Optimal. Leaf size=6 \[ \log \left (e^x+x\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.01, antiderivative size = 6, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {6816}
\begin {gather*} \log \left (x+e^x\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 6816
Rubi steps
\begin {align*} \int \frac {1+e^x}{e^x+x} \, dx &=\log \left (e^x+x\right )\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.01, size = 6, normalized size = 1.00 \begin {gather*} \log \left (e^x+x\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.01, size = 6, normalized size = 1.00
method | result | size |
derivativedivides | \(\ln \left ({\mathrm e}^{x}+x \right )\) | \(6\) |
default | \(\ln \left ({\mathrm e}^{x}+x \right )\) | \(6\) |
norman | \(\ln \left ({\mathrm e}^{x}+x \right )\) | \(6\) |
risch | \(\ln \left ({\mathrm e}^{x}+x \right )\) | \(6\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.30, size = 5, normalized size = 0.83 \begin {gather*} \log \left (x + e^{x}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.35, size = 5, normalized size = 0.83 \begin {gather*} \log \left (x + e^{x}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.03, size = 5, normalized size = 0.83 \begin {gather*} \log {\left (x + e^{x} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 3.48, size = 5, normalized size = 0.83 \begin {gather*} \log \left (x + e^{x}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.03, size = 5, normalized size = 0.83 \begin {gather*} \ln \left (x+{\mathrm {e}}^x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________