Optimal. Leaf size=18 \[ -e^{2 e^2+2 x}+x+x^2 \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.00, antiderivative size = 18, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {2225}
\begin {gather*} x^2+x-e^{2 x+2 e^2} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 2225
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=x+x^2-2 \int e^{2 e^2+2 x} \, dx\\ &=-e^{2 e^2+2 x}+x+x^2\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.01, size = 16, normalized size = 0.89 \begin {gather*} -e^{2 \left (e^2+x\right )}+x+x^2 \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.18, size = 15, normalized size = 0.83
method | result | size |
default | \(x -{\mathrm e}^{2 x +2 \,{\mathrm e}^{2}}+x^{2}\) | \(15\) |
norman | \(x -{\mathrm e}^{2 x +2 \,{\mathrm e}^{2}}+x^{2}\) | \(15\) |
risch | \(x -{\mathrm e}^{2 x +2 \,{\mathrm e}^{2}}+x^{2}\) | \(17\) |
derivativedivides | \(\left (x +{\mathrm e}^{2}\right )^{2}+x +{\mathrm e}^{2}-{\mathrm e}^{2 x +2 \,{\mathrm e}^{2}}-2 \left (x +{\mathrm e}^{2}\right ) {\mathrm e}^{2}\) | \(28\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.26, size = 16, normalized size = 0.89 \begin {gather*} x^{2} + x - e^{\left (2 \, x + 2 \, e^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.38, size = 16, normalized size = 0.89 \begin {gather*} x^{2} + x - e^{\left (2 \, x + 2 \, e^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.03, size = 14, normalized size = 0.78 \begin {gather*} x^{2} + x - e^{2 x + 2 e^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.40, size = 16, normalized size = 0.89 \begin {gather*} x^{2} + x - e^{\left (2 \, x + 2 \, e^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.08, size = 16, normalized size = 0.89 \begin {gather*} x-{\mathrm {e}}^{2\,{\mathrm {e}}^2}\,{\mathrm {e}}^{2\,x}+x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________