Optimal. Leaf size=19 \[ e^{\frac {3-5 x}{-22+e^{19/5}}+x} \]
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Rubi [A] time = 0.04, antiderivative size = 29, normalized size of antiderivative = 1.53, number of steps used = 3, number of rules used = 3, integrand size = 41, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.073, Rules used = {12, 2227, 2194} \begin {gather*} e^{-\frac {3-\left (27-e^{19/5}\right ) x}{22-e^{19/5}}} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2194
Rule 2227
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\left (27-e^{19/5}\right ) \int e^{\frac {3-27 x+e^{19/5} x}{-22+e^{19/5}}} \, dx}{22-e^{19/5}}\\ &=\frac {\left (27-e^{19/5}\right ) \int e^{\frac {3-\left (27-e^{19/5}\right ) x}{-22+e^{19/5}}} \, dx}{22-e^{19/5}}\\ &=e^{-\frac {3-\left (27-e^{19/5}\right ) x}{22-e^{19/5}}}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.03, size = 23, normalized size = 1.21 \begin {gather*} e^{\frac {3+\left (-27+e^{19/5}\right ) x}{-22+e^{19/5}}} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.56, size = 17, normalized size = 0.89 \begin {gather*} e^{\left (\frac {x e^{\frac {19}{5}} - 27 \, x + 3}{e^{\frac {19}{5}} - 22}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.25, size = 17, normalized size = 0.89 \begin {gather*} e^{\left (\frac {x e^{\frac {19}{5}} - 27 \, x + 3}{e^{\frac {19}{5}} - 22}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 18, normalized size = 0.95
method | result | size |
gosper | \({\mathrm e}^{\frac {x \,{\mathrm e}^{\frac {19}{5}}-27 x +3}{{\mathrm e}^{\frac {19}{5}}-22}}\) | \(18\) |
derivativedivides | \({\mathrm e}^{\frac {x \,{\mathrm e}^{\frac {19}{5}}-27 x +3}{{\mathrm e}^{\frac {19}{5}}-22}}\) | \(18\) |
default | \({\mathrm e}^{\frac {x \,{\mathrm e}^{\frac {19}{5}}-27 x +3}{{\mathrm e}^{\frac {19}{5}}-22}}\) | \(18\) |
norman | \({\mathrm e}^{\frac {x \,{\mathrm e}^{\frac {19}{5}}-27 x +3}{{\mathrm e}^{\frac {19}{5}}-22}}\) | \(18\) |
risch | \({\mathrm e}^{\frac {x \,{\mathrm e}^{\frac {19}{5}}-27 x +3}{{\mathrm e}^{\frac {19}{5}}-22}}\) | \(18\) |
meijerg | \(-\frac {{\mathrm e}^{\frac {3}{{\mathrm e}^{\frac {19}{5}}-22}+\frac {19}{5}} \left (1-{\mathrm e}^{\frac {x \left ({\mathrm e}^{\frac {19}{5}}-27\right )}{{\mathrm e}^{\frac {19}{5}}-22}}\right )}{{\mathrm e}^{\frac {19}{5}}-27}+\frac {27 \,{\mathrm e}^{\frac {3}{{\mathrm e}^{\frac {19}{5}}-22}} \left (1-{\mathrm e}^{\frac {x \left ({\mathrm e}^{\frac {19}{5}}-27\right )}{{\mathrm e}^{\frac {19}{5}}-22}}\right )}{{\mathrm e}^{\frac {19}{5}}-27}\) | \(72\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.41, size = 17, normalized size = 0.89 \begin {gather*} e^{\left (\frac {x e^{\frac {19}{5}} - 27 \, x + 3}{e^{\frac {19}{5}} - 22}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.11, size = 31, normalized size = 1.63 \begin {gather*} {\mathrm {e}}^{-\frac {27\,x}{{\mathrm {e}}^{19/5}-22}}\,{\mathrm {e}}^{\frac {x\,{\mathrm {e}}^{19/5}}{{\mathrm {e}}^{19/5}-22}}\,{\mathrm {e}}^{\frac {3}{{\mathrm {e}}^{19/5}-22}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.13, size = 19, normalized size = 1.00 \begin {gather*} e^{\frac {- 27 x + x e^{\frac {19}{5}} + 3}{-22 + e^{\frac {19}{5}}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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