Optimal. Leaf size=17 \[ \log \left (2+e^{2 e-2 e^4}-x\right ) \]
________________________________________________________________________________________
Rubi [A] time = 0.02, antiderivative size = 20, normalized size of antiderivative = 1.18, number of steps used = 3, number of rules used = 3, integrand size = 31, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.097, Rules used = {12, 33, 31} \begin {gather*} \log \left (e^{2 e^4} (2-x)+e^{2 e}\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 31
Rule 33
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=e^{-2 e \left (1-e^3\right )} \int \frac {1}{-1+e^{-2 e+2 e^4} (-2+x)} \, dx\\ &=e^{-2 e \left (1-e^3\right )} \operatorname {Subst}\left (\int \frac {1}{-1+e^{-2 e+2 e^4} x} \, dx,x,-2+x\right )\\ &=\log \left (e^{2 e}+e^{2 e^4} (2-x)\right )\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.01, size = 20, normalized size = 1.18 \begin {gather*} \log \left (-e^{2 e}+e^{2 e^4} (-2+x)\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.72, size = 17, normalized size = 1.00 \begin {gather*} \log \left ({\left (x - 2\right )} e^{\left (2 \, e^{4} - 2 \, e\right )} - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.26, size = 18, normalized size = 1.06 \begin {gather*} \log \left ({\left | {\left (x - 2\right )} e^{\left (2 \, e^{4} - 2 \, e\right )} - 1 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.46, size = 24, normalized size = 1.41
method | result | size |
risch | \(\ln \left ({\mathrm e}^{2 \,{\mathrm e}^{4}} x -2 \,{\mathrm e}^{2 \,{\mathrm e}^{4}}-{\mathrm e}^{2 \,{\mathrm e}}\right )\) | \(24\) |
default | \(\ln \left ({\mathrm e}^{2 \,{\mathrm e}^{4}-2 \,{\mathrm e}} x -2 \,{\mathrm e}^{2 \,{\mathrm e}^{4}-2 \,{\mathrm e}}-1\right )\) | \(32\) |
norman | \(\ln \left ({\mathrm e}^{2 \,{\mathrm e}^{4}-2 \,{\mathrm e}} x -2 \,{\mathrm e}^{2 \,{\mathrm e}^{4}-2 \,{\mathrm e}}-1\right )\) | \(32\) |
meijerg | \(-\frac {\left (1+2 \,{\mathrm e}^{2 \,{\mathrm e}^{4}-2 \,{\mathrm e}}\right ) \ln \left (1+\frac {x \,{\mathrm e}^{2 \,{\mathrm e}^{4}-2 \,{\mathrm e}}}{-2 \,{\mathrm e}^{2 \,{\mathrm e}^{4}-2 \,{\mathrm e}}-1}\right )}{-2 \,{\mathrm e}^{2 \,{\mathrm e}^{4}-2 \,{\mathrm e}}-1}\) | \(64\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.35, size = 17, normalized size = 1.00 \begin {gather*} \log \left ({\left (x - 2\right )} e^{\left (2 \, e^{4} - 2 \, e\right )} - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.27, size = 35, normalized size = 2.06 \begin {gather*} {\mathrm {e}}^{2\,\mathrm {e}-2\,{\mathrm {e}}^4}\,{\mathrm {e}}^{2\,\mathrm {e}\,\left ({\mathrm {e}}^3-1\right )}\,\ln \left (x-{\mathrm {e}}^{-2\,\mathrm {e}\,\left ({\mathrm {e}}^3-1\right )}-2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.08, size = 24, normalized size = 1.41 \begin {gather*} \log {\left (x e^{2 e^{4}} - 2 e^{2 e^{4}} - e^{2 e} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________