Integrand size = 62, antiderivative size = 29 \[ \int \frac {35 x+8 e^2 x+7 x^2+26 x^3+\left (-5 x-e^2 x-2 x^2-3 x^3\right ) \log (x)+e^3 x (5-17 x+2 x \log (x))}{x} \, dx=\left (-5-e^2-x+e^3 x-x^2\right ) (5+x (-9+\log (x))) \]
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Leaf count is larger than twice the leaf count of optimal. \(85\) vs. \(2(29)=58\).
Time = 0.06 (sec) , antiderivative size = 85, normalized size of antiderivative = 2.93, number of steps used = 8, number of rules used = 5, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.081, Rules used = {6, 14, 2403, 2332, 2341} \[ \int \frac {35 x+8 e^2 x+7 x^2+26 x^3+\left (-5 x-e^2 x-2 x^2-3 x^3\right ) \log (x)+e^3 x (5-17 x+2 x \log (x))}{x} \, dx=9 x^3+x^3 (-\log (x))+\frac {1}{2} \left (1-e^3\right ) x^2+\frac {1}{2} \left (7-17 e^3\right ) x^2-\left (1-e^3\right ) x^2 \log (x)+\left (35+e^2 (8+5 e)\right ) x+\left (5+e^2\right ) x-\left (5+e^2\right ) x \log (x) \]
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Rule 6
Rule 14
Rule 2332
Rule 2341
Rule 2403
Rubi steps \begin{align*} \text {integral}& = \int \frac {\left (35+8 e^2\right ) x+7 x^2+26 x^3+\left (-5 x-e^2 x-2 x^2-3 x^3\right ) \log (x)+e^3 x (5-17 x+2 x \log (x))}{x} \, dx \\ & = \int \left (35 \left (1+\frac {1}{35} e^2 (8+5 e)\right )+7 \left (1-\frac {17 e^3}{7}\right ) x+26 x^2+\left (-5-e^2-2 \left (1-e^3\right ) x-3 x^2\right ) \log (x)\right ) \, dx \\ & = \left (35+e^2 (8+5 e)\right ) x+\frac {1}{2} \left (7-17 e^3\right ) x^2+\frac {26 x^3}{3}+\int \left (-5-e^2-2 \left (1-e^3\right ) x-3 x^2\right ) \log (x) \, dx \\ & = \left (35+e^2 (8+5 e)\right ) x+\frac {1}{2} \left (7-17 e^3\right ) x^2+\frac {26 x^3}{3}+\int \left (-5 \left (1+\frac {e^2}{5}\right ) \log (x)+2 (-1+e) \left (1+e+e^2\right ) x \log (x)-3 x^2 \log (x)\right ) \, dx \\ & = \left (35+e^2 (8+5 e)\right ) x+\frac {1}{2} \left (7-17 e^3\right ) x^2+\frac {26 x^3}{3}-3 \int x^2 \log (x) \, dx-\left (5+e^2\right ) \int \log (x) \, dx+\left (2 (-1+e) \left (1+e+e^2\right )\right ) \int x \log (x) \, dx \\ & = \left (5+e^2\right ) x+\left (35+e^2 (8+5 e)\right ) x+\frac {1}{2} (1-e) \left (1+e+e^2\right ) x^2+\frac {1}{2} \left (7-17 e^3\right ) x^2+9 x^3-\left (5+e^2\right ) x \log (x)-(1-e) \left (1+e+e^2\right ) x^2 \log (x)-x^3 \log (x) \\ \end{align*}
Leaf count is larger than twice the leaf count of optimal. \(70\) vs. \(2(29)=58\).
Time = 0.02 (sec) , antiderivative size = 70, normalized size of antiderivative = 2.41 \[ \int \frac {35 x+8 e^2 x+7 x^2+26 x^3+\left (-5 x-e^2 x-2 x^2-3 x^3\right ) \log (x)+e^3 x (5-17 x+2 x \log (x))}{x} \, dx=40 x+9 e^2 x+5 e^3 x+4 x^2-9 e^3 x^2+9 x^3-5 x \log (x)-e^2 x \log (x)-x^2 \log (x)+e^3 x^2 \log (x)-x^3 \log (x) \]
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Time = 0.32 (sec) , antiderivative size = 56, normalized size of antiderivative = 1.93
method | result | size |
norman | \(\left (4-9 \,{\mathrm e}^{3}\right ) x^{2}+\left (40+9 \,{\mathrm e}^{2}+5 \,{\mathrm e}^{3}\right ) x +\left (-{\mathrm e}^{2}-5\right ) x \ln \left (x \right )+\left ({\mathrm e}^{3}-1\right ) x^{2} \ln \left (x \right )+9 x^{3}-x^{3} \ln \left (x \right )\) | \(56\) |
risch | \(\left (x^{2} {\mathrm e}^{3}-{\mathrm e}^{2} x -x^{3}-x^{2}-5 x \right ) \ln \left (x \right )-9 x^{2} {\mathrm e}^{3}+5 x \,{\mathrm e}^{3}+9 \,{\mathrm e}^{2} x +9 x^{3}+4 x^{2}+40 x\) | \(60\) |
default | \(40 x +{\mathrm e}^{3} \left (x^{2} \ln \left (x \right )-9 x^{2}+5 x \right )-x^{3} \ln \left (x \right )+9 x^{3}-{\mathrm e}^{2} \left (x \ln \left (x \right )-x \right )-x^{2} \ln \left (x \right )+4 x^{2}-5 x \ln \left (x \right )+8 \,{\mathrm e}^{2} x\) | \(69\) |
parts | \(40 x +{\mathrm e}^{3} \left (x^{2} \ln \left (x \right )-9 x^{2}+5 x \right )-x^{3} \ln \left (x \right )+9 x^{3}-{\mathrm e}^{2} \left (x \ln \left (x \right )-x \right )-x^{2} \ln \left (x \right )+4 x^{2}-5 x \ln \left (x \right )+8 \,{\mathrm e}^{2} x\) | \(69\) |
parallelrisch | \(-\frac {x^{5} \ln \left (x \right )+x^{3} {\mathrm e}^{2} \ln \left (x \right )-9 x^{5}+x^{4} \ln \left (x \right )-{\mathrm e}^{3+\ln \left (x \right )} \ln \left (x \right ) x^{3}-9 x^{3} {\mathrm e}^{2}-4 x^{4}+5 x^{3} \ln \left (x \right )+9 x^{3} {\mathrm e}^{3+\ln \left (x \right )}-40 x^{3}-5 \,{\mathrm e}^{3+\ln \left (x \right )} x^{2}}{x^{2}}\) | \(88\) |
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Leaf count of result is larger than twice the leaf count of optimal. 57 vs. \(2 (25) = 50\).
Time = 0.27 (sec) , antiderivative size = 57, normalized size of antiderivative = 1.97 \[ \int \frac {35 x+8 e^2 x+7 x^2+26 x^3+\left (-5 x-e^2 x-2 x^2-3 x^3\right ) \log (x)+e^3 x (5-17 x+2 x \log (x))}{x} \, dx=9 \, x^{3} + 4 \, x^{2} - {\left (9 \, x^{2} - 5 \, x\right )} e^{3} + 9 \, x e^{2} - {\left (x^{3} - x^{2} e^{3} + x^{2} + x e^{2} + 5 \, x\right )} \log \left (x\right ) + 40 \, x \]
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Leaf count of result is larger than twice the leaf count of optimal. 53 vs. \(2 (22) = 44\).
Time = 0.08 (sec) , antiderivative size = 53, normalized size of antiderivative = 1.83 \[ \int \frac {35 x+8 e^2 x+7 x^2+26 x^3+\left (-5 x-e^2 x-2 x^2-3 x^3\right ) \log (x)+e^3 x (5-17 x+2 x \log (x))}{x} \, dx=9 x^{3} + x^{2} \cdot \left (4 - 9 e^{3}\right ) + x \left (40 + 9 e^{2} + 5 e^{3}\right ) + \left (- x^{3} - x^{2} + x^{2} e^{3} - x e^{2} - 5 x\right ) \log {\left (x \right )} \]
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Leaf count of result is larger than twice the leaf count of optimal. 79 vs. \(2 (25) = 50\).
Time = 0.20 (sec) , antiderivative size = 79, normalized size of antiderivative = 2.72 \[ \int \frac {35 x+8 e^2 x+7 x^2+26 x^3+\left (-5 x-e^2 x-2 x^2-3 x^3\right ) \log (x)+e^3 x (5-17 x+2 x \log (x))}{x} \, dx=-x^{3} \log \left (x\right ) + 9 \, x^{3} - \frac {17}{2} \, x^{2} e^{3} - x^{2} \log \left (x\right ) + 4 \, x^{2} + \frac {1}{2} \, {\left (2 \, x^{2} \log \left (x\right ) - x^{2}\right )} e^{3} + 5 \, x e^{3} - {\left (x \log \left (x\right ) - x\right )} e^{2} + 8 \, x e^{2} - 5 \, x \log \left (x\right ) + 40 \, x \]
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Leaf count of result is larger than twice the leaf count of optimal. 65 vs. \(2 (25) = 50\).
Time = 0.28 (sec) , antiderivative size = 65, normalized size of antiderivative = 2.24 \[ \int \frac {35 x+8 e^2 x+7 x^2+26 x^3+\left (-5 x-e^2 x-2 x^2-3 x^3\right ) \log (x)+e^3 x (5-17 x+2 x \log (x))}{x} \, dx=-x^{3} \log \left (x\right ) + x^{2} e^{3} \log \left (x\right ) + 9 \, x^{3} - 9 \, x^{2} e^{3} - x^{2} \log \left (x\right ) - x e^{2} \log \left (x\right ) + 4 \, x^{2} + 5 \, x e^{3} + 9 \, x e^{2} - 5 \, x \log \left (x\right ) + 40 \, x \]
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Time = 15.19 (sec) , antiderivative size = 47, normalized size of antiderivative = 1.62 \[ \int \frac {35 x+8 e^2 x+7 x^2+26 x^3+\left (-5 x-e^2 x-2 x^2-3 x^3\right ) \log (x)+e^3 x (5-17 x+2 x \log (x))}{x} \, dx=x^2\,\left (\ln \left (x\right )\,\left ({\mathrm {e}}^3-1\right )-9\,{\mathrm {e}}^3+4\right )-x^3\,\left (\ln \left (x\right )-9\right )+x\,\left (9\,{\mathrm {e}}^2+5\,{\mathrm {e}}^3-\ln \left (x\right )\,\left ({\mathrm {e}}^2+5\right )+40\right ) \]
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