Optimal. Leaf size=16 \[ e^{4096 e^{8 x^2} x^2} x \]
________________________________________________________________________________________
Rubi [B] time = 0.03, antiderivative size = 54, normalized size of antiderivative = 3.38, number of steps used = 1, number of rules used = 1, integrand size = 36, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.028, Rules used = {2288} \begin {gather*} \frac {e^{4096 e^{8 x^2} x^2+8 x^2} \left (8 x^4+x^2\right )}{e^{8 x^2} x+8 e^{8 x^2} x^3} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 2288
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {e^{8 x^2+4096 e^{8 x^2} x^2} \left (x^2+8 x^4\right )}{e^{8 x^2} x+8 e^{8 x^2} x^3}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.02, size = 16, normalized size = 1.00 \begin {gather*} e^{4096 e^{8 x^2} x^2} x \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 1.06, size = 14, normalized size = 0.88 \begin {gather*} x e^{\left (4096 \, x^{2} e^{\left (8 \, x^{2}\right )}\right )} \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 {\left (8192 \, {\left (8 \, x^{4} + x^{2}\right )} e^{\left (8 \, x^{2}\right )} + 1\right )} e^{\left (4096 \, x^{2} e^{\left (8 \, x^{2}\right )}\right )}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.12, size = 15, normalized size = 0.94
method | result | size |
risch | \({\mathrm e}^{4096 x^{2} {\mathrm e}^{8 x^{2}}} x\) | \(15\) |
norman | \({\mathrm e}^{4096 x^{2} {\mathrm e}^{8 x^{2}}} x\) | \(17\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.40, size = 14, normalized size = 0.88 \begin {gather*} x e^{\left (4096 \, x^{2} e^{\left (8 \, x^{2}\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 5.52, size = 14, normalized size = 0.88 \begin {gather*} x\,{\mathrm {e}}^{4096\,x^2\,{\mathrm {e}}^{8\,x^2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 10.11, size = 14, normalized size = 0.88 \begin {gather*} x e^{4096 x^{2} e^{8 x^{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________