Optimal. Leaf size=28 \[ \frac {e^{5-\left (-14-\frac {4 x}{5}\right )^2}}{3-e^5 (2+x)} \]
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Rubi [A] time = 0.34, antiderivative size = 32, normalized size of antiderivative = 1.14, number of steps used = 4, number of rules used = 4, integrand size = 63, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.063, Rules used = {6741, 27, 12, 2289} \begin {gather*} \frac {e^{\frac {1}{25} \left (-16 x^2-560 x-4775\right )}}{-e^5 x-2 e^5+3} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 27
Rule 2289
Rule 6741
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{\frac {1}{25} \left (-4775-560 x-16 x^2\right )} \left (-5 \left (336-229 e^5\right )-48 \left (2-13 e^5\right ) x+32 e^5 x^2\right )}{25 \left (3-2 e^5\right )^2-50 e^5 \left (3-2 e^5\right ) x+25 e^{10} x^2} \, dx\\ &=\int \frac {e^{\frac {1}{25} \left (-4775-560 x-16 x^2\right )} \left (-5 \left (336-229 e^5\right )-48 \left (2-13 e^5\right ) x+32 e^5 x^2\right )}{25 \left (-3+2 e^5+e^5 x\right )^2} \, dx\\ &=\frac {1}{25} \int \frac {e^{\frac {1}{25} \left (-4775-560 x-16 x^2\right )} \left (-5 \left (336-229 e^5\right )-48 \left (2-13 e^5\right ) x+32 e^5 x^2\right )}{\left (-3+2 e^5+e^5 x\right )^2} \, dx\\ &=\frac {e^{\frac {1}{25} \left (-4775-560 x-16 x^2\right )}}{3-2 e^5-e^5 x}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.19, size = 29, normalized size = 1.04 \begin {gather*} -\frac {e^{-191-\frac {112 x}{5}-\frac {16 x^2}{25}}}{-3+e^5 (2+x)} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.56, size = 23, normalized size = 0.82 \begin {gather*} -\frac {e^{\left (-\frac {16}{25} \, x^{2} - \frac {112}{5} \, x - 191\right )}}{{\left (x + 2\right )} e^{5} - 3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 27, normalized size = 0.96 \begin {gather*} -\frac {e^{\left (-\frac {16}{25} \, x^{2} - \frac {112}{5} \, x\right )}}{x e^{196} + 2 \, e^{196} - 3 \, e^{191}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.54, size = 26, normalized size = 0.93
method | result | size |
gosper | \(-\frac {{\mathrm e}^{-\frac {16}{25} x^{2}-\frac {112}{5} x -191}}{x \,{\mathrm e}^{5}+2 \,{\mathrm e}^{5}-3}\) | \(26\) |
norman | \(-\frac {{\mathrm e}^{-\frac {16}{25} x^{2}-\frac {112}{5} x -191}}{x \,{\mathrm e}^{5}+2 \,{\mathrm e}^{5}-3}\) | \(26\) |
risch | \(-\frac {{\mathrm e}^{-\frac {16}{25} x^{2}-\frac {112}{5} x -191}}{x \,{\mathrm e}^{5}+2 \,{\mathrm e}^{5}-3}\) | \(26\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.42, size = 27, normalized size = 0.96 \begin {gather*} -\frac {e^{\left (-\frac {16}{25} \, x^{2} - \frac {112}{5} \, x\right )}}{x e^{196} + 2 \, e^{196} - 3 \, e^{191}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.02, size = 26, normalized size = 0.93 \begin {gather*} -\frac {{\mathrm {e}}^{-\frac {112\,x}{5}}\,{\mathrm {e}}^{-191}\,{\mathrm {e}}^{-\frac {16\,x^2}{25}}}{2\,{\mathrm {e}}^5+x\,{\mathrm {e}}^5-3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.20, size = 29, normalized size = 1.04 \begin {gather*} - \frac {e^{- \frac {16 x^{2}}{25} - \frac {112 x}{5} - 191}}{x e^{5} - 3 + 2 e^{5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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