Optimal. Leaf size=19 \[ e^{2+e^{\frac {15}{2} (-4+x) x^2}-x} \]
________________________________________________________________________________________
Rubi [A] time = 0.15, antiderivative size = 24, normalized size of antiderivative = 1.26, number of steps used = 2, number of rules used = 2, integrand size = 57, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.035, Rules used = {12, 6706} \begin {gather*} e^{e^{-\frac {15}{2} \left (4 x^2-x^3\right )}-x+2} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 6706
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{2} \int e^{2+e^{\frac {1}{2} \left (-60 x^2+15 x^3\right )}-x} \left (-2+e^{\frac {1}{2} \left (-60 x^2+15 x^3\right )} \left (-120 x+45 x^2\right )\right ) \, dx\\ &=e^{2+e^{-\frac {15}{2} \left (4 x^2-x^3\right )}-x}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.35, size = 19, normalized size = 1.00 \begin {gather*} e^{2+e^{\frac {15}{2} (-4+x) x^2}-x} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.60, size = 18, normalized size = 0.95 \begin {gather*} e^{\left (-x + e^{\left (\frac {15}{2} \, x^{3} - 30 \, x^{2}\right )} + 2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.65, size = 18, normalized size = 0.95 \begin {gather*} e^{\left (-x + e^{\left (\frac {15}{2} \, x^{3} - 30 \, x^{2}\right )} + 2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.10, size = 16, normalized size = 0.84
method | result | size |
risch | \({\mathrm e}^{{\mathrm e}^{\frac {15 \left (x -4\right ) x^{2}}{2}}-x +2}\) | \(16\) |
norman | \({\mathrm e}^{{\mathrm e}^{\frac {15}{2} x^{3}-30 x^{2}}+2-x}\) | \(19\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.67, size = 18, normalized size = 0.95 \begin {gather*} e^{\left (-x + e^{\left (\frac {15}{2} \, x^{3} - 30 \, x^{2}\right )} + 2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.10, size = 21, normalized size = 1.11 \begin {gather*} {\mathrm {e}}^{-x}\,{\mathrm {e}}^2\,{\mathrm {e}}^{{\mathrm {e}}^{\frac {15\,x^3}{2}}\,{\mathrm {e}}^{-30\,x^2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.38, size = 17, normalized size = 0.89 \begin {gather*} e^{- x + e^{\frac {15 x^{3}}{2} - 30 x^{2}} + 2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________