Optimal. Leaf size=30 \[ e^{16 e^{-5/x} x^3 \left (-e^x+2 x+(9+x)^2\right )^2} \]
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Rubi [F] time = 29.59, 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 \exp \left (-\frac {5}{x}+e^{-5/x} \left (104976 x^3+16 e^{2 x} x^3+51840 x^4+8992 x^5+640 x^6+16 x^7+e^x \left (-2592 x^3-640 x^4-32 x^5\right )\right )\right ) \left (524880 x+574128 x^2+252320 x^3+48160 x^4+3920 x^5+112 x^6+e^{2 x} \left (80 x+48 x^2+32 x^3\right )+e^x \left (-12960 x-10976 x^2-5312 x^3-800 x^4-32 x^5\right )\right ) \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (524880 \exp \left (-\frac {5}{x}+e^{-5/x} \left (104976 x^3+16 e^{2 x} x^3+51840 x^4+8992 x^5+640 x^6+16 x^7+e^x \left (-2592 x^3-640 x^4-32 x^5\right )\right )\right ) x+574128 \exp \left (-\frac {5}{x}+e^{-5/x} \left (104976 x^3+16 e^{2 x} x^3+51840 x^4+8992 x^5+640 x^6+16 x^7+e^x \left (-2592 x^3-640 x^4-32 x^5\right )\right )\right ) x^2+252320 \exp \left (-\frac {5}{x}+e^{-5/x} \left (104976 x^3+16 e^{2 x} x^3+51840 x^4+8992 x^5+640 x^6+16 x^7+e^x \left (-2592 x^3-640 x^4-32 x^5\right )\right )\right ) x^3+48160 \exp \left (-\frac {5}{x}+e^{-5/x} \left (104976 x^3+16 e^{2 x} x^3+51840 x^4+8992 x^5+640 x^6+16 x^7+e^x \left (-2592 x^3-640 x^4-32 x^5\right )\right )\right ) x^4+3920 \exp \left (-\frac {5}{x}+e^{-5/x} \left (104976 x^3+16 e^{2 x} x^3+51840 x^4+8992 x^5+640 x^6+16 x^7+e^x \left (-2592 x^3-640 x^4-32 x^5\right )\right )\right ) x^5+112 \exp \left (-\frac {5}{x}+e^{-5/x} \left (104976 x^3+16 e^{2 x} x^3+51840 x^4+8992 x^5+640 x^6+16 x^7+e^x \left (-2592 x^3-640 x^4-32 x^5\right )\right )\right ) x^6+16 \exp \left (-\frac {5}{x}+2 x+e^{-5/x} \left (104976 x^3+16 e^{2 x} x^3+51840 x^4+8992 x^5+640 x^6+16 x^7+e^x \left (-2592 x^3-640 x^4-32 x^5\right )\right )\right ) x \left (5+3 x+2 x^2\right )-32 \exp \left (-\frac {5}{x}+x+e^{-5/x} \left (104976 x^3+16 e^{2 x} x^3+51840 x^4+8992 x^5+640 x^6+16 x^7+e^x \left (-2592 x^3-640 x^4-32 x^5\right )\right )\right ) x \left (405+343 x+166 x^2+25 x^3+x^4\right )\right ) \, dx\\ &=16 \int \exp \left (-\frac {5}{x}+2 x+e^{-5/x} \left (104976 x^3+16 e^{2 x} x^3+51840 x^4+8992 x^5+640 x^6+16 x^7+e^x \left (-2592 x^3-640 x^4-32 x^5\right )\right )\right ) x \left (5+3 x+2 x^2\right ) \, dx-32 \int \exp \left (-\frac {5}{x}+x+e^{-5/x} \left (104976 x^3+16 e^{2 x} x^3+51840 x^4+8992 x^5+640 x^6+16 x^7+e^x \left (-2592 x^3-640 x^4-32 x^5\right )\right )\right ) x \left (405+343 x+166 x^2+25 x^3+x^4\right ) \, dx+112 \int \exp \left (-\frac {5}{x}+e^{-5/x} \left (104976 x^3+16 e^{2 x} x^3+51840 x^4+8992 x^5+640 x^6+16 x^7+e^x \left (-2592 x^3-640 x^4-32 x^5\right )\right )\right ) x^6 \, dx+3920 \int \exp \left (-\frac {5}{x}+e^{-5/x} \left (104976 x^3+16 e^{2 x} x^3+51840 x^4+8992 x^5+640 x^6+16 x^7+e^x \left (-2592 x^3-640 x^4-32 x^5\right )\right )\right ) x^5 \, dx+48160 \int \exp \left (-\frac {5}{x}+e^{-5/x} \left (104976 x^3+16 e^{2 x} x^3+51840 x^4+8992 x^5+640 x^6+16 x^7+e^x \left (-2592 x^3-640 x^4-32 x^5\right )\right )\right ) x^4 \, dx+252320 \int \exp \left (-\frac {5}{x}+e^{-5/x} \left (104976 x^3+16 e^{2 x} x^3+51840 x^4+8992 x^5+640 x^6+16 x^7+e^x \left (-2592 x^3-640 x^4-32 x^5\right )\right )\right ) x^3 \, dx+524880 \int \exp \left (-\frac {5}{x}+e^{-5/x} \left (104976 x^3+16 e^{2 x} x^3+51840 x^4+8992 x^5+640 x^6+16 x^7+e^x \left (-2592 x^3-640 x^4-32 x^5\right )\right )\right ) x \, dx+574128 \int \exp \left (-\frac {5}{x}+e^{-5/x} \left (104976 x^3+16 e^{2 x} x^3+51840 x^4+8992 x^5+640 x^6+16 x^7+e^x \left (-2592 x^3-640 x^4-32 x^5\right )\right )\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 = 0.21, size = 29, normalized size = 0.97 \begin {gather*} e^{16 e^{-5/x} x^3 \left (81-e^x+20 x+x^2\right )^2} \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.73, size = 84, normalized size = 2.80 \begin {gather*} e^{\left (\frac {16 \, x^{4} e^{\left (2 \, x - \frac {5}{x}\right )} - 32 \, {\left (x^{6} + 20 \, x^{5} + 81 \, x^{4}\right )} e^{\left (x - \frac {5}{x}\right )} + 16 \, {\left (x^{8} + 40 \, x^{7} + 562 \, x^{6} + 3240 \, x^{5} + 6561 \, x^{4}\right )} e^{\left (-\frac {5}{x}\right )} - 5}{x} + \frac {5}{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 1.89, size = 234, normalized size = 7.80 \begin {gather*} e^{\left (\frac {{\left (16 \, x^{8} e^{\left (\frac {2 \, {\left (x^{2} - 5\right )}}{x}\right )} + 640 \, x^{7} e^{\left (\frac {2 \, {\left (x^{2} - 5\right )}}{x}\right )} - 32 \, x^{6} e^{\left (\frac {2 \, x^{2} - 5}{x} + \frac {x^{2} - 5}{x}\right )} + 8992 \, x^{6} e^{\left (\frac {2 \, {\left (x^{2} - 5\right )}}{x}\right )} - 640 \, x^{5} e^{\left (\frac {2 \, x^{2} - 5}{x} + \frac {x^{2} - 5}{x}\right )} + 51840 \, x^{5} e^{\left (\frac {2 \, {\left (x^{2} - 5\right )}}{x}\right )} + 16 \, x^{4} e^{\left (\frac {2 \, {\left (2 \, x^{2} - 5\right )}}{x}\right )} - 2592 \, x^{4} e^{\left (\frac {2 \, x^{2} - 5}{x} + \frac {x^{2} - 5}{x}\right )} + 104976 \, x^{4} e^{\left (\frac {2 \, {\left (x^{2} - 5\right )}}{x}\right )} - 5 \, e^{\left (\frac {2 \, x^{2} - 5}{x}\right )}\right )} e^{\left (-\frac {2 \, x^{2} - 5}{x}\right )}}{x} + \frac {2 \, x^{2} - 5}{x} - \frac {2 \, {\left (x^{2} - 5\right )}}{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 238.70, size = 55, normalized size = 1.83
method | result | size |
risch | \({\mathrm e}^{-16 x^{3} \left (-x^{4}+2 \,{\mathrm e}^{x} x^{2}-40 x^{3}+40 \,{\mathrm e}^{x} x -562 x^{2}+162 \,{\mathrm e}^{x}-{\mathrm e}^{2 x}-3240 x -6561\right ) {\mathrm e}^{-\frac {5}{x}}}\) | \(55\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 9.77, size = 111, normalized size = 3.70 \begin {gather*} e^{\left (16 \, x^{7} e^{\left (-\frac {5}{x}\right )} + 640 \, x^{6} e^{\left (-\frac {5}{x}\right )} - 32 \, x^{5} e^{\left (x - \frac {5}{x}\right )} + 8992 \, x^{5} e^{\left (-\frac {5}{x}\right )} - 640 \, x^{4} e^{\left (x - \frac {5}{x}\right )} + 51840 \, x^{4} e^{\left (-\frac {5}{x}\right )} + 16 \, x^{3} e^{\left (2 \, x - \frac {5}{x}\right )} - 2592 \, x^{3} e^{\left (x - \frac {5}{x}\right )} + 104976 \, x^{3} e^{\left (-\frac {5}{x}\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.45, size = 119, normalized size = 3.97 \begin {gather*} {\mathrm {e}}^{-32\,x^5\,{\mathrm {e}}^{-\frac {5}{x}}\,{\mathrm {e}}^x}\,{\mathrm {e}}^{-640\,x^4\,{\mathrm {e}}^{-\frac {5}{x}}\,{\mathrm {e}}^x}\,{\mathrm {e}}^{-2592\,x^3\,{\mathrm {e}}^{-\frac {5}{x}}\,{\mathrm {e}}^x}\,{\mathrm {e}}^{16\,x^7\,{\mathrm {e}}^{-\frac {5}{x}}}\,{\mathrm {e}}^{640\,x^6\,{\mathrm {e}}^{-\frac {5}{x}}}\,{\mathrm {e}}^{8992\,x^5\,{\mathrm {e}}^{-\frac {5}{x}}}\,{\mathrm {e}}^{51840\,x^4\,{\mathrm {e}}^{-\frac {5}{x}}}\,{\mathrm {e}}^{104976\,x^3\,{\mathrm {e}}^{-\frac {5}{x}}}\,{\mathrm {e}}^{16\,x^3\,{\mathrm {e}}^{2\,x}\,{\mathrm {e}}^{-\frac {5}{x}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 11.10, size = 61, normalized size = 2.03 \begin {gather*} e^{\left (16 x^{7} + 640 x^{6} + 8992 x^{5} + 51840 x^{4} + 16 x^{3} e^{2 x} + 104976 x^{3} + \left (- 32 x^{5} - 640 x^{4} - 2592 x^{3}\right ) e^{x}\right ) e^{- \frac {5}{x}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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