Optimal. Leaf size=30 \[ 3+4 e^{-2-\frac {2-x}{x^2}-4 x+4 (5+2 x)^2} \]
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Rubi [A] time = 0.27, antiderivative size = 29, normalized size of antiderivative = 0.97, number of steps used = 1, number of rules used = 1, integrand size = 46, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.022, Rules used = {6706} \begin {gather*} 4 e^{-\frac {-16 x^4-76 x^3-98 x^2-x+2}{x^2}} \end {gather*}
Antiderivative was successfully verified.
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Rule 6706
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=4 e^{-\frac {2-x-98 x^2-76 x^3-16 x^4}{x^2}}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.13, size = 22, normalized size = 0.73 \begin {gather*} 4 e^{98-\frac {2}{x^2}+\frac {1}{x}+76 x+16 x^2} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.86, size = 25, normalized size = 0.83 \begin {gather*} 4 \, e^{\left (\frac {16 \, x^{4} + 76 \, x^{3} + 98 \, x^{2} + x - 2}{x^{2}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.22, size = 21, normalized size = 0.70 \begin {gather*} 4 \, e^{\left (16 \, x^{2} + 76 \, x + \frac {1}{x} - \frac {2}{x^{2}} + 98\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.16, size = 26, normalized size = 0.87
method | result | size |
risch | \(4 \,{\mathrm e}^{\frac {16 x^{4}+76 x^{3}+98 x^{2}+x -2}{x^{2}}}\) | \(26\) |
gosper | \(4 \,{\mathrm e}^{\frac {16 x^{4}+76 x^{3}+98 x^{2}+x -2}{x^{2}}}\) | \(29\) |
norman | \(4 \,{\mathrm e}^{-\frac {-16 x^{4}-76 x^{3}-98 x^{2}-x +2}{x^{2}}}\) | \(30\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.53, size = 21, normalized size = 0.70 \begin {gather*} 4 \, e^{\left (16 \, x^{2} + 76 \, x + \frac {1}{x} - \frac {2}{x^{2}} + 98\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.22, size = 24, normalized size = 0.80 \begin {gather*} 4\,{\mathrm {e}}^{76\,x}\,{\mathrm {e}}^{1/x}\,{\mathrm {e}}^{98}\,{\mathrm {e}}^{-\frac {2}{x^2}}\,{\mathrm {e}}^{16\,x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.15, size = 24, normalized size = 0.80 \begin {gather*} 4 e^{- \frac {- 16 x^{4} - 76 x^{3} - 98 x^{2} - x + 2}{x^{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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