Optimal. Leaf size=4 \[ \text {Ei}(a x) \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.01, antiderivative size = 4, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {2209}
\begin {gather*} \text {ExpIntegralEi}(a x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 2209
Rubi steps
\begin {align*} \int \frac {e^{a x}}{x} \, dx &=\text {Ei}(a x)\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.01, size = 4, normalized size = 1.00 \begin {gather*} \text {Ei}(a x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.01, size = 9, normalized size = 2.25
method | result | size |
derivativedivides | \(-\expIntegral \left (1, -a x \right )\) | \(9\) |
default | \(-\expIntegral \left (1, -a x \right )\) | \(9\) |
risch | \(-\expIntegral \left (1, -a x \right )\) | \(9\) |
meijerg | \(\ln \left (x \right )+\ln \left (-a \right )-\ln \left (-a x \right )-\expIntegral \left (1, -a x \right )\) | \(23\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 3.62, size = 4, normalized size = 1.00 \begin {gather*} {\rm Ei}\left (a x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 1.12, size = 4, normalized size = 1.00 \begin {gather*} {\rm Ei}\left (a x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.34, size = 3, normalized size = 0.75 \begin {gather*} \operatorname {Ei}{\left (a x \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.65, size = 4, normalized size = 1.00 \begin {gather*} {\rm Ei}\left (a x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.01, size = 4, normalized size = 1.00 \begin {gather*} \mathrm {ei}\left (a\,x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________