Optimal. Leaf size=14 \[ e^{\frac {1}{t}} t-\text {Ei}\left (\frac {1}{t}\right ) \]
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Rubi [A]
time = 0.01, antiderivative size = 14, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 2, integrand size = 5, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.400, Rules used = {2237, 2241}
\begin {gather*} e^{\frac {1}{t}} t-\text {Ei}\left (\frac {1}{t}\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 2237
Rule 2241
Rubi steps
\begin {align*} \int e^{\frac {1}{t}} \, dt &=e^{\frac {1}{t}} t+\int \frac {e^{\frac {1}{t}}}{t} \, dt\\ &=e^{\frac {1}{t}} t-\text {Ei}\left (\frac {1}{t}\right )\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 14, normalized size = 1.00 \begin {gather*} e^{\frac {1}{t}} t-\text {Ei}\left (\frac {1}{t}\right ) \end {gather*}
Antiderivative was successfully verified.
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Mathics [A]
time = 2.09, size = 14, normalized size = 1.00 \begin {gather*} t E^{\frac {1}{t}}-\text {ExpIntegralEi}\left [\frac {1}{t}\right ] \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.02, size = 15, normalized size = 1.07
method | result | size |
derivativedivides | \({\mathrm e}^{\frac {1}{t}} t +\expIntegral \left (1, -\frac {1}{t}\right )\) | \(15\) |
default | \({\mathrm e}^{\frac {1}{t}} t +\expIntegral \left (1, -\frac {1}{t}\right )\) | \(15\) |
risch | \({\mathrm e}^{\frac {1}{t}} t +\expIntegral \left (1, -\frac {1}{t}\right )\) | \(15\) |
meijerg | \(t +1+\ln \left (t \right )-i \pi -\frac {t \left (\frac {2}{t}+2\right )}{2}+{\mathrm e}^{\frac {1}{t}} t +\ln \left (-\frac {1}{t}\right )+\expIntegral \left (1, -\frac {1}{t}\right )\) | \(39\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.37, size = 9, normalized size = 0.64 \begin {gather*} -\Gamma \left (-1, -\frac {1}{t}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 13, normalized size = 0.93 \begin {gather*} t e^{\frac {1}{t}} - {\rm Ei}\left (\frac {1}{t}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.55, size = 10, normalized size = 0.71 \begin {gather*} t e^{\frac {1}{t}} - \operatorname {Ei}{\left (\frac {1}{t} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.00, size = 14, normalized size = 1.00 \begin {gather*} -\left (\frac {\mathrm {Ei}\left (\frac 1{t}\right )}{t}-\mathrm {e}^{\frac 1{t}}\right ) t \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.02, size = 9, normalized size = 0.64 \begin {gather*} t\,\mathrm {expint}\left (2,-\frac {1}{t}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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