Optimal. Leaf size=4 \[ \text{LogIntegral}(x+1) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0037252, antiderivative size = 4, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 6, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.333, Rules used = {2389, 2298} \[ \text{LogIntegral}(x+1) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 2389
Rule 2298
Rubi steps
\begin{align*} \int \frac{1}{\log (1+x)} \, dx &=\operatorname{Subst}\left (\int \frac{1}{\log (x)} \, dx,x,1+x\right )\\ &=\text{li}(1+x)\\ \end{align*}
Mathematica [A] time = 0.0101527, size = 5, normalized size = 1.25 \[ \text{ExpIntegralEi}(\log (x+1)) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [B] time = 0.002, size = 11, normalized size = 2.8 \begin{align*} -{\it Ei} \left ( 1,-\ln \left ( 1+x \right ) \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.03548, size = 7, normalized size = 1.75 \begin{align*}{\rm Ei}\left (\log \left (x + 1\right )\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.85379, size = 28, normalized size = 7. \begin{align*} \logintegral \left (x + 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.471035, size = 3, normalized size = 0.75 \begin{align*} \operatorname{li}{\left (x + 1 \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.08028, size = 7, normalized size = 1.75 \begin{align*}{\rm Ei}\left (\log \left (x + 1\right )\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]