Optimal. Leaf size=2 \[ \text {Ei}(t) \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.01, antiderivative size = 2, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {2209}
\begin {gather*} \text {ExpIntegralEi}(t) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 2209
Rubi steps
\begin {align*} \int \frac {e^t}{t} \, dt &=\text {Ei}(t)\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.01, size = 2, normalized size = 1.00 \begin {gather*} \text {Ei}(t) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(7\) vs.
\(2(2)=4\).
time = 0.01, size = 8, normalized size = 4.00
method | result | size |
default | \(-\expIntegral \left (1, -t \right )\) | \(8\) |
risch | \(-\expIntegral \left (1, -t \right )\) | \(8\) |
meijerg | \(\ln \left (t \right )+i \pi -\ln \left (-t \right )-\expIntegral \left (1, -t \right )\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 4.66, size = 2, normalized size = 1.00 \begin {gather*} {\rm Ei}\left (t\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.87, size = 2, normalized size = 1.00 \begin {gather*} {\rm Ei}\left (t\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.31, size = 2, normalized size = 1.00 \begin {gather*} \operatorname {Ei}{\left (t \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.45, size = 2, normalized size = 1.00 \begin {gather*} {\rm Ei}\left (t\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.01, size = 2, normalized size = 1.00 \begin {gather*} \mathrm {ei}\left (t\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________