Integrand size = 129, antiderivative size = 21 \[ \int \frac {468512 \log (5 x)+e^{2-2 x} x^2 \left (702768 \log (5 x)+(702768-702768 x) \log ^2(5 x)\right )+e^{1-x} x \left (937024 \log (5 x)+(468512-468512 x) \log ^2(5 x)\right )+e^{3-3 x} x^3 \left (234256 \log (5 x)+(351384-351384 x) \log ^2(5 x)\right )+e^{4-4 x} x^4 \left (29282 \log (5 x)+(58564-58564 x) \log ^2(5 x)\right )}{x} \, dx=14641 \left (2+e^{1-x} x\right )^4 \log ^2(5 x) \]
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Leaf count is larger than twice the leaf count of optimal. \(79\) vs. \(2(21)=42\).
Time = 0.20 (sec) , antiderivative size = 79, normalized size of antiderivative = 3.76, number of steps used = 7, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.023, Rules used = {14, 2338, 2326} \[ \int \frac {468512 \log (5 x)+e^{2-2 x} x^2 \left (702768 \log (5 x)+(702768-702768 x) \log ^2(5 x)\right )+e^{1-x} x \left (937024 \log (5 x)+(468512-468512 x) \log ^2(5 x)\right )+e^{3-3 x} x^3 \left (234256 \log (5 x)+(351384-351384 x) \log ^2(5 x)\right )+e^{4-4 x} x^4 \left (29282 \log (5 x)+(58564-58564 x) \log ^2(5 x)\right )}{x} \, dx=14641 e^{4-4 x} x^4 \log ^2(5 x)+117128 e^{3-3 x} x^3 \log ^2(5 x)+351384 e^{2-2 x} x^2 \log ^2(5 x)+468512 e^{1-x} x \log ^2(5 x)+234256 \log ^2(5 x) \]
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Rule 14
Rule 2326
Rule 2338
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {468512 \log (5 x)}{x}-468512 e^{1-x} \log (5 x) (-2-\log (5 x)+x \log (5 x))-702768 e^{2-2 x} x \log (5 x) (-1-\log (5 x)+x \log (5 x))-29282 e^{4-4 x} x^3 \log (5 x) (-1-2 \log (5 x)+2 x \log (5 x))-117128 e^{3-3 x} x^2 \log (5 x) (-2-3 \log (5 x)+3 x \log (5 x))\right ) \, dx \\ & = -\left (29282 \int e^{4-4 x} x^3 \log (5 x) (-1-2 \log (5 x)+2 x \log (5 x)) \, dx\right )-117128 \int e^{3-3 x} x^2 \log (5 x) (-2-3 \log (5 x)+3 x \log (5 x)) \, dx+468512 \int \frac {\log (5 x)}{x} \, dx-468512 \int e^{1-x} \log (5 x) (-2-\log (5 x)+x \log (5 x)) \, dx-702768 \int e^{2-2 x} x \log (5 x) (-1-\log (5 x)+x \log (5 x)) \, dx \\ & = 234256 \log ^2(5 x)+468512 e^{1-x} x \log ^2(5 x)+351384 e^{2-2 x} x^2 \log ^2(5 x)+117128 e^{3-3 x} x^3 \log ^2(5 x)+14641 e^{4-4 x} x^4 \log ^2(5 x) \\ \end{align*}
Time = 0.45 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.14 \[ \int \frac {468512 \log (5 x)+e^{2-2 x} x^2 \left (702768 \log (5 x)+(702768-702768 x) \log ^2(5 x)\right )+e^{1-x} x \left (937024 \log (5 x)+(468512-468512 x) \log ^2(5 x)\right )+e^{3-3 x} x^3 \left (234256 \log (5 x)+(351384-351384 x) \log ^2(5 x)\right )+e^{4-4 x} x^4 \left (29282 \log (5 x)+(58564-58564 x) \log ^2(5 x)\right )}{x} \, dx=14641 e^{-4 x} \left (2 e^x+e x\right )^4 \log ^2(5 x) \]
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Leaf count of result is larger than twice the leaf count of optimal. \(79\) vs. \(2(34)=68\).
Time = 2.25 (sec) , antiderivative size = 80, normalized size of antiderivative = 3.81
method | result | size |
parallelrisch | \(234256 \ln \left (5 x \right )^{2}+351384 \,{\mathrm e}^{2-2 x} \ln \left (5 x \right )^{2} x^{2}+468512 \ln \left (5 x \right )^{2} {\mathrm e}^{1+\ln \left (x \right )-x}+117128 \,{\mathrm e}^{-3 x +3} \ln \left (5 x \right )^{2} x^{3}+14641 \,{\mathrm e}^{4-4 x} \ln \left (5 x \right )^{2} x^{4}\) | \(80\) |
risch | \(234256 \ln \left (x \right )^{2}+468512 \ln \left (5\right ) \ln \left (x \right )+\left (14641 \ln \left (5\right )^{2}+29282 \ln \left (5\right ) \ln \left (x \right )+14641 \ln \left (x \right )^{2}\right ) x^{4} {\mathrm e}^{4-4 x}+\left (117128 \ln \left (5\right )^{2}+234256 \ln \left (5\right ) \ln \left (x \right )+117128 \ln \left (x \right )^{2}\right ) x^{3} {\mathrm e}^{-3 x +3}+\left (351384 \ln \left (5\right )^{2}+702768 \ln \left (5\right ) \ln \left (x \right )+351384 \ln \left (x \right )^{2}\right ) x^{2} {\mathrm e}^{2-2 x}+\left (468512 \ln \left (5\right )^{2}+937024 \ln \left (5\right ) \ln \left (x \right )+468512 \ln \left (x \right )^{2}\right ) x \,{\mathrm e}^{1-x}\) | \(128\) |
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Leaf count of result is larger than twice the leaf count of optimal. 119 vs. \(2 (20) = 40\).
Time = 0.27 (sec) , antiderivative size = 119, normalized size of antiderivative = 5.67 \[ \int \frac {468512 \log (5 x)+e^{2-2 x} x^2 \left (702768 \log (5 x)+(702768-702768 x) \log ^2(5 x)\right )+e^{1-x} x \left (937024 \log (5 x)+(468512-468512 x) \log ^2(5 x)\right )+e^{3-3 x} x^3 \left (234256 \log (5 x)+(351384-351384 x) \log ^2(5 x)\right )+e^{4-4 x} x^4 \left (29282 \log (5 x)+(58564-58564 x) \log ^2(5 x)\right )}{x} \, dx=468512 \, {\left (\log \left (5\right )^{2} + 2 \, \log \left (5\right ) \log \left (x\right ) + \log \left (x\right )^{2}\right )} e^{\left (-x + \log \left (x\right ) + 1\right )} + 351384 \, {\left (\log \left (5\right )^{2} + 2 \, \log \left (5\right ) \log \left (x\right ) + \log \left (x\right )^{2}\right )} e^{\left (-2 \, x + 2 \, \log \left (x\right ) + 2\right )} + 117128 \, {\left (\log \left (5\right )^{2} + 2 \, \log \left (5\right ) \log \left (x\right ) + \log \left (x\right )^{2}\right )} e^{\left (-3 \, x + 3 \, \log \left (x\right ) + 3\right )} + 14641 \, {\left (\log \left (5\right )^{2} + 2 \, \log \left (5\right ) \log \left (x\right ) + \log \left (x\right )^{2}\right )} e^{\left (-4 \, x + 4 \, \log \left (x\right ) + 4\right )} + 468512 \, \log \left (5\right ) \log \left (x\right ) + 234256 \, \log \left (x\right )^{2} \]
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Leaf count of result is larger than twice the leaf count of optimal. 78 vs. \(2 (29) = 58\).
Time = 0.27 (sec) , antiderivative size = 78, normalized size of antiderivative = 3.71 \[ \int \frac {468512 \log (5 x)+e^{2-2 x} x^2 \left (702768 \log (5 x)+(702768-702768 x) \log ^2(5 x)\right )+e^{1-x} x \left (937024 \log (5 x)+(468512-468512 x) \log ^2(5 x)\right )+e^{3-3 x} x^3 \left (234256 \log (5 x)+(351384-351384 x) \log ^2(5 x)\right )+e^{4-4 x} x^4 \left (29282 \log (5 x)+(58564-58564 x) \log ^2(5 x)\right )}{x} \, dx=14641 x^{4} e^{4 - 4 x} \log {\left (5 x \right )}^{2} + 117128 x^{3} e^{3 - 3 x} \log {\left (5 x \right )}^{2} + 351384 x^{2} e^{2 - 2 x} \log {\left (5 x \right )}^{2} + 468512 x e^{1 - x} \log {\left (5 x \right )}^{2} + 234256 \log {\left (5 x \right )}^{2} \]
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Leaf count of result is larger than twice the leaf count of optimal. 155 vs. \(2 (20) = 40\).
Time = 0.36 (sec) , antiderivative size = 155, normalized size of antiderivative = 7.38 \[ \int \frac {468512 \log (5 x)+e^{2-2 x} x^2 \left (702768 \log (5 x)+(702768-702768 x) \log ^2(5 x)\right )+e^{1-x} x \left (937024 \log (5 x)+(468512-468512 x) \log ^2(5 x)\right )+e^{3-3 x} x^3 \left (234256 \log (5 x)+(351384-351384 x) \log ^2(5 x)\right )+e^{4-4 x} x^4 \left (29282 \log (5 x)+(58564-58564 x) \log ^2(5 x)\right )}{x} \, dx=468512 \, {\left (x e \log \left (5\right )^{2} + 2 \, x e \log \left (5\right ) \log \left (x\right ) + x e \log \left (x\right )^{2}\right )} e^{\left (-x\right )} + 351384 \, {\left (x^{2} e^{2} \log \left (5\right )^{2} + 2 \, x^{2} e^{2} \log \left (5\right ) \log \left (x\right ) + x^{2} e^{2} \log \left (x\right )^{2}\right )} e^{\left (-2 \, x\right )} + 117128 \, {\left (x^{3} e^{3} \log \left (5\right )^{2} + 2 \, x^{3} e^{3} \log \left (5\right ) \log \left (x\right ) + x^{3} e^{3} \log \left (x\right )^{2}\right )} e^{\left (-3 \, x\right )} + 14641 \, {\left (x^{4} e^{4} \log \left (5\right )^{2} + 2 \, x^{4} e^{4} \log \left (5\right ) \log \left (x\right ) + x^{4} e^{4} \log \left (x\right )^{2}\right )} e^{\left (-4 \, x\right )} + 234256 \, \log \left (5 \, x\right )^{2} \]
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Leaf count of result is larger than twice the leaf count of optimal. 187 vs. \(2 (20) = 40\).
Time = 0.27 (sec) , antiderivative size = 187, normalized size of antiderivative = 8.90 \[ \int \frac {468512 \log (5 x)+e^{2-2 x} x^2 \left (702768 \log (5 x)+(702768-702768 x) \log ^2(5 x)\right )+e^{1-x} x \left (937024 \log (5 x)+(468512-468512 x) \log ^2(5 x)\right )+e^{3-3 x} x^3 \left (234256 \log (5 x)+(351384-351384 x) \log ^2(5 x)\right )+e^{4-4 x} x^4 \left (29282 \log (5 x)+(58564-58564 x) \log ^2(5 x)\right )}{x} \, dx=14641 \, x^{4} e^{\left (-4 \, x + 4\right )} \log \left (5\right )^{2} + 29282 \, x^{4} e^{\left (-4 \, x + 4\right )} \log \left (5\right ) \log \left (x\right ) + 14641 \, x^{4} e^{\left (-4 \, x + 4\right )} \log \left (x\right )^{2} + 117128 \, x^{3} e^{\left (-3 \, x + 3\right )} \log \left (5\right )^{2} + 234256 \, x^{3} e^{\left (-3 \, x + 3\right )} \log \left (5\right ) \log \left (x\right ) + 117128 \, x^{3} e^{\left (-3 \, x + 3\right )} \log \left (x\right )^{2} + 351384 \, x^{2} e^{\left (-2 \, x + 2\right )} \log \left (5\right )^{2} + 702768 \, x^{2} e^{\left (-2 \, x + 2\right )} \log \left (5\right ) \log \left (x\right ) + 351384 \, x^{2} e^{\left (-2 \, x + 2\right )} \log \left (x\right )^{2} + 468512 \, x e^{\left (-x + 1\right )} \log \left (5\right )^{2} + 937024 \, x e^{\left (-x + 1\right )} \log \left (5\right ) \log \left (x\right ) + 468512 \, x e^{\left (-x + 1\right )} \log \left (x\right )^{2} + 468512 \, \log \left (5\right ) \log \left (x\right ) + 234256 \, \log \left (x\right )^{2} \]
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Time = 10.91 (sec) , antiderivative size = 75, normalized size of antiderivative = 3.57 \[ \int \frac {468512 \log (5 x)+e^{2-2 x} x^2 \left (702768 \log (5 x)+(702768-702768 x) \log ^2(5 x)\right )+e^{1-x} x \left (937024 \log (5 x)+(468512-468512 x) \log ^2(5 x)\right )+e^{3-3 x} x^3 \left (234256 \log (5 x)+(351384-351384 x) \log ^2(5 x)\right )+e^{4-4 x} x^4 \left (29282 \log (5 x)+(58564-58564 x) \log ^2(5 x)\right )}{x} \, dx=234256\,{\ln \left (5\,x\right )}^2+468512\,x\,{\ln \left (5\,x\right )}^2\,{\mathrm {e}}^{1-x}+351384\,x^2\,{\ln \left (5\,x\right )}^2\,{\mathrm {e}}^{2-2\,x}+117128\,x^3\,{\ln \left (5\,x\right )}^2\,{\mathrm {e}}^{3-3\,x}+14641\,x^4\,{\ln \left (5\,x\right )}^2\,{\mathrm {e}}^{4-4\,x} \]
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