Optimal. Leaf size=27 \[ \frac {1}{5} e^{\left (-1+(5-x)^2 \left (\frac {e^x}{x}+x\right )\right )^2} \]
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Rubi [F] time = 22.19, 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 (\frac {x^2-50 x^3+645 x^4-502 x^5+150 x^6-20 x^7+x^8+e^{2 x} \left (625-500 x+150 x^2-20 x^3+x^4\right )+e^x \left (-50 x+1270 x^2-1002 x^3+300 x^4-40 x^5+2 x^6\right )}{x^2}\right ) \left (-50 x^3+1290 x^4-1506 x^5+600 x^6-100 x^7+6 x^8+e^{2 x} \left (-1250+1750 x-1000 x^2+280 x^3-38 x^4+2 x^5\right )+e^x \left (50 x-50 x^2+268 x^3-402 x^4+180 x^5-32 x^6+2 x^7\right )\right )}{5 x^3} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{5} \int \frac {\exp \left (\frac {x^2-50 x^3+645 x^4-502 x^5+150 x^6-20 x^7+x^8+e^{2 x} \left (625-500 x+150 x^2-20 x^3+x^4\right )+e^x \left (-50 x+1270 x^2-1002 x^3+300 x^4-40 x^5+2 x^6\right )}{x^2}\right ) \left (-50 x^3+1290 x^4-1506 x^5+600 x^6-100 x^7+6 x^8+e^{2 x} \left (-1250+1750 x-1000 x^2+280 x^3-38 x^4+2 x^5\right )+e^x \left (50 x-50 x^2+268 x^3-402 x^4+180 x^5-32 x^6+2 x^7\right )\right )}{x^3} \, dx\\ &=\frac {1}{5} \int \frac {2 \exp \left (\frac {\left (e^x (-5+x)^2+x \left (-1+25 x-10 x^2+x^3\right )\right )^2}{x^2}\right ) (5-x) \left (-e^{2 x} (-5+x)^2 \left (5-4 x+x^2\right )-x^3 \left (5-128 x+125 x^2-35 x^3+3 x^4\right )-e^x x \left (-5+4 x-26 x^2+35 x^3-11 x^4+x^5\right )\right )}{x^3} \, dx\\ &=\frac {2}{5} \int \frac {\exp \left (\frac {\left (e^x (-5+x)^2+x \left (-1+25 x-10 x^2+x^3\right )\right )^2}{x^2}\right ) (5-x) \left (-e^{2 x} (-5+x)^2 \left (5-4 x+x^2\right )-x^3 \left (5-128 x+125 x^2-35 x^3+3 x^4\right )-e^x x \left (-5+4 x-26 x^2+35 x^3-11 x^4+x^5\right )\right )}{x^3} \, dx\\ &=\frac {2}{5} \int \left (\frac {\exp \left (2 x+\frac {\left (e^x (-5+x)^2+x \left (-1+25 x-10 x^2+x^3\right )\right )^2}{x^2}\right ) (-5+x)^3 \left (5-4 x+x^2\right )}{x^3}+\exp \left (\frac {\left (e^x (-5+x)^2+x \left (-1+25 x-10 x^2+x^3\right )\right )^2}{x^2}\right ) (-5+x) (-5+3 x) \left (-1+25 x-10 x^2+x^3\right )+\frac {\exp \left (x+\frac {\left (e^x (-5+x)^2+x \left (-1+25 x-10 x^2+x^3\right )\right )^2}{x^2}\right ) (-5+x) \left (-5+4 x-26 x^2+35 x^3-11 x^4+x^5\right )}{x^2}\right ) \, dx\\ &=\frac {2}{5} \int \frac {\exp \left (2 x+\frac {\left (e^x (-5+x)^2+x \left (-1+25 x-10 x^2+x^3\right )\right )^2}{x^2}\right ) (-5+x)^3 \left (5-4 x+x^2\right )}{x^3} \, dx+\frac {2}{5} \int \exp \left (\frac {\left (e^x (-5+x)^2+x \left (-1+25 x-10 x^2+x^3\right )\right )^2}{x^2}\right ) (-5+x) (-5+3 x) \left (-1+25 x-10 x^2+x^3\right ) \, dx+\frac {2}{5} \int \frac {\exp \left (x+\frac {\left (e^x (-5+x)^2+x \left (-1+25 x-10 x^2+x^3\right )\right )^2}{x^2}\right ) (-5+x) \left (-5+4 x-26 x^2+35 x^3-11 x^4+x^5\right )}{x^2} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}
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Mathematica [A] time = 0.19, size = 37, normalized size = 1.37 \begin {gather*} \frac {1}{5} e^{\frac {\left (e^x (-5+x)^2+x \left (-1+25 x-10 x^2+x^3\right )\right )^2}{x^2}} \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.59, size = 93, normalized size = 3.44 \begin {gather*} \frac {1}{5} \, e^{\left (\frac {x^{8} - 20 \, x^{7} + 150 \, x^{6} - 502 \, x^{5} + 645 \, x^{4} - 50 \, x^{3} + x^{2} + {\left (x^{4} - 20 \, x^{3} + 150 \, x^{2} - 500 \, x + 625\right )} e^{\left (2 \, x\right )} + 2 \, {\left (x^{6} - 20 \, x^{5} + 150 \, x^{4} - 501 \, x^{3} + 635 \, x^{2} - 25 \, x\right )} e^{x}}{x^{2}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 1.14, size = 107, normalized size = 3.96 \begin {gather*} \frac {1}{5} \, e^{\left (x^{6} - 20 \, x^{5} + 2 \, x^{4} e^{x} + 150 \, x^{4} - 40 \, x^{3} e^{x} - 502 \, x^{3} + x^{2} e^{\left (2 \, x\right )} + 300 \, x^{2} e^{x} + 645 \, x^{2} - 20 \, x e^{\left (2 \, x\right )} - 1002 \, x e^{x} - 50 \, x - \frac {500 \, e^{\left (2 \, x\right )}}{x} - \frac {50 \, e^{x}}{x} + \frac {625 \, e^{\left (2 \, x\right )}}{x^{2}} + 150 \, e^{\left (2 \, x\right )} + 1270 \, e^{x} + 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.19, size = 119, normalized size = 4.41
method | result | size |
risch | \(\frac {{\mathrm e}^{\frac {x^{8}+2 x^{6} {\mathrm e}^{x}-20 x^{7}-40 x^{5} {\mathrm e}^{x}+150 x^{6}+{\mathrm e}^{2 x} x^{4}+300 \,{\mathrm e}^{x} x^{4}-502 x^{5}-20 \,{\mathrm e}^{2 x} x^{3}-1002 \,{\mathrm e}^{x} x^{3}+645 x^{4}+150 \,{\mathrm e}^{2 x} x^{2}+1270 \,{\mathrm e}^{x} x^{2}-50 x^{3}-500 x \,{\mathrm e}^{2 x}-50 \,{\mathrm e}^{x} x +x^{2}+625 \,{\mathrm e}^{2 x}}{x^{2}}}}{5}\) | \(119\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 1.19, size = 107, normalized size = 3.96 \begin {gather*} \frac {1}{5} \, e^{\left (x^{6} - 20 \, x^{5} + 2 \, x^{4} e^{x} + 150 \, x^{4} - 40 \, x^{3} e^{x} - 502 \, x^{3} + x^{2} e^{\left (2 \, x\right )} + 300 \, x^{2} e^{x} + 645 \, x^{2} - 20 \, x e^{\left (2 \, x\right )} - 1002 \, x e^{x} - 50 \, x - \frac {500 \, e^{\left (2 \, x\right )}}{x} - \frac {50 \, e^{x}}{x} + \frac {625 \, e^{\left (2 \, x\right )}}{x^{2}} + 150 \, e^{\left (2 \, x\right )} + 1270 \, e^{x} + 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 9.17, size = 123, normalized size = 4.56 \begin {gather*} \frac {{\mathrm {e}}^{150\,{\mathrm {e}}^{2\,x}}\,{\mathrm {e}}^{-1002\,x\,{\mathrm {e}}^x}\,{\mathrm {e}}^{-50\,x}\,{\mathrm {e}}^{x^6}\,\mathrm {e}\,{\mathrm {e}}^{-20\,x\,{\mathrm {e}}^{2\,x}}\,{\mathrm {e}}^{2\,x^4\,{\mathrm {e}}^x}\,{\mathrm {e}}^{-40\,x^3\,{\mathrm {e}}^x}\,{\mathrm {e}}^{-\frac {50\,{\mathrm {e}}^x}{x}}\,{\mathrm {e}}^{300\,x^2\,{\mathrm {e}}^x}\,{\mathrm {e}}^{-20\,x^5}\,{\mathrm {e}}^{150\,x^4}\,{\mathrm {e}}^{-502\,x^3}\,{\mathrm {e}}^{645\,x^2}\,{\mathrm {e}}^{1270\,{\mathrm {e}}^x}\,{\mathrm {e}}^{x^2\,{\mathrm {e}}^{2\,x}}\,{\mathrm {e}}^{-\frac {500\,{\mathrm {e}}^{2\,x}}{x}}\,{\mathrm {e}}^{\frac {625\,{\mathrm {e}}^{2\,x}}{x^2}}}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.76, size = 94, normalized size = 3.48 \begin {gather*} \frac {e^{\frac {x^{8} - 20 x^{7} + 150 x^{6} - 502 x^{5} + 645 x^{4} - 50 x^{3} + x^{2} + \left (x^{4} - 20 x^{3} + 150 x^{2} - 500 x + 625\right ) e^{2 x} + \left (2 x^{6} - 40 x^{5} + 300 x^{4} - 1002 x^{3} + 1270 x^{2} - 50 x\right ) e^{x}}{x^{2}}}}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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