Integrand size = 9, antiderivative size = 4 \[ \int \frac {e^{a t}}{t} \, dt=\operatorname {ExpIntegralEi}(a t) \]
[Out]
Time = 0.01 (sec) , antiderivative size = 4, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {2209} \[ \int \frac {e^{a t}}{t} \, dt=\operatorname {ExpIntegralEi}(a t) \]
[In]
[Out]
Rule 2209
Rubi steps \begin{align*} \text {integral}& = \operatorname {ExpIntegralEi}(a t) \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 4, normalized size of antiderivative = 1.00 \[ \int \frac {e^{a t}}{t} \, dt=\operatorname {ExpIntegralEi}(a t) \]
[In]
[Out]
Time = 0.03 (sec) , antiderivative size = 9, normalized size of antiderivative = 2.25
method | result | size |
derivativedivides | \(-\operatorname {Ei}_{1}\left (-a t \right )\) | \(9\) |
default | \(-\operatorname {Ei}_{1}\left (-a t \right )\) | \(9\) |
risch | \(-\operatorname {Ei}_{1}\left (-a t \right )\) | \(9\) |
meijerg | \(\ln \left (t \right )+\ln \left (-a \right )-\ln \left (-a t \right )-\operatorname {Ei}_{1}\left (-a t \right )\) | \(23\) |
[In]
[Out]
none
Time = 0.23 (sec) , antiderivative size = 4, normalized size of antiderivative = 1.00 \[ \int \frac {e^{a t}}{t} \, dt={\rm Ei}\left (a t\right ) \]
[In]
[Out]
Time = 0.41 (sec) , antiderivative size = 3, normalized size of antiderivative = 0.75 \[ \int \frac {e^{a t}}{t} \, dt=\operatorname {Ei}{\left (a t \right )} \]
[In]
[Out]
none
Time = 0.21 (sec) , antiderivative size = 4, normalized size of antiderivative = 1.00 \[ \int \frac {e^{a t}}{t} \, dt={\rm Ei}\left (a t\right ) \]
[In]
[Out]
none
Time = 0.28 (sec) , antiderivative size = 4, normalized size of antiderivative = 1.00 \[ \int \frac {e^{a t}}{t} \, dt={\rm Ei}\left (a t\right ) \]
[In]
[Out]
Time = 0.01 (sec) , antiderivative size = 4, normalized size of antiderivative = 1.00 \[ \int \frac {e^{a t}}{t} \, dt=\mathrm {ei}\left (a\,t\right ) \]
[In]
[Out]