Integrand size = 7, antiderivative size = 11 \[ \int \frac {e^t}{t^2} \, dt=-\frac {e^t}{t}+\operatorname {ExpIntegralEi}(t) \]
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Time = 0.01 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.286, Rules used = {2208, 2209} \[ \int \frac {e^t}{t^2} \, dt=\operatorname {ExpIntegralEi}(t)-\frac {e^t}{t} \]
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Rule 2208
Rule 2209
Rubi steps \begin{align*} \text {integral}& = -\frac {e^t}{t}+\int \frac {e^t}{t} \, dt \\ & = -\frac {e^t}{t}+\operatorname {ExpIntegralEi}(t) \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.00 \[ \int \frac {e^t}{t^2} \, dt=-\frac {e^t}{t}+\operatorname {ExpIntegralEi}(t) \]
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Time = 0.03 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.45
method | result | size |
default | \(-\frac {{\mathrm e}^{t}}{t}-\operatorname {Ei}_{1}\left (-t \right )\) | \(16\) |
risch | \(-\frac {{\mathrm e}^{t}}{t}-\operatorname {Ei}_{1}\left (-t \right )\) | \(16\) |
meijerg | \(-\frac {1}{t}-1+\ln \left (t \right )+i \pi +\frac {2+2 t}{2 t}-\frac {{\mathrm e}^{t}}{t}-\ln \left (-t \right )-\operatorname {Ei}_{1}\left (-t \right )\) | \(44\) |
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none
Time = 0.24 (sec) , antiderivative size = 13, normalized size of antiderivative = 1.18 \[ \int \frac {e^t}{t^2} \, dt=\frac {t {\rm Ei}\left (t\right ) - e^{t}}{t} \]
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Time = 0.60 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.64 \[ \int \frac {e^t}{t^2} \, dt=\operatorname {Ei}{\left (t \right )} - \frac {e^{t}}{t} \]
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none
Time = 0.22 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.45 \[ \int \frac {e^t}{t^2} \, dt=\Gamma \left (-1, -t\right ) \]
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none
Time = 0.27 (sec) , antiderivative size = 13, normalized size of antiderivative = 1.18 \[ \int \frac {e^t}{t^2} \, dt=\frac {t {\rm Ei}\left (t\right ) - e^{t}}{t} \]
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Time = 0.02 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.27 \[ \int \frac {e^t}{t^2} \, dt=-\frac {{\mathrm {e}}^t}{t}-\mathrm {expint}\left (-t\right ) \]
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