Optimal. Leaf size=28 \[ e^{e^{-\frac {5}{x}+x+x^2} x \left (4-x+8 x^2 \log (x)\right )} \]
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Rubi [F]
time = 17.27, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps
used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {}
\begin {gather*} \int \frac {\exp \left (e^{\frac {-5+x^2+x^3}{x}} \left (4 x-x^2\right )+8 e^{\frac {-5+x^2+x^3}{x}} x^3 \log (x)\right ) \left (e^{\frac {-5+x^2+x^3}{x}} \left (20-x+2 x^2+15 x^3-2 x^4\right )+e^{\frac {-5+x^2+x^3}{x}} \left (40 x^2+24 x^3+8 x^4+16 x^5\right ) \log (x)\right )}{x} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{-1+8 e^{-\frac {5}{x}+x+x^2} x^3} \left (20-x+2 x^2+15 x^3-2 x^4+8 x^2 \left (5+3 x+x^2+2 x^3\right ) \log (x)\right ) \, dx\\ &=\int \left (-e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{8 e^{-\frac {5}{x}+x+x^2} x^3}+20 e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{-1+8 e^{-\frac {5}{x}+x+x^2} x^3}+2 e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{1+8 e^{-\frac {5}{x}+x+x^2} x^3}+15 e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{2+8 e^{-\frac {5}{x}+x+x^2} x^3}-2 e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{3+8 e^{-\frac {5}{x}+x+x^2} x^3}+8 e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{1+8 e^{-\frac {5}{x}+x+x^2} x^3} \left (5+3 x+x^2+2 x^3\right ) \log (x)\right ) \, dx\\ &=2 \int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{1+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx-2 \int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{3+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx+8 \int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{1+8 e^{-\frac {5}{x}+x+x^2} x^3} \left (5+3 x+x^2+2 x^3\right ) \log (x) \, dx+15 \int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{2+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx+20 \int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{-1+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx-\int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx\\ &=2 \int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{1+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx-2 \int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{3+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx-8 \int \frac {5 \int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{1+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx+3 \int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{2+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx+\int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{3+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx+2 \int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{4+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx}{x} \, dx+15 \int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{2+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx+20 \int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{-1+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx+(8 \log (x)) \int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{3+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx+(16 \log (x)) \int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{4+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx+(24 \log (x)) \int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{2+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx+(40 \log (x)) \int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{1+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx-\int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx\\ &=2 \int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{1+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx-2 \int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{3+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx-8 \int \left (\frac {5 \int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{1+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx+3 \int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{2+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx+\int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{3+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx}{x}+\frac {2 \int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{4+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx}{x}\right ) \, dx+15 \int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{2+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx+20 \int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{-1+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx+(8 \log (x)) \int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{3+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx+(16 \log (x)) \int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{4+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx+(24 \log (x)) \int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{2+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx+(40 \log (x)) \int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{1+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx-\int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx\\ &=2 \int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{1+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx-2 \int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{3+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx-8 \int \frac {5 \int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{1+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx+3 \int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{2+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx+\int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{3+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx}{x} \, dx+15 \int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{2+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx-16 \int \frac {\int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{4+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx}{x} \, dx+20 \int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{-1+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx+(8 \log (x)) \int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{3+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx+(16 \log (x)) \int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{4+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx+(24 \log (x)) \int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{2+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx+(40 \log (x)) \int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{1+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx-\int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx\\ &=2 \int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{1+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx-2 \int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{3+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx-8 \int \left (\frac {5 \int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{1+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx+3 \int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{2+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx}{x}+\frac {\int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{3+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx}{x}\right ) \, dx+15 \int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{2+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx-16 \int \frac {\int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{4+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx}{x} \, dx+20 \int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{-1+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx+(8 \log (x)) \int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{3+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx+(16 \log (x)) \int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{4+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx+(24 \log (x)) \int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{2+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx+(40 \log (x)) \int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{1+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx-\int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx\\ &=2 \int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{1+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx-2 \int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{3+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx-8 \int \frac {5 \int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{1+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx+3 \int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{2+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx}{x} \, dx-8 \int \frac {\int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{3+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx}{x} \, dx+15 \int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{2+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx-16 \int \frac {\int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{4+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx}{x} \, dx+20 \int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{-1+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx+(8 \log (x)) \int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{3+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx+(16 \log (x)) \int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{4+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx+(24 \log (x)) \int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{2+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx+(40 \log (x)) \int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{1+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx-\int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx\\ &=2 \int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{1+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx-2 \int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{3+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx-8 \int \left (\frac {5 \int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{1+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx}{x}+\frac {3 \int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{2+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx}{x}\right ) \, dx-8 \int \frac {\int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{3+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx}{x} \, dx+15 \int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{2+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx-16 \int \frac {\int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{4+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx}{x} \, dx+20 \int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{-1+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx+(8 \log (x)) \int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{3+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx+(16 \log (x)) \int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{4+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx+(24 \log (x)) \int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{2+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx+(40 \log (x)) \int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{1+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx-\int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx\\ &=2 \int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{1+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx-2 \int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{3+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx-8 \int \frac {\int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{3+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx}{x} \, dx+15 \int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{2+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx-16 \int \frac {\int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{4+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx}{x} \, dx+20 \int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{-1+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx-24 \int \frac {\int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{2+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx}{x} \, dx-40 \int \frac {\int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{1+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx}{x} \, dx+(8 \log (x)) \int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{3+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx+(16 \log (x)) \int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{4+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx+(24 \log (x)) \int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{2+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx+(40 \log (x)) \int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{1+8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx-\int e^{-\frac {5}{x}+x-e^{-\frac {5}{x}+x+x^2} (-4+x) x+x^2} x^{8 e^{-\frac {5}{x}+x+x^2} x^3} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.11, size = 40, normalized size = 1.43 \begin {gather*} e^{-e^{-\frac {5}{x}+x+x^2} (-4+x) x} x^{8 e^{-\frac {5}{x}+x+x^2} x^3} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.12, size = 42, normalized size = 1.50
method | result | size |
risch | \(x^{8 \,{\mathrm e}^{\frac {x^{3}+x^{2}-5}{x}} x^{3}} {\mathrm e}^{-\left (x -4\right ) x \,{\mathrm e}^{\frac {x^{3}+x^{2}-5}{x}}}\) | \(42\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.60, size = 50, normalized size = 1.79 \begin {gather*} e^{\left (8 \, x^{3} e^{\left (x^{2} + x - \frac {5}{x}\right )} \log \left (x\right ) - x^{2} e^{\left (x^{2} + x - \frac {5}{x}\right )} + 4 \, x e^{\left (x^{2} + x - \frac {5}{x}\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.44, size = 44, normalized size = 1.57 \begin {gather*} e^{\left (8 \, x^{3} e^{\left (\frac {x^{3} + x^{2} - 5}{x}\right )} \log \left (x\right ) - {\left (x^{2} - 4 \, x\right )} e^{\left (\frac {x^{3} + x^{2} - 5}{x}\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.59, size = 39, normalized size = 1.39 \begin {gather*} e^{8 x^{3} e^{\frac {x^{3} + x^{2} - 5}{x}} \log {\left (x \right )} + \left (- x^{2} + 4 x\right ) e^{\frac {x^{3} + x^{2} - 5}{x}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.45, size = 50, normalized size = 1.79 \begin {gather*} e^{\left (8 \, x^{3} e^{\left (x^{2} + x - \frac {5}{x}\right )} \log \left (x\right ) - x^{2} e^{\left (x^{2} + x - \frac {5}{x}\right )} + 4 \, x e^{\left (x^{2} + x - \frac {5}{x}\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.85, size = 54, normalized size = 1.93 \begin {gather*} x^{8\,x^3\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^{-\frac {5}{x}}\,{\mathrm {e}}^x}\,{\mathrm {e}}^{-x^2\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^{-\frac {5}{x}}\,{\mathrm {e}}^x}\,{\mathrm {e}}^{4\,x\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^{-\frac {5}{x}}\,{\mathrm {e}}^x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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