Optimal. Leaf size=15 \[ -1+e^{\left (e^{2 x}-x\right )^2} \]
________________________________________________________________________________________
Rubi [A] time = 0.15, antiderivative size = 19, normalized size of antiderivative = 1.27, number of steps used = 1, number of rules used = 1, integrand size = 42, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.024, Rules used = {6706} \begin {gather*} e^{x^2-2 e^{2 x} x+e^{4 x}} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 6706
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=e^{e^{4 x}-2 e^{2 x} x+x^2}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.15, size = 13, normalized size = 0.87 \begin {gather*} e^{\left (e^{2 x}-x\right )^2} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.47, size = 16, normalized size = 1.07 \begin {gather*} e^{\left (x^{2} - 2 \, x e^{\left (2 \, x\right )} + e^{\left (4 \, x\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.25, size = 16, normalized size = 1.07 \begin {gather*} e^{\left (x^{2} - 2 \, x e^{\left (2 \, x\right )} + e^{\left (4 \, x\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.04, size = 17, normalized size = 1.13
method | result | size |
norman | \({\mathrm e}^{{\mathrm e}^{4 x}-2 x \,{\mathrm e}^{2 x}+x^{2}}\) | \(17\) |
risch | \({\mathrm e}^{{\mathrm e}^{4 x}-2 x \,{\mathrm e}^{2 x}+x^{2}}\) | \(17\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.60, size = 16, normalized size = 1.07 \begin {gather*} e^{\left (x^{2} - 2 \, x e^{\left (2 \, x\right )} + e^{\left (4 \, x\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 1.35, size = 18, normalized size = 1.20 \begin {gather*} {\mathrm {e}}^{x^2}\,{\mathrm {e}}^{-2\,x\,{\mathrm {e}}^{2\,x}}\,{\mathrm {e}}^{{\mathrm {e}}^{4\,x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.19, size = 17, normalized size = 1.13 \begin {gather*} e^{x^{2} - 2 x e^{2 x} + e^{4 x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________