Integrand size = 86, antiderivative size = 18 \[ \int \frac {e^{-4 x} \left (e^{4 e^4} (256-1024 x)+e^{4 e^4} (192-1024 x) \log (x)+e^{4 e^4} (48-384 x) \log ^2(x)+e^{4 e^4} (4-64 x) \log ^3(x)-4 e^{4 e^4} x \log ^4(x)\right )}{x} \, dx=e^{4 e^4-4 x} (4+\log (x))^4 \]
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Time = 0.32 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.61, number of steps used = 3, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.035, Rules used = {6820, 12, 2326} \[ \int \frac {e^{-4 x} \left (e^{4 e^4} (256-1024 x)+e^{4 e^4} (192-1024 x) \log (x)+e^{4 e^4} (48-384 x) \log ^2(x)+e^{4 e^4} (4-64 x) \log ^3(x)-4 e^{4 e^4} x \log ^4(x)\right )}{x} \, dx=\frac {e^{4 e^4-4 x} (\log (x)+4)^3 (4 x+x \log (x))}{x} \]
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Rule 12
Rule 2326
Rule 6820
Rubi steps \begin{align*} \text {integral}& = \int \frac {4 e^{4 e^4-4 x} (4+\log (x))^3 (1-4 x-x \log (x))}{x} \, dx \\ & = 4 \int \frac {e^{4 e^4-4 x} (4+\log (x))^3 (1-4 x-x \log (x))}{x} \, dx \\ & = \frac {e^{4 e^4-4 x} (4+\log (x))^3 (4 x+x \log (x))}{x} \\ \end{align*}
Time = 0.03 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.00 \[ \int \frac {e^{-4 x} \left (e^{4 e^4} (256-1024 x)+e^{4 e^4} (192-1024 x) \log (x)+e^{4 e^4} (48-384 x) \log ^2(x)+e^{4 e^4} (4-64 x) \log ^3(x)-4 e^{4 e^4} x \log ^4(x)\right )}{x} \, dx=e^{4 e^4-4 x} (4+\log (x))^4 \]
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Leaf count of result is larger than twice the leaf count of optimal. \(56\) vs. \(2(18)=36\).
Time = 0.22 (sec) , antiderivative size = 57, normalized size of antiderivative = 3.17
method | result | size |
parallelrisch | \(\left ({\mathrm e}^{4 \,{\mathrm e}^{4}} \ln \left (x \right )^{4}+16 \,{\mathrm e}^{4 \,{\mathrm e}^{4}} \ln \left (x \right )^{3}+96 \,{\mathrm e}^{4 \,{\mathrm e}^{4}} \ln \left (x \right )^{2}+256 \,{\mathrm e}^{4 \,{\mathrm e}^{4}} \ln \left (x \right )+256 \,{\mathrm e}^{4 \,{\mathrm e}^{4}}\right ) {\mathrm e}^{-4 x}\) | \(57\) |
risch | \(\ln \left (x \right )^{4} {\mathrm e}^{4 \,{\mathrm e}^{4}-4 x}+16 \ln \left (x \right )^{3} {\mathrm e}^{4 \,{\mathrm e}^{4}-4 x}+96 \ln \left (x \right )^{2} {\mathrm e}^{4 \,{\mathrm e}^{4}-4 x}+256 \ln \left (x \right ) {\mathrm e}^{4 \,{\mathrm e}^{4}-4 x}+256 \,{\mathrm e}^{4 \,{\mathrm e}^{4}-4 x}\) | \(70\) |
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Leaf count of result is larger than twice the leaf count of optimal. 69 vs. \(2 (16) = 32\).
Time = 0.31 (sec) , antiderivative size = 69, normalized size of antiderivative = 3.83 \[ \int \frac {e^{-4 x} \left (e^{4 e^4} (256-1024 x)+e^{4 e^4} (192-1024 x) \log (x)+e^{4 e^4} (48-384 x) \log ^2(x)+e^{4 e^4} (4-64 x) \log ^3(x)-4 e^{4 e^4} x \log ^4(x)\right )}{x} \, dx=e^{\left (-4 \, x + 4 \, e^{4}\right )} \log \left (x\right )^{4} + 16 \, e^{\left (-4 \, x + 4 \, e^{4}\right )} \log \left (x\right )^{3} + 96 \, e^{\left (-4 \, x + 4 \, e^{4}\right )} \log \left (x\right )^{2} + 256 \, e^{\left (-4 \, x + 4 \, e^{4}\right )} \log \left (x\right ) + 256 \, e^{\left (-4 \, x + 4 \, e^{4}\right )} \]
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Leaf count of result is larger than twice the leaf count of optimal. 63 vs. \(2 (17) = 34\).
Time = 0.27 (sec) , antiderivative size = 63, normalized size of antiderivative = 3.50 \[ \int \frac {e^{-4 x} \left (e^{4 e^4} (256-1024 x)+e^{4 e^4} (192-1024 x) \log (x)+e^{4 e^4} (48-384 x) \log ^2(x)+e^{4 e^4} (4-64 x) \log ^3(x)-4 e^{4 e^4} x \log ^4(x)\right )}{x} \, dx=\left (e^{4 e^{4}} \log {\left (x \right )}^{4} + 16 e^{4 e^{4}} \log {\left (x \right )}^{3} + 96 e^{4 e^{4}} \log {\left (x \right )}^{2} + 256 e^{4 e^{4}} \log {\left (x \right )} + 256 e^{4 e^{4}}\right ) e^{- 4 x} \]
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Leaf count of result is larger than twice the leaf count of optimal. 63 vs. \(2 (16) = 32\).
Time = 0.29 (sec) , antiderivative size = 63, normalized size of antiderivative = 3.50 \[ \int \frac {e^{-4 x} \left (e^{4 e^4} (256-1024 x)+e^{4 e^4} (192-1024 x) \log (x)+e^{4 e^4} (48-384 x) \log ^2(x)+e^{4 e^4} (4-64 x) \log ^3(x)-4 e^{4 e^4} x \log ^4(x)\right )}{x} \, dx={\left (e^{\left (4 \, e^{4}\right )} \log \left (x\right )^{4} + 16 \, e^{\left (4 \, e^{4}\right )} \log \left (x\right )^{3} + 96 \, e^{\left (4 \, e^{4}\right )} \log \left (x\right )^{2}\right )} e^{\left (-4 \, x\right )} + 256 \, e^{\left (-4 \, x + 4 \, e^{4}\right )} \log \left (x\right ) + 256 \, e^{\left (-4 \, x + 4 \, e^{4}\right )} \]
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Leaf count of result is larger than twice the leaf count of optimal. 69 vs. \(2 (16) = 32\).
Time = 0.26 (sec) , antiderivative size = 69, normalized size of antiderivative = 3.83 \[ \int \frac {e^{-4 x} \left (e^{4 e^4} (256-1024 x)+e^{4 e^4} (192-1024 x) \log (x)+e^{4 e^4} (48-384 x) \log ^2(x)+e^{4 e^4} (4-64 x) \log ^3(x)-4 e^{4 e^4} x \log ^4(x)\right )}{x} \, dx=e^{\left (-4 \, x + 4 \, e^{4}\right )} \log \left (x\right )^{4} + 16 \, e^{\left (-4 \, x + 4 \, e^{4}\right )} \log \left (x\right )^{3} + 96 \, e^{\left (-4 \, x + 4 \, e^{4}\right )} \log \left (x\right )^{2} + 256 \, e^{\left (-4 \, x + 4 \, e^{4}\right )} \log \left (x\right ) + 256 \, e^{\left (-4 \, x + 4 \, e^{4}\right )} \]
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Time = 12.52 (sec) , antiderivative size = 69, normalized size of antiderivative = 3.83 \[ \int \frac {e^{-4 x} \left (e^{4 e^4} (256-1024 x)+e^{4 e^4} (192-1024 x) \log (x)+e^{4 e^4} (48-384 x) \log ^2(x)+e^{4 e^4} (4-64 x) \log ^3(x)-4 e^{4 e^4} x \log ^4(x)\right )}{x} \, dx={\mathrm {e}}^{4\,{\mathrm {e}}^4-4\,x}\,{\ln \left (x\right )}^4+16\,{\mathrm {e}}^{4\,{\mathrm {e}}^4-4\,x}\,{\ln \left (x\right )}^3+96\,{\mathrm {e}}^{4\,{\mathrm {e}}^4-4\,x}\,{\ln \left (x\right )}^2+256\,{\mathrm {e}}^{4\,{\mathrm {e}}^4-4\,x}\,\ln \left (x\right )+256\,{\mathrm {e}}^{4\,{\mathrm {e}}^4-4\,x} \]
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