Optimal. Leaf size=33 \[ e^{\frac {1}{2} \left (\frac {6}{5-16 \left (\frac {2-x}{x}-x\right )^4}-x\right )} \]
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Rubi [F]
time = 180.00, 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*} \text {\$Aborted} \end {gather*}
Verification is not applicable to the result.
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Rubi steps
Aborted
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Mathematica [A]
time = 0.08, size = 55, normalized size = 1.67 \begin {gather*} e^{-\frac {x}{2}-\frac {3 x^4}{256-512 x-128 x^2+640 x^3+11 x^4-320 x^5-32 x^6+64 x^7+16 x^8}} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.29, size = 87, normalized size = 2.64
method | result | size |
gosper | \({\mathrm e}^{-\frac {x \left (16 x^{8}+64 x^{7}-32 x^{6}-320 x^{5}+11 x^{4}+646 x^{3}-128 x^{2}-512 x +256\right )}{2 \left (16 x^{8}+64 x^{7}-32 x^{6}-320 x^{5}+11 x^{4}+640 x^{3}-128 x^{2}-512 x +256\right )}}\) | \(87\) |
risch | \({\mathrm e}^{-\frac {x \left (16 x^{8}+64 x^{7}-32 x^{6}-320 x^{5}+11 x^{4}+646 x^{3}-128 x^{2}-512 x +256\right )}{2 \left (16 x^{8}+64 x^{7}-32 x^{6}-320 x^{5}+11 x^{4}+640 x^{3}-128 x^{2}-512 x +256\right )}}\) | \(87\) |
norman | \(\frac {-512 x \,{\mathrm e}^{\frac {-16 x^{9}-64 x^{8}+32 x^{7}+320 x^{6}-11 x^{5}-646 x^{4}+128 x^{3}+512 x^{2}-256 x}{32 x^{8}+128 x^{7}-64 x^{6}-640 x^{5}+22 x^{4}+1280 x^{3}-256 x^{2}-1024 x +512}}-128 x^{2} {\mathrm e}^{\frac {-16 x^{9}-64 x^{8}+32 x^{7}+320 x^{6}-11 x^{5}-646 x^{4}+128 x^{3}+512 x^{2}-256 x}{32 x^{8}+128 x^{7}-64 x^{6}-640 x^{5}+22 x^{4}+1280 x^{3}-256 x^{2}-1024 x +512}}+640 x^{3} {\mathrm e}^{\frac {-16 x^{9}-64 x^{8}+32 x^{7}+320 x^{6}-11 x^{5}-646 x^{4}+128 x^{3}+512 x^{2}-256 x}{32 x^{8}+128 x^{7}-64 x^{6}-640 x^{5}+22 x^{4}+1280 x^{3}-256 x^{2}-1024 x +512}}+11 x^{4} {\mathrm e}^{\frac {-16 x^{9}-64 x^{8}+32 x^{7}+320 x^{6}-11 x^{5}-646 x^{4}+128 x^{3}+512 x^{2}-256 x}{32 x^{8}+128 x^{7}-64 x^{6}-640 x^{5}+22 x^{4}+1280 x^{3}-256 x^{2}-1024 x +512}}-320 x^{5} {\mathrm e}^{\frac {-16 x^{9}-64 x^{8}+32 x^{7}+320 x^{6}-11 x^{5}-646 x^{4}+128 x^{3}+512 x^{2}-256 x}{32 x^{8}+128 x^{7}-64 x^{6}-640 x^{5}+22 x^{4}+1280 x^{3}-256 x^{2}-1024 x +512}}-32 x^{6} {\mathrm e}^{\frac {-16 x^{9}-64 x^{8}+32 x^{7}+320 x^{6}-11 x^{5}-646 x^{4}+128 x^{3}+512 x^{2}-256 x}{32 x^{8}+128 x^{7}-64 x^{6}-640 x^{5}+22 x^{4}+1280 x^{3}-256 x^{2}-1024 x +512}}+64 x^{7} {\mathrm e}^{\frac {-16 x^{9}-64 x^{8}+32 x^{7}+320 x^{6}-11 x^{5}-646 x^{4}+128 x^{3}+512 x^{2}-256 x}{32 x^{8}+128 x^{7}-64 x^{6}-640 x^{5}+22 x^{4}+1280 x^{3}-256 x^{2}-1024 x +512}}+16 x^{8} {\mathrm e}^{\frac {-16 x^{9}-64 x^{8}+32 x^{7}+320 x^{6}-11 x^{5}-646 x^{4}+128 x^{3}+512 x^{2}-256 x}{32 x^{8}+128 x^{7}-64 x^{6}-640 x^{5}+22 x^{4}+1280 x^{3}-256 x^{2}-1024 x +512}}+256 \,{\mathrm e}^{\frac {-16 x^{9}-64 x^{8}+32 x^{7}+320 x^{6}-11 x^{5}-646 x^{4}+128 x^{3}+512 x^{2}-256 x}{32 x^{8}+128 x^{7}-64 x^{6}-640 x^{5}+22 x^{4}+1280 x^{3}-256 x^{2}-1024 x +512}}}{16 x^{8}+64 x^{7}-32 x^{6}-320 x^{5}+11 x^{4}+640 x^{3}-128 x^{2}-512 x +256}\) | \(877\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 52 vs.
\(2 (24) = 48\).
time = 28.96, size = 52, normalized size = 1.58 \begin {gather*} e^{\left (-\frac {3 \, x^{4}}{16 \, x^{8} + 64 \, x^{7} - 32 \, x^{6} - 320 \, x^{5} + 11 \, x^{4} + 640 \, x^{3} - 128 \, x^{2} - 512 \, x + 256} - \frac {1}{2} \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 89 vs.
\(2 (24) = 48\).
time = 0.34, size = 89, normalized size = 2.70 \begin {gather*} e^{\left (-\frac {16 \, x^{9} + 64 \, x^{8} - 32 \, x^{7} - 320 \, x^{6} + 11 \, x^{5} + 646 \, x^{4} - 128 \, x^{3} - 512 \, x^{2} + 256 \, x}{2 \, {\left (16 \, x^{8} + 64 \, x^{7} - 32 \, x^{6} - 320 \, x^{5} + 11 \, x^{4} + 640 \, x^{3} - 128 \, x^{2} - 512 \, x + 256\right )}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 85 vs.
\(2 (29) = 58\).
time = 0.76, size = 85, normalized size = 2.58 \begin {gather*} e^{\frac {- 16 x^{9} - 64 x^{8} + 32 x^{7} + 320 x^{6} - 11 x^{5} - 646 x^{4} + 128 x^{3} + 512 x^{2} - 256 x}{32 x^{8} + 128 x^{7} - 64 x^{6} - 640 x^{5} + 22 x^{4} + 1280 x^{3} - 256 x^{2} - 1024 x + 512}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 423 vs.
\(2 (24) = 48\).
time = 0.47, size = 423, normalized size = 12.82 \begin {gather*} e^{\left (-\frac {8 \, x^{9}}{16 \, x^{8} + 64 \, x^{7} - 32 \, x^{6} - 320 \, x^{5} + 11 \, x^{4} + 640 \, x^{3} - 128 \, x^{2} - 512 \, x + 256} - \frac {32 \, x^{8}}{16 \, x^{8} + 64 \, x^{7} - 32 \, x^{6} - 320 \, x^{5} + 11 \, x^{4} + 640 \, x^{3} - 128 \, x^{2} - 512 \, x + 256} + \frac {16 \, x^{7}}{16 \, x^{8} + 64 \, x^{7} - 32 \, x^{6} - 320 \, x^{5} + 11 \, x^{4} + 640 \, x^{3} - 128 \, x^{2} - 512 \, x + 256} + \frac {160 \, x^{6}}{16 \, x^{8} + 64 \, x^{7} - 32 \, x^{6} - 320 \, x^{5} + 11 \, x^{4} + 640 \, x^{3} - 128 \, x^{2} - 512 \, x + 256} - \frac {11 \, x^{5}}{2 \, {\left (16 \, x^{8} + 64 \, x^{7} - 32 \, x^{6} - 320 \, x^{5} + 11 \, x^{4} + 640 \, x^{3} - 128 \, x^{2} - 512 \, x + 256\right )}} - \frac {323 \, x^{4}}{16 \, x^{8} + 64 \, x^{7} - 32 \, x^{6} - 320 \, x^{5} + 11 \, x^{4} + 640 \, x^{3} - 128 \, x^{2} - 512 \, x + 256} + \frac {64 \, x^{3}}{16 \, x^{8} + 64 \, x^{7} - 32 \, x^{6} - 320 \, x^{5} + 11 \, x^{4} + 640 \, x^{3} - 128 \, x^{2} - 512 \, x + 256} + \frac {256 \, x^{2}}{16 \, x^{8} + 64 \, x^{7} - 32 \, x^{6} - 320 \, x^{5} + 11 \, x^{4} + 640 \, x^{3} - 128 \, x^{2} - 512 \, x + 256} - \frac {128 \, x}{16 \, x^{8} + 64 \, x^{7} - 32 \, x^{6} - 320 \, x^{5} + 11 \, x^{4} + 640 \, x^{3} - 128 \, x^{2} - 512 \, x + 256}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.51, size = 431, normalized size = 13.06 \begin {gather*} {\mathrm {e}}^{-\frac {128\,x}{16\,x^8+64\,x^7-32\,x^6-320\,x^5+11\,x^4+640\,x^3-128\,x^2-512\,x+256}}\,{\mathrm {e}}^{-\frac {8\,x^9}{16\,x^8+64\,x^7-32\,x^6-320\,x^5+11\,x^4+640\,x^3-128\,x^2-512\,x+256}}\,{\mathrm {e}}^{\frac {16\,x^7}{16\,x^8+64\,x^7-32\,x^6-320\,x^5+11\,x^4+640\,x^3-128\,x^2-512\,x+256}}\,{\mathrm {e}}^{-\frac {32\,x^8}{16\,x^8+64\,x^7-32\,x^6-320\,x^5+11\,x^4+640\,x^3-128\,x^2-512\,x+256}}\,{\mathrm {e}}^{\frac {64\,x^3}{16\,x^8+64\,x^7-32\,x^6-320\,x^5+11\,x^4+640\,x^3-128\,x^2-512\,x+256}}\,{\mathrm {e}}^{\frac {160\,x^6}{16\,x^8+64\,x^7-32\,x^6-320\,x^5+11\,x^4+640\,x^3-128\,x^2-512\,x+256}}\,{\mathrm {e}}^{\frac {256\,x^2}{16\,x^8+64\,x^7-32\,x^6-320\,x^5+11\,x^4+640\,x^3-128\,x^2-512\,x+256}}\,{\mathrm {e}}^{-\frac {323\,x^4}{16\,x^8+64\,x^7-32\,x^6-320\,x^5+11\,x^4+640\,x^3-128\,x^2-512\,x+256}}\,{\mathrm {e}}^{-\frac {11\,x^5}{32\,x^8+128\,x^7-64\,x^6-640\,x^5+22\,x^4+1280\,x^3-256\,x^2-1024\,x+512}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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