Integrand size = 125, antiderivative size = 25 \[ \int \frac {e^{4 x} (3-4 x)+4 e^{3 x} x+25 x^2+25 x^4+\left (-12 e^{2 x} x^2+e^{3 x} \left (-8 x+12 x^2\right )\right ) \log (x)+\left (12 e^x x^3+e^{2 x} \left (6 x^2-12 x^3\right )\right ) \log ^2(x)+\left (-4 x^4+4 e^x x^4\right ) \log ^3(x)-x^4 \log ^4(x)}{25 x^4} \, dx=-\frac {1}{x}+x-\frac {1}{25} x \left (-\frac {e^x}{x}+\log (x)\right )^4 \]
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Leaf count is larger than twice the leaf count of optimal. \(69\) vs. \(2(25)=50\).
Time = 0.19 (sec) , antiderivative size = 69, normalized size of antiderivative = 2.76, number of steps used = 18, number of rules used = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {12, 14, 2228, 2233, 2326, 2333, 2332} \[ \int \frac {e^{4 x} (3-4 x)+4 e^{3 x} x+25 x^2+25 x^4+\left (-12 e^{2 x} x^2+e^{3 x} \left (-8 x+12 x^2\right )\right ) \log (x)+\left (12 e^x x^3+e^{2 x} \left (6 x^2-12 x^3\right )\right ) \log ^2(x)+\left (-4 x^4+4 e^x x^4\right ) \log ^3(x)-x^4 \log ^4(x)}{25 x^4} \, dx=-\frac {e^{4 x}}{25 x^3}+\frac {4 e^{3 x} \log (x)}{25 x^2}+x-\frac {1}{x}-\frac {1}{25} x \log ^4(x)+\frac {4}{25} e^x \log ^3(x)-\frac {6 e^{2 x} \log ^2(x)}{25 x} \]
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Rule 12
Rule 14
Rule 2228
Rule 2233
Rule 2326
Rule 2332
Rule 2333
Rubi steps \begin{align*} \text {integral}& = \frac {1}{25} \int \frac {e^{4 x} (3-4 x)+4 e^{3 x} x+25 x^2+25 x^4+\left (-12 e^{2 x} x^2+e^{3 x} \left (-8 x+12 x^2\right )\right ) \log (x)+\left (12 e^x x^3+e^{2 x} \left (6 x^2-12 x^3\right )\right ) \log ^2(x)+\left (-4 x^4+4 e^x x^4\right ) \log ^3(x)-x^4 \log ^4(x)}{x^4} \, dx \\ & = \frac {1}{25} \int \left (-\frac {e^{4 x} (-3+4 x)}{x^4}+\frac {4 e^x \log ^2(x) (3+x \log (x))}{x}-\frac {6 e^{2 x} \log (x) (2-\log (x)+2 x \log (x))}{x^2}+\frac {4 e^{3 x} (1-2 \log (x)+3 x \log (x))}{x^3}+\frac {25+25 x^2-4 x^2 \log ^3(x)-x^2 \log ^4(x)}{x^2}\right ) \, dx \\ & = -\left (\frac {1}{25} \int \frac {e^{4 x} (-3+4 x)}{x^4} \, dx\right )+\frac {1}{25} \int \frac {25+25 x^2-4 x^2 \log ^3(x)-x^2 \log ^4(x)}{x^2} \, dx+\frac {4}{25} \int \frac {e^x \log ^2(x) (3+x \log (x))}{x} \, dx+\frac {4}{25} \int \frac {e^{3 x} (1-2 \log (x)+3 x \log (x))}{x^3} \, dx-\frac {6}{25} \int \frac {e^{2 x} \log (x) (2-\log (x)+2 x \log (x))}{x^2} \, dx \\ & = -\frac {e^{4 x}}{25 x^3}+\frac {4 e^{3 x} \log (x)}{25 x^2}-\frac {6 e^{2 x} \log ^2(x)}{25 x}+\frac {4}{25} e^x \log ^3(x)+\frac {1}{25} \int \left (\frac {25 \left (1+x^2\right )}{x^2}-4 \log ^3(x)-\log ^4(x)\right ) \, dx \\ & = -\frac {e^{4 x}}{25 x^3}+\frac {4 e^{3 x} \log (x)}{25 x^2}-\frac {6 e^{2 x} \log ^2(x)}{25 x}+\frac {4}{25} e^x \log ^3(x)-\frac {1}{25} \int \log ^4(x) \, dx-\frac {4}{25} \int \log ^3(x) \, dx+\int \frac {1+x^2}{x^2} \, dx \\ & = -\frac {e^{4 x}}{25 x^3}+\frac {4 e^{3 x} \log (x)}{25 x^2}-\frac {6 e^{2 x} \log ^2(x)}{25 x}+\frac {4}{25} e^x \log ^3(x)-\frac {4}{25} x \log ^3(x)-\frac {1}{25} x \log ^4(x)+\frac {4}{25} \int \log ^3(x) \, dx+\frac {12}{25} \int \log ^2(x) \, dx+\int \left (1+\frac {1}{x^2}\right ) \, dx \\ & = -\frac {e^{4 x}}{25 x^3}-\frac {1}{x}+x+\frac {4 e^{3 x} \log (x)}{25 x^2}-\frac {6 e^{2 x} \log ^2(x)}{25 x}+\frac {12}{25} x \log ^2(x)+\frac {4}{25} e^x \log ^3(x)-\frac {1}{25} x \log ^4(x)-\frac {12}{25} \int \log ^2(x) \, dx-\frac {24}{25} \int \log (x) \, dx \\ & = -\frac {e^{4 x}}{25 x^3}-\frac {1}{x}+\frac {49 x}{25}+\frac {4 e^{3 x} \log (x)}{25 x^2}-\frac {24}{25} x \log (x)-\frac {6 e^{2 x} \log ^2(x)}{25 x}+\frac {4}{25} e^x \log ^3(x)-\frac {1}{25} x \log ^4(x)+\frac {24}{25} \int \log (x) \, dx \\ & = -\frac {e^{4 x}}{25 x^3}-\frac {1}{x}+x+\frac {4 e^{3 x} \log (x)}{25 x^2}-\frac {6 e^{2 x} \log ^2(x)}{25 x}+\frac {4}{25} e^x \log ^3(x)-\frac {1}{25} x \log ^4(x) \\ \end{align*}
Leaf count is larger than twice the leaf count of optimal. \(65\) vs. \(2(25)=50\).
Time = 0.09 (sec) , antiderivative size = 65, normalized size of antiderivative = 2.60 \[ \int \frac {e^{4 x} (3-4 x)+4 e^{3 x} x+25 x^2+25 x^4+\left (-12 e^{2 x} x^2+e^{3 x} \left (-8 x+12 x^2\right )\right ) \log (x)+\left (12 e^x x^3+e^{2 x} \left (6 x^2-12 x^3\right )\right ) \log ^2(x)+\left (-4 x^4+4 e^x x^4\right ) \log ^3(x)-x^4 \log ^4(x)}{25 x^4} \, dx=\frac {1}{25} \left (-\frac {e^{4 x}}{x^3}-\frac {25}{x}+25 x+\frac {4 e^{3 x} \log (x)}{x^2}-\frac {6 e^{2 x} \log ^2(x)}{x}+4 e^x \log ^3(x)-x \log ^4(x)\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. \(55\) vs. \(2(22)=44\).
Time = 0.17 (sec) , antiderivative size = 56, normalized size of antiderivative = 2.24
method | result | size |
default | \(\frac {4 \,{\mathrm e}^{x} \ln \left (x \right )^{3}}{25}+\frac {4 \ln \left (x \right ) {\mathrm e}^{3 x}}{25 x^{2}}-\frac {6 \,{\mathrm e}^{2 x} \ln \left (x \right )^{2}}{25 x}-\frac {x \ln \left (x \right )^{4}}{25}+x -\frac {1}{x}-\frac {{\mathrm e}^{4 x}}{25 x^{3}}\) | \(56\) |
parallelrisch | \(-\frac {x^{4} \ln \left (x \right )^{4}-4 \ln \left (x \right )^{3} {\mathrm e}^{x} x^{3}+6 \,{\mathrm e}^{2 x} \ln \left (x \right )^{2} x^{2}-25 x^{4}-4 \ln \left (x \right ) {\mathrm e}^{3 x} x +25 x^{2}+{\mathrm e}^{4 x}}{25 x^{3}}\) | \(62\) |
risch | \(-\frac {x \ln \left (x \right )^{4}}{25}+\frac {4 \,{\mathrm e}^{x} \ln \left (x \right )^{3}}{25}-\frac {6 \,{\mathrm e}^{2 x} \ln \left (x \right )^{2}}{25 x}+\frac {4 \ln \left (x \right ) {\mathrm e}^{3 x}}{25 x^{2}}+\frac {25 x^{4}-{\mathrm e}^{4 x}-25 x^{2}}{25 x^{3}}\) | \(63\) |
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Leaf count of result is larger than twice the leaf count of optimal. 61 vs. \(2 (23) = 46\).
Time = 0.26 (sec) , antiderivative size = 61, normalized size of antiderivative = 2.44 \[ \int \frac {e^{4 x} (3-4 x)+4 e^{3 x} x+25 x^2+25 x^4+\left (-12 e^{2 x} x^2+e^{3 x} \left (-8 x+12 x^2\right )\right ) \log (x)+\left (12 e^x x^3+e^{2 x} \left (6 x^2-12 x^3\right )\right ) \log ^2(x)+\left (-4 x^4+4 e^x x^4\right ) \log ^3(x)-x^4 \log ^4(x)}{25 x^4} \, dx=-\frac {x^{4} \log \left (x\right )^{4} - 4 \, x^{3} e^{x} \log \left (x\right )^{3} + 6 \, x^{2} e^{\left (2 \, x\right )} \log \left (x\right )^{2} - 25 \, x^{4} - 4 \, x e^{\left (3 \, x\right )} \log \left (x\right ) + 25 \, x^{2} + e^{\left (4 \, x\right )}}{25 \, x^{3}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 70 vs. \(2 (17) = 34\).
Time = 0.17 (sec) , antiderivative size = 70, normalized size of antiderivative = 2.80 \[ \int \frac {e^{4 x} (3-4 x)+4 e^{3 x} x+25 x^2+25 x^4+\left (-12 e^{2 x} x^2+e^{3 x} \left (-8 x+12 x^2\right )\right ) \log (x)+\left (12 e^x x^3+e^{2 x} \left (6 x^2-12 x^3\right )\right ) \log ^2(x)+\left (-4 x^4+4 e^x x^4\right ) \log ^3(x)-x^4 \log ^4(x)}{25 x^4} \, dx=- \frac {x \log {\left (x \right )}^{4}}{25} + x - \frac {1}{x} + \frac {62500 x^{6} e^{x} \log {\left (x \right )}^{3} - 93750 x^{5} e^{2 x} \log {\left (x \right )}^{2} + 62500 x^{4} e^{3 x} \log {\left (x \right )} - 15625 x^{3} e^{4 x}}{390625 x^{6}} \]
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\[ \int \frac {e^{4 x} (3-4 x)+4 e^{3 x} x+25 x^2+25 x^4+\left (-12 e^{2 x} x^2+e^{3 x} \left (-8 x+12 x^2\right )\right ) \log (x)+\left (12 e^x x^3+e^{2 x} \left (6 x^2-12 x^3\right )\right ) \log ^2(x)+\left (-4 x^4+4 e^x x^4\right ) \log ^3(x)-x^4 \log ^4(x)}{25 x^4} \, dx=\int { -\frac {x^{4} \log \left (x\right )^{4} - 25 \, x^{4} - 4 \, {\left (x^{4} e^{x} - x^{4}\right )} \log \left (x\right )^{3} - 6 \, {\left (2 \, x^{3} e^{x} - {\left (2 \, x^{3} - x^{2}\right )} e^{\left (2 \, x\right )}\right )} \log \left (x\right )^{2} - 25 \, x^{2} + {\left (4 \, x - 3\right )} e^{\left (4 \, x\right )} - 4 \, x e^{\left (3 \, x\right )} + 4 \, {\left (3 \, x^{2} e^{\left (2 \, x\right )} - {\left (3 \, x^{2} - 2 \, x\right )} e^{\left (3 \, x\right )}\right )} \log \left (x\right )}{25 \, x^{4}} \,d x } \]
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Leaf count of result is larger than twice the leaf count of optimal. 61 vs. \(2 (23) = 46\).
Time = 0.35 (sec) , antiderivative size = 61, normalized size of antiderivative = 2.44 \[ \int \frac {e^{4 x} (3-4 x)+4 e^{3 x} x+25 x^2+25 x^4+\left (-12 e^{2 x} x^2+e^{3 x} \left (-8 x+12 x^2\right )\right ) \log (x)+\left (12 e^x x^3+e^{2 x} \left (6 x^2-12 x^3\right )\right ) \log ^2(x)+\left (-4 x^4+4 e^x x^4\right ) \log ^3(x)-x^4 \log ^4(x)}{25 x^4} \, dx=-\frac {x^{4} \log \left (x\right )^{4} - 4 \, x^{3} e^{x} \log \left (x\right )^{3} + 6 \, x^{2} e^{\left (2 \, x\right )} \log \left (x\right )^{2} - 25 \, x^{4} - 4 \, x e^{\left (3 \, x\right )} \log \left (x\right ) + 25 \, x^{2} + e^{\left (4 \, x\right )}}{25 \, x^{3}} \]
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Timed out. \[ \int \frac {e^{4 x} (3-4 x)+4 e^{3 x} x+25 x^2+25 x^4+\left (-12 e^{2 x} x^2+e^{3 x} \left (-8 x+12 x^2\right )\right ) \log (x)+\left (12 e^x x^3+e^{2 x} \left (6 x^2-12 x^3\right )\right ) \log ^2(x)+\left (-4 x^4+4 e^x x^4\right ) \log ^3(x)-x^4 \log ^4(x)}{25 x^4} \, dx=-\int -\frac {\frac {4\,x\,{\mathrm {e}}^{3\,x}}{25}-\frac {\ln \left (x\right )\,\left ({\mathrm {e}}^{3\,x}\,\left (8\,x-12\,x^2\right )+12\,x^2\,{\mathrm {e}}^{2\,x}\right )}{25}+\frac {{\ln \left (x\right )}^3\,\left (4\,x^4\,{\mathrm {e}}^x-4\,x^4\right )}{25}-\frac {x^4\,{\ln \left (x\right )}^4}{25}+\frac {{\ln \left (x\right )}^2\,\left (12\,x^3\,{\mathrm {e}}^x+{\mathrm {e}}^{2\,x}\,\left (6\,x^2-12\,x^3\right )\right )}{25}-\frac {{\mathrm {e}}^{4\,x}\,\left (4\,x-3\right )}{25}+x^2+x^4}{x^4} \,d x \]
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