Optimal. Leaf size=13 \[ \left (-3+e^{-1+x} x\right )^{e^3} \]
________________________________________________________________________________________
Rubi [A] time = 0.27, antiderivative size = 21, normalized size of antiderivative = 1.62, number of steps used = 3, number of rules used = 3, integrand size = 45, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {12, 6688, 6686} \begin {gather*} e^{-e^3} \left (e^x x-3 e\right )^{e^3} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 6686
Rule 6688
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=e^3 \int \frac {(-1-x) \left (e^{-1+x} \left (-3 e^{1-x}+x\right )\right )^{e^3}}{3 e^{1-x}-x} \, dx\\ &=e^3 \int e^{-e^3+x} (1+x) \left (-3 e+e^x x\right )^{-1+e^3} \, dx\\ &=e^{-e^3} \left (-3 e+e^x x\right )^{e^3}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.05, size = 13, normalized size = 1.00 \begin {gather*} \left (-3+e^{-1+x} x\right )^{e^3} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.54, size = 11, normalized size = 0.85 \begin {gather*} {\left (x e^{\left (x - 1\right )} - 3\right )}^{e^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\left ({\left (x - 3 \, e^{\left (-x + 1\right )}\right )} e^{\left (x - 1\right )}\right )^{e^{3}} {\left (x + 1\right )} e^{3}}{x - 3 \, e^{\left (-x + 1\right )}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.23, size = 25, normalized size = 1.92
method | result | size |
norman | \({\mathrm e}^{{\mathrm e}^{3} \ln \left (\left (-3 \,{\mathrm e}^{1-x}+x \right ) {\mathrm e}^{x -1}\right )}\) | \(25\) |
risch | \({\mathrm e}^{-\frac {{\mathrm e}^{3} \left (i \pi \mathrm {csgn}\left (i \left (-3 \,{\mathrm e}^{1-x}+x \right ) {\mathrm e}^{x -1}\right )^{3}-i \pi \mathrm {csgn}\left (i \left (-3 \,{\mathrm e}^{1-x}+x \right ) {\mathrm e}^{x -1}\right )^{2} \mathrm {csgn}\left (i {\mathrm e}^{x -1}\right )-i \pi \mathrm {csgn}\left (i \left (-3 \,{\mathrm e}^{1-x}+x \right ) {\mathrm e}^{x -1}\right )^{2} \mathrm {csgn}\left (i \left (-3 \,{\mathrm e}^{1-x}+x \right )\right )+i \pi \,\mathrm {csgn}\left (i \left (-3 \,{\mathrm e}^{1-x}+x \right ) {\mathrm e}^{x -1}\right ) \mathrm {csgn}\left (i {\mathrm e}^{x -1}\right ) \mathrm {csgn}\left (i \left (-3 \,{\mathrm e}^{1-x}+x \right )\right )+2 \ln \left ({\mathrm e}^{1-x}\right )-2 \ln \left (-3 \,{\mathrm e}^{1-x}+x \right )\right )}{2}}\) | \(167\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.39, size = 19, normalized size = 1.46 \begin {gather*} e^{\left (e^{3} \log \left (x e^{x} - 3 \, e\right ) - e^{3}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 7.33, size = 11, normalized size = 0.85 \begin {gather*} {\left (x\,{\mathrm {e}}^{x-1}-3\right )}^{{\mathrm {e}}^3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 15.87, size = 15, normalized size = 1.15 \begin {gather*} \left (\left (x - 3 e^{1 - x}\right ) e^{x - 1}\right )^{e^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________