Optimal. Leaf size=13 \[ e^{\left (-8-e^3\right ) x^2} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.03, antiderivative size = 12, normalized size of antiderivative = 0.92, number of steps
used = 4, number of rules used = 4, integrand size = 27, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.148, Rules used = {6, 12, 2257,
2240} \begin {gather*} e^{-\left (\left (8+e^3\right ) x^2\right )} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 6
Rule 12
Rule 2240
Rule 2257
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int e^{-8 x^2-e^3 x^2} \left (-16-2 e^3\right ) x \, dx\\ &=-\left (\left (2 \left (8+e^3\right )\right ) \int e^{-8 x^2-e^3 x^2} x \, dx\right )\\ &=-\left (\left (2 \left (8+e^3\right )\right ) \int e^{-\left (\left (8+e^3\right ) x^2\right )} x \, dx\right )\\ &=e^{-\left (\left (8+e^3\right ) x^2\right )}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.05, size = 12, normalized size = 0.92 \begin {gather*} e^{-\left (\left (8+e^3\right ) x^2\right )} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(45\) vs.
\(2(11)=22\).
time = 0.38, size = 46, normalized size = 3.54
method | result | size |
risch | \({\mathrm e}^{-x^{2} \left ({\mathrm e}^{3}+8\right )}\) | \(11\) |
gosper | \({\mathrm e}^{-x^{2} {\mathrm e}^{3}-8 x^{2}}\) | \(15\) |
derivativedivides | \({\mathrm e}^{-x^{2} {\mathrm e}^{3}-8 x^{2}}\) | \(15\) |
norman | \({\mathrm e}^{-x^{2} {\mathrm e}^{3}-8 x^{2}}\) | \(15\) |
meijerg | \(\frac {\left (-2 \,{\mathrm e}^{3}-16\right ) \left (1-{\mathrm e}^{-x^{2} \left ({\mathrm e}^{3}+8\right )}\right )}{2 \,{\mathrm e}^{3}+16}\) | \(29\) |
default | \(-\frac {8 \,{\mathrm e}^{x^{2} \left (-8-{\mathrm e}^{3}\right )}}{-8-{\mathrm e}^{3}}-\frac {{\mathrm e}^{3+x^{2} \left (-8-{\mathrm e}^{3}\right )}}{-8-{\mathrm e}^{3}}\) | \(46\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.26, size = 14, normalized size = 1.08 \begin {gather*} e^{\left (-x^{2} e^{3} - 8 \, x^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.44, size = 14, normalized size = 1.08 \begin {gather*} e^{\left (-x^{2} e^{3} - 8 \, x^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.04, size = 14, normalized size = 1.08 \begin {gather*} e^{- x^{2} e^{3} - 8 x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.40, size = 14, normalized size = 1.08 \begin {gather*} e^{\left (-x^{2} e^{3} - 8 \, x^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 5.31, size = 14, normalized size = 1.08 \begin {gather*} {\mathrm {e}}^{-x^2\,{\mathrm {e}}^3-8\,x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________