Optimal. Leaf size=21 \[ \log \left (e \left (-5+e^x+2 x-\frac {2 \left (x+x^2\right )}{x}\right )\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.01, antiderivative size = 8, normalized size of antiderivative = 0.38, number of steps
used = 2, number of rules used = 2, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.182, Rules used = {2278, 31}
\begin {gather*} \log \left (7-e^x\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 31
Rule 2278
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\text {Subst}\left (\int \frac {1}{-7+x} \, dx,x,e^x\right )\\ &=\log \left (7-e^x\right )\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.01, size = 6, normalized size = 0.29 \begin {gather*} \log \left (-7+e^x\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.14, size = 6, normalized size = 0.29
method | result | size |
derivativedivides | \(\ln \left (-7+{\mathrm e}^{x}\right )\) | \(6\) |
default | \(\ln \left (-7+{\mathrm e}^{x}\right )\) | \(6\) |
norman | \(\ln \left (-7+{\mathrm e}^{x}\right )\) | \(6\) |
risch | \(\ln \left (-7+{\mathrm e}^{x}\right )\) | \(6\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.26, size = 5, normalized size = 0.24 \begin {gather*} \log \left (e^{x} - 7\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.36, size = 5, normalized size = 0.24 \begin {gather*} \log \left (e^{x} - 7\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.02, size = 5, normalized size = 0.24 \begin {gather*} \log {\left (e^{x} - 7 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.38, size = 6, normalized size = 0.29 \begin {gather*} \log \left ({\left | e^{x} - 7 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.05, size = 5, normalized size = 0.24 \begin {gather*} \ln \left ({\mathrm {e}}^x-7\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________