Optimal. Leaf size=30 \[ \frac {e^{-\frac {3 \left (\frac {24}{4-\frac {2}{x}}+(1+x)^2\right )^2}{e^4}}}{x} \]
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Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(204\) vs. \(2(30)=60\).
time = 1.43, antiderivative size = 204, normalized size of antiderivative = 6.80, number of steps
used = 1, number of rules used = 1, integrand size = 128, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.008, Rules used = {2326}
\begin {gather*} \frac {\left (8 x^7+12 x^6+42 x^5-23 x^4-51 x^3-57 x^2+5 x\right ) \exp \left (-\frac {3 \left (4 x^6+12 x^5+57 x^4+68 x^3+138 x^2-24 x+1\right )}{e^4 \left (4 x^2-4 x+1\right )}-4\right )}{\left (-8 x^5+12 x^4-6 x^3+x^2\right ) \left (\frac {3 \left (-2 x^5-5 x^4-19 x^3-17 x^2-23 x+2\right )}{e^4 \left (4 x^2-4 x+1\right )}-\frac {(1-2 x) \left (4 x^6+12 x^5+57 x^4+68 x^3+138 x^2-24 x+1\right )}{e^4 \left (4 x^2-4 x+1\right )^2}\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 2326
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\exp \left (-4-\frac {3 \left (1-24 x+138 x^2+68 x^3+57 x^4+12 x^5+4 x^6\right )}{e^4 \left (1-4 x+4 x^2\right )}\right ) \left (5 x-57 x^2-51 x^3-23 x^4+42 x^5+12 x^6+8 x^7\right )}{\left (x^2-6 x^3+12 x^4-8 x^5\right ) \left (\frac {3 \left (2-23 x-17 x^2-19 x^3-5 x^4-2 x^5\right )}{e^4 \left (1-4 x+4 x^2\right )}-\frac {(1-2 x) \left (1-24 x+138 x^2+68 x^3+57 x^4+12 x^5+4 x^6\right )}{e^4 \left (1-4 x+4 x^2\right )^2}\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.07, size = 35, normalized size = 1.17 \begin {gather*} \frac {e^{-\frac {3 \left (-1+12 x+3 x^2+2 x^3\right )^2}{e^4 (1-2 x)^2}}}{x} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.45, size = 34, normalized size = 1.13
method | result | size |
risch | \(\frac {{\mathrm e}^{-\frac {3 \left (2 x^{3}+3 x^{2}+12 x -1\right )^{2} {\mathrm e}^{-4}}{\left (2 x -1\right )^{2}}}}{x}\) | \(34\) |
gosper | \(\frac {{\mathrm e}^{-\frac {3 \left (4 x^{6}+12 x^{5}+57 x^{4}+68 x^{3}+138 x^{2}-24 x +1\right ) {\mathrm e}^{-4}}{4 x^{2}-4 x +1}}}{x}\) | \(56\) |
norman | \(\frac {\left (4 x^{2}-4 x +1\right ) {\mathrm e}^{-\frac {\left (12 x^{6}+36 x^{5}+171 x^{4}+204 x^{3}+414 x^{2}-72 x +3\right ) {\mathrm e}^{-4}}{4 x^{2}-4 x +1}}}{x \left (2 x -1\right )^{2}}\) | \(72\) |
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. 69 vs.
\(2 (26) = 52\).
time = 0.86, size = 69, normalized size = 2.30 \begin {gather*} \frac {e^{\left (-3 \, x^{4} e^{\left (-4\right )} - 12 \, x^{3} e^{\left (-4\right )} - 54 \, x^{2} e^{\left (-4\right )} - 102 \, x e^{\left (-4\right )} - \frac {108}{4 \, x^{2} e^{4} - 4 \, x e^{4} + e^{4}} - \frac {297}{2 \, x e^{4} - e^{4}} - 192 \, e^{\left (-4\right )}\right )}}{x} \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. 67 vs.
\(2 (26) = 52\).
time = 0.36, size = 67, normalized size = 2.23 \begin {gather*} \frac {e^{\left (-\frac {{\left (12 \, x^{6} + 36 \, x^{5} + 171 \, x^{4} + 204 \, x^{3} + 414 \, x^{2} + 4 \, {\left (4 \, x^{2} - 4 \, x + 1\right )} e^{4} - 72 \, x + 3\right )} e^{\left (-4\right )}}{4 \, x^{2} - 4 \, x + 1} + 4\right )}}{x} \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. 48 vs.
\(2 (22) = 44\).
time = 0.24, size = 48, normalized size = 1.60 \begin {gather*} \frac {e^{- \frac {12 x^{6} + 36 x^{5} + 171 x^{4} + 204 x^{3} + 414 x^{2} - 72 x + 3}{\left (4 x^{2} - 4 x + 1\right ) e^{4}}}}{x} \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. 58 vs.
\(2 (26) = 52\).
time = 0.96, size = 58, normalized size = 1.93 \begin {gather*} \frac {e^{\left (-\frac {3 \, {\left (4 \, x^{6} + 12 \, x^{5} + 57 \, x^{4} + 68 \, x^{3} + 134 \, x^{2} - 20 \, x\right )}}{4 \, x^{2} e^{4} - 4 \, x e^{4} + e^{4}} - 3 \, e^{\left (-4\right )}\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.82, size = 139, normalized size = 4.63 \begin {gather*} \frac {{\mathrm {e}}^{\frac {72\,x\,{\mathrm {e}}^{-4}}{4\,x^2-4\,x+1}}\,{\mathrm {e}}^{-\frac {12\,x^6\,{\mathrm {e}}^{-4}}{4\,x^2-4\,x+1}}\,{\mathrm {e}}^{-\frac {36\,x^5\,{\mathrm {e}}^{-4}}{4\,x^2-4\,x+1}}\,{\mathrm {e}}^{-\frac {171\,x^4\,{\mathrm {e}}^{-4}}{4\,x^2-4\,x+1}}\,{\mathrm {e}}^{-\frac {204\,x^3\,{\mathrm {e}}^{-4}}{4\,x^2-4\,x+1}}\,{\mathrm {e}}^{-\frac {414\,x^2\,{\mathrm {e}}^{-4}}{4\,x^2-4\,x+1}}\,{\mathrm {e}}^{-\frac {3\,{\mathrm {e}}^{-4}}{4\,x^2-4\,x+1}}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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