Integrand size = 7, antiderivative size = 2 \[ \int \frac {e^t}{t} \, dt=\operatorname {ExpIntegralEi}(t) \]
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Time = 0.01 (sec) , antiderivative size = 2, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {2209} \[ \int \frac {e^t}{t} \, dt=\operatorname {ExpIntegralEi}(t) \]
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Rule 2209
Rubi steps \begin{align*} \text {integral}& = \operatorname {ExpIntegralEi}(t) \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 2, normalized size of antiderivative = 1.00 \[ \int \frac {e^t}{t} \, dt=\operatorname {ExpIntegralEi}(t) \]
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Leaf count of result is larger than twice the leaf count of optimal. \(7\) vs. \(2(2)=4\).
Time = 0.04 (sec) , antiderivative size = 8, normalized size of antiderivative = 4.00
method | result | size |
default | \(-\operatorname {Ei}_{1}\left (-t \right )\) | \(8\) |
risch | \(-\operatorname {Ei}_{1}\left (-t \right )\) | \(8\) |
meijerg | \(\ln \left (t \right )+i \pi -\ln \left (-t \right )-\operatorname {Ei}_{1}\left (-t \right )\) | \(21\) |
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none
Time = 0.23 (sec) , antiderivative size = 2, normalized size of antiderivative = 1.00 \[ \int \frac {e^t}{t} \, dt={\rm Ei}\left (t\right ) \]
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Time = 0.39 (sec) , antiderivative size = 2, normalized size of antiderivative = 1.00 \[ \int \frac {e^t}{t} \, dt=\operatorname {Ei}{\left (t \right )} \]
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none
Time = 0.22 (sec) , antiderivative size = 2, normalized size of antiderivative = 1.00 \[ \int \frac {e^t}{t} \, dt={\rm Ei}\left (t\right ) \]
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none
Time = 0.29 (sec) , antiderivative size = 2, normalized size of antiderivative = 1.00 \[ \int \frac {e^t}{t} \, dt={\rm Ei}\left (t\right ) \]
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Time = 0.01 (sec) , antiderivative size = 2, normalized size of antiderivative = 1.00 \[ \int \frac {e^t}{t} \, dt=\mathrm {ei}\left (t\right ) \]
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