Optimal. Leaf size=22 \[ e^{e^x+\frac {1024 e^{-5 (5+2 x)^4}}{x^5}} \]
________________________________________________________________________________________
Rubi [A] time = 0.92, antiderivative size = 33, normalized size of antiderivative = 1.50, number of steps used = 1, number of rules used = 1, integrand size = 90, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.011, Rules used = {6706} \begin {gather*} \exp \left (\frac {1024 e^{-80 x^4-800 x^3-3000 x^2-5000 x-3125}}{x^5}+e^x\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 6706
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\exp \left (e^x+\frac {1024 e^{-3125-5000 x-3000 x^2-800 x^3-80 x^4}}{x^5}\right )\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.15, size = 22, normalized size = 1.00 \begin {gather*} e^{e^x+\frac {1024 e^{-5 (5+2 x)^4}}{x^5}} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.62, size = 35, normalized size = 1.59 \begin {gather*} e^{\left (\frac {x^{5} e^{x} + 1024 \, e^{\left (-80 \, x^{4} - 800 \, x^{3} - 3000 \, x^{2} - 5000 \, x - 3125\right )}}{x^{5}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.36, size = 30, normalized size = 1.36 \begin {gather*} e^{\left (\frac {1024 \, e^{\left (-80 \, x^{4} - 800 \, x^{3} - 3000 \, x^{2} - 5000 \, x - 3125\right )}}{x^{5}} + e^{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.08, size = 25, normalized size = 1.14
method | result | size |
risch | \({\mathrm e}^{\frac {x^{5} {\mathrm e}^{x}+1024 \,{\mathrm e}^{-5 \left (5+2 x \right )^{4}}}{x^{5}}}\) | \(25\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.61, size = 30, normalized size = 1.36 \begin {gather*} e^{\left (\frac {1024 \, e^{\left (-80 \, x^{4} - 800 \, x^{3} - 3000 \, x^{2} - 5000 \, x - 3125\right )}}{x^{5}} + e^{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 5.25, size = 34, normalized size = 1.55 \begin {gather*} {\mathrm {e}}^{\frac {1024\,{\mathrm {e}}^{-5000\,x}\,{\mathrm {e}}^{-3125}\,{\mathrm {e}}^{-80\,x^4}\,{\mathrm {e}}^{-800\,x^3}\,{\mathrm {e}}^{-3000\,x^2}}{x^5}}\,{\mathrm {e}}^{{\mathrm {e}}^x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.60, size = 32, normalized size = 1.45 \begin {gather*} e^{e^{x} + \frac {1024 e^{- 80 x^{4} - 800 x^{3} - 3000 x^{2} - 5000 x - 3125}}{x^{5}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________