Optimal. Leaf size=30 \[ x+e^{25+\left (11-e^5\right )^2+\left (\frac {x}{3}-x^2\right )^2} x \]
________________________________________________________________________________________
Rubi [B] time = 0.08, antiderivative size = 63, normalized size of antiderivative = 2.10, number of steps used = 3, number of rules used = 2, integrand size = 55, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.036, Rules used = {12, 2288} \begin {gather*} \frac {\left (18 x^4-9 x^3+x^2\right ) \exp \left (\frac {1}{9} \left (9 x^4-6 x^3+x^2+9 \left (146-22 e^5+e^{10}\right )\right )\right )}{18 x^3-9 x^2+x}+x \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 2288
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{9} \int \left (9+e^{\frac {1}{9} \left (1314-198 e^5+9 e^{10}+x^2-6 x^3+9 x^4\right )} \left (9+2 x^2-18 x^3+36 x^4\right )\right ) \, dx\\ &=x+\frac {1}{9} \int e^{\frac {1}{9} \left (1314-198 e^5+9 e^{10}+x^2-6 x^3+9 x^4\right )} \left (9+2 x^2-18 x^3+36 x^4\right ) \, dx\\ &=x+\frac {\exp \left (\frac {1}{9} \left (9 \left (146-22 e^5+e^{10}\right )+x^2-6 x^3+9 x^4\right )\right ) \left (x^2-9 x^3+18 x^4\right )}{x-9 x^2+18 x^3}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.06, size = 33, normalized size = 1.10 \begin {gather*} \left (1+e^{146-22 e^5+e^{10}+\frac {x^2}{9}-\frac {2 x^3}{3}+x^4}\right ) x \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 1.03, size = 26, normalized size = 0.87 \begin {gather*} x e^{\left (x^{4} - \frac {2}{3} \, x^{3} + \frac {1}{9} \, x^{2} + e^{10} - 22 \, e^{5} + 146\right )} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.18, size = 26, normalized size = 0.87 \begin {gather*} x e^{\left (x^{4} - \frac {2}{3} \, x^{3} + \frac {1}{9} \, x^{2} + e^{10} - 22 \, e^{5} + 146\right )} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.08, size = 27, normalized size = 0.90
method | result | size |
risch | \(x +x \,{\mathrm e}^{{\mathrm e}^{10}-22 \,{\mathrm e}^{5}+x^{4}-\frac {2 x^{3}}{3}+\frac {x^{2}}{9}+146}\) | \(27\) |
default | \(x +x \,{\mathrm e}^{{\mathrm e}^{10}-22 \,{\mathrm e}^{5}+x^{4}-\frac {2 x^{3}}{3}+\frac {x^{2}}{9}+146}\) | \(29\) |
norman | \(x +x \,{\mathrm e}^{{\mathrm e}^{10}-22 \,{\mathrm e}^{5}+x^{4}-\frac {2 x^{3}}{3}+\frac {x^{2}}{9}+146}\) | \(29\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.62, size = 26, normalized size = 0.87 \begin {gather*} x e^{\left (x^{4} - \frac {2}{3} \, x^{3} + \frac {1}{9} \, x^{2} + e^{10} - 22 \, e^{5} + 146\right )} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 1.40, size = 30, normalized size = 1.00 \begin {gather*} x+\frac {x\,{\left ({\mathrm {e}}^{x^2}\right )}^{1/9}\,{\mathrm {e}}^{-22\,{\mathrm {e}}^5}\,{\mathrm {e}}^{x^4}\,{\mathrm {e}}^{146}\,{\mathrm {e}}^{{\mathrm {e}}^{10}}}{{\left ({\mathrm {e}}^{x^3}\right )}^{2/3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.14, size = 29, normalized size = 0.97 \begin {gather*} x e^{x^{4} - \frac {2 x^{3}}{3} + \frac {x^{2}}{9} - 22 e^{5} + 146 + e^{10}} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________