x^{4} \ln \left (2\right )+180 x^{5}+81 x^{2} \ln \left (2\right )^{2}-690 x^{3} \ln \left (2\right )+1050 x^{4}-450 x^{2} \ln \left (2\right )+1500 x^{3}+625 x^{2}\) | \(82\) |
parts | \(9 x^{4} \ln \left (2\right )^{2}-18 x^{5} \ln \left (2\right )+9 x^{6}+54 x^{3} \ln \left (2\right )^{2}-234 x^{4} \ln \left (2\right )+180 x^{5}+81 x^{2} \ln \left (2\right )^{2}-690 x^{3} \ln \left (2\right )+1050 x^{4}-450 x^{2} \ln \left (2\right )+1500 x^{3}+625 x^{2}\) | \(82\) |
default | \(9 x^{6}+\frac {2 \left (-45 \ln \left (2\right )+450\right ) x^{5}}{5}+\frac {\left (-108 \ln \left (2\right )+300+\left (3 \ln \left (2\right )-30\right ) \left (6 \ln \left (2\right )-60\right )\right ) x^{4}}{2}+\frac {2 \left (\left (9 \ln \left (2\right )-25\right ) \left (6 \ln \left (2\right )-60\right )+\left (3 \ln \left (2\right )-30\right ) \left (9 \ln \left (2\right )-25\right )\right ) x^{3}}{3}+\left (9 \ln \left (2\right )-25\right )^{2} x^{2}\) | \(86\) |
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Leaf count of result is larger than twice the leaf count of optimal. 71 vs. \(2 (25) = 50\).
Time = 0.24 (sec) , antiderivative size = 71, normalized size of antiderivative = 2.96 \[ \int \left (1250 x+4500 x^2+4200 x^3+900 x^4+54 x^5+\left (-300 x-990 x^2-792 x^3-90 x^4\right ) \log (2)+\left (18 x+54 x^2+36 x^3\right ) \log ^2(2)+\left (-300 x-540 x^2-72 x^3+\left (36 x+54 x^2\right ) \log (2)\right ) \log (4)+18 x \log ^2(4)\right ) \, dx=9 \, x^{6} + 180 \, x^{5} + 1050 \, x^{4} + 1500 \, x^{3} + 9 \, {\left (x^{4} + 6 \, x^{3} + 9 \, x^{2}\right )} \log \left (2\right )^{2} + 625 \, x^{2} - 6 \, {\left (3 \, x^{5} + 39 \, x^{4} + 115 \, x^{3} + 75 \, x^{2}\right )} \log \left (2\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. 65 vs. \(2 (22) = 44\).
Time = 0.03 (sec) , antiderivative size = 65, normalized size of antiderivative = 2.71 \[ \int \left (1250 x+4500 x^2+4200 x^3+900 x^4+54 x^5+\left (-300 x-990 x^2-792 x^3-90 x^4\right ) \log (2)+\left (18 x+54 x^2+36 x^3\right ) \log ^2(2)+\left (-300 x-540 x^2-72 x^3+\left (36 x+54 x^2\right ) \log (2)\right ) \log (4)+18 x \log ^2(4)\right ) \, dx=9 x^{6} + x^{5} \cdot \left (180 - 18 \log {\left (2 \right )}\right ) + x^{4} \left (- 234 \log {\left (2 \right )} + 9 \log {\left (2 \right )}^{2} + 1050\right ) + x^{3} \left (- 690 \log {\left (2 \right )} + 54 \log {\left (2 \right )}^{2} + 1500\right ) + x^{2} \left (- 450 \log {\left (2 \right )} + 81 \log {\left (2 \right )}^{2} + 625\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. 109 vs. \(2 (25) = 50\).
Time = 0.22 (sec) , antiderivative size = 109, normalized size of antiderivative = 4.54 \[ \int \left (1250 x+4500 x^2+4200 x^3+900 x^4+54 x^5+\left (-300 x-990 x^2-792 x^3-90 x^4\right ) \log (2)+\left (18 x+54 x^2+36 x^3\right ) \log ^2(2)+\left (-300 x-540 x^2-72 x^3+\left (36 x+54 x^2\right ) \log (2)\right ) \log (4)+18 x \log ^2(4)\right ) \, dx=9 \, x^{6} + 180 \, x^{5} + 1050 \, x^{4} + 36 \, x^{2} \log \left (2\right )^{2} + 1500 \, x^{3} + 9 \, {\left (x^{4} + 2 \, x^{3} + x^{2}\right )} \log \left (2\right )^{2} + 625 \, x^{2} - 6 \, {\left (3 \, x^{5} + 33 \, x^{4} + 55 \, x^{3} + 25 \, x^{2}\right )} \log \left (2\right ) - 12 \, {\left (3 \, x^{4} + 30 \, x^{3} + 25 \, x^{2} - 3 \, {\left (x^{3} + x^{2}\right )} \log \left (2\right )\right )} \log \left (2\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. 109 vs. \(2 (25) = 50\).
Time = 0.26 (sec) , antiderivative size = 109, normalized size of antiderivative = 4.54 \[ \int \left (1250 x+4500 x^2+4200 x^3+900 x^4+54 x^5+\left (-300 x-990 x^2-792 x^3-90 x^4\right ) \log (2)+\left (18 x+54 x^2+36 x^3\right ) \log ^2(2)+\left (-300 x-540 x^2-72 x^3+\left (36 x+54 x^2\right ) \log (2)\right ) \log (4)+18 x \log ^2(4)\right ) \, dx=9 \, x^{6} + 180 \, x^{5} + 1050 \, x^{4} + 36 \, x^{2} \log \left (2\right )^{2} + 1500 \, x^{3} + 9 \, {\left (x^{4} + 2 \, x^{3} + x^{2}\right )} \log \left (2\right )^{2} + 625 \, x^{2} - 6 \, {\left (3 \, x^{5} + 33 \, x^{4} + 55 \, x^{3} + 25 \, x^{2}\right )} \log \left (2\right ) - 12 \, {\left (3 \, x^{4} + 30 \, x^{3} + 25 \, x^{2} - 3 \, {\left (x^{3} + x^{2}\right )} \log \left (2\right )\right )} \log \left (2\right ) \]
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Time = 13.49 (sec) , antiderivative size = 59, normalized size of antiderivative = 2.46 \[ \int \left (1250 x+4500 x^2+4200 x^3+900 x^4+54 x^5+\left (-300 x-990 x^2-792 x^3-90 x^4\right ) \log (2)+\left (18 x+54 x^2+36 x^3\right ) \log ^2(2)+\left (-300 x-540 x^2-72 x^3+\left (36 x+54 x^2\right ) \log (2)\right ) \log (4)+18 x \log ^2(4)\right ) \, dx=9\,x^6+\left (180-18\,\ln \left (2\right )\right )\,x^5+\left (9\,{\ln \left (2\right )}^2-234\,\ln \left (2\right )+1050\right )\,x^4+\left (54\,{\ln \left (2\right )}^2-690\,\ln \left (2\right )+1500\right )\,x^3+{\left (\ln \left (512\right )-25\right )}^2\,x^2 \]
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