Optimal. Leaf size=16 \[ e^{\frac {278}{5}-\frac {2 e^4}{25}-2 x} \]
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Rubi [A]
time = 0.00, antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 2, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {12, 2225}
\begin {gather*} e^{\frac {2}{25} \left (-25 x-e^4+695\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2225
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\left (2 \int e^{\frac {2}{25} \left (695-e^4-25 x\right )} \, dx\right )\\ &=e^{\frac {2}{25} \left (695-e^4-25 x\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.08, size = 15, normalized size = 0.94 \begin {gather*} e^{-\frac {2}{25} \left (-695+e^4\right )-2 x} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.03, size = 13, normalized size = 0.81
method | result | size |
risch | \({\mathrm e}^{-\frac {2 \,{\mathrm e}^{4}}{25}-2 x +\frac {278}{5}}\) | \(11\) |
gosper | \({\mathrm e}^{-\frac {2 \,{\mathrm e}^{4}}{25}-2 x +\frac {278}{5}}\) | \(13\) |
derivativedivides | \({\mathrm e}^{-\frac {2 \,{\mathrm e}^{4}}{25}-2 x +\frac {278}{5}}\) | \(13\) |
default | \({\mathrm e}^{-\frac {2 \,{\mathrm e}^{4}}{25}-2 x +\frac {278}{5}}\) | \(13\) |
norman | \({\mathrm e}^{-\frac {2 \,{\mathrm e}^{4}}{25}-2 x +\frac {278}{5}}\) | \(13\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 10, normalized size = 0.62 \begin {gather*} e^{\left (-2 \, x - \frac {2}{25} \, e^{4} + \frac {278}{5}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 10, normalized size = 0.62 \begin {gather*} e^{\left (-2 \, x - \frac {2}{25} \, e^{4} + \frac {278}{5}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 14, normalized size = 0.88 \begin {gather*} e^{- 2 x - \frac {2 e^{4}}{25} + \frac {278}{5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 10, normalized size = 0.62 \begin {gather*} e^{\left (-2 \, x - \frac {2}{25} \, e^{4} + \frac {278}{5}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 12, normalized size = 0.75 \begin {gather*} {\mathrm {e}}^{-\frac {2\,{\mathrm {e}}^4}{25}}\,{\mathrm {e}}^{-2\,x}\,{\mathrm {e}}^{278/5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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