Optimal. Leaf size=19 \[ \frac {1}{3} e^{4+4 e^4+x-x^2} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.01, antiderivative size = 20, normalized size of antiderivative = 1.05, number of steps
used = 2, number of rules used = 2, integrand size = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.083, Rules used = {12, 2268}
\begin {gather*} \frac {1}{3} e^{-x^2+x+4 \left (1+e^4\right )} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 2268
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{3} \int e^{4+4 e^4+x-x^2} (1-2 x) \, dx\\ &=\frac {1}{3} e^{4 \left (1+e^4\right )+x-x^2}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.03, size = 19, normalized size = 1.00 \begin {gather*} \frac {1}{3} e^{4+4 e^4+x-x^2} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.29, size = 21, normalized size = 1.11
method | result | size |
risch | \(\frac {{\mathrm e}^{4+4 \,{\mathrm e}^{4}-x^{2}+x}}{3}\) | \(16\) |
gosper | \({\mathrm e}^{-\ln \left (3\right )+4 \,{\mathrm e}^{4}-x^{2}+x +4}\) | \(18\) |
derivativedivides | \({\mathrm e}^{-\ln \left (3\right )+4 \,{\mathrm e}^{4}-x^{2}+x +2} {\mathrm e}^{2}\) | \(21\) |
default | \({\mathrm e}^{-\ln \left (3\right )+4 \,{\mathrm e}^{4}-x^{2}+x +2} {\mathrm e}^{2}\) | \(21\) |
norman | \({\mathrm e}^{-\ln \left (3\right )+4 \,{\mathrm e}^{4}-x^{2}+x +2} {\mathrm e}^{2}\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.37, size = 15, normalized size = 0.79 \begin {gather*} \frac {1}{3} \, e^{\left (-x^{2} + x + 4 \, e^{4} + 4\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.35, size = 17, normalized size = 0.89 \begin {gather*} e^{\left (-x^{2} + x + 4 \, e^{4} - \log \left (3\right ) + 4\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.04, size = 17, normalized size = 0.89 \begin {gather*} \frac {e^{2} e^{- x^{2} + x + 2 + 4 e^{4}}}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.39, size = 17, normalized size = 0.89 \begin {gather*} e^{\left (-x^{2} + x + 4 \, e^{4} - \log \left (3\right ) + 4\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.10, size = 17, normalized size = 0.89 \begin {gather*} \frac {{\mathrm {e}}^{4\,{\mathrm {e}}^4}\,{\mathrm {e}}^4\,{\mathrm {e}}^{-x^2}\,{\mathrm {e}}^x}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________