Optimal. Leaf size=28 \[ e^2 \left (-\frac {2 e^{\left (-5+e^x-x-x^2\right )^2}}{x}+x\right ) \]
________________________________________________________________________________________
Rubi [B] time = 11.39, antiderivative size = 138, normalized size of antiderivative = 4.93, number of steps used = 3, number of rules used = 2, integrand size = 107, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.019, Rules used = {14, 2288} \begin {gather*} e^2 x-\frac {2 \left (2 x^4-e^x x^3+3 x^3-3 e^x x^2+11 x^2-6 e^x x+e^{2 x} x+5 x\right ) \exp \left (x^4+2 x^3+11 x^2-2 e^x \left (x^2+x+5\right )+10 x+e^{2 x}+27\right )}{x^2 \left (2 x^3+3 x^2-e^x \left (x^2+x+5\right )+11 x+e^{2 x}-e^x (2 x+1)+5\right )} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 14
Rule 2288
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (e^2-\frac {2 \exp \left (27+e^{2 x}+10 x+11 x^2+2 x^3+x^4-2 e^x \left (5+x+x^2\right )\right ) \left (-1+10 x-12 e^x x+2 e^{2 x} x+22 x^2-6 e^x x^2+6 x^3-2 e^x x^3+4 x^4\right )}{x^2}\right ) \, dx\\ &=e^2 x-2 \int \frac {\exp \left (27+e^{2 x}+10 x+11 x^2+2 x^3+x^4-2 e^x \left (5+x+x^2\right )\right ) \left (-1+10 x-12 e^x x+2 e^{2 x} x+22 x^2-6 e^x x^2+6 x^3-2 e^x x^3+4 x^4\right )}{x^2} \, dx\\ &=e^2 x-\frac {2 \exp \left (27+e^{2 x}+10 x+11 x^2+2 x^3+x^4-2 e^x \left (5+x+x^2\right )\right ) \left (5 x-6 e^x x+e^{2 x} x+11 x^2-3 e^x x^2+3 x^3-e^x x^3+2 x^4\right )}{x^2 \left (5+e^{2 x}+11 x+3 x^2+2 x^3-e^x (1+2 x)-e^x \left (5+x+x^2\right )\right )}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.17, size = 47, normalized size = 1.68 \begin {gather*} -\frac {2 e^{27+e^{2 x}+10 x+11 x^2+2 x^3+x^4-2 e^x \left (5+x+x^2\right )}}{x}+e^2 x \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [B] time = 0.68, size = 59, normalized size = 2.11 \begin {gather*} \frac {x^{2} e^{2} - 2 \, e^{\left ({\left ({\left (x^{4} + 2 \, x^{3} + 11 \, x^{2} + 10 \, x + 25\right )} e^{4} - 2 \, {\left (x^{2} + x + 5\right )} e^{\left (x + 4\right )} + e^{\left (2 \, x + 4\right )}\right )} e^{\left (-4\right )} + 2\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [B] time = 0.24, size = 52, normalized size = 1.86 \begin {gather*} \frac {x^{2} e^{2} - 2 \, e^{\left (x^{4} + 2 \, x^{3} - 2 \, x^{2} e^{x} + 11 \, x^{2} - 2 \, x e^{x} + 10 \, x + e^{\left (2 \, x\right )} - 10 \, e^{x} + 27\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.15, size = 50, normalized size = 1.79
method | result | size |
risch | \({\mathrm e}^{2} x -\frac {2 \,{\mathrm e}^{27+x^{4}-2 \,{\mathrm e}^{x} x^{2}+2 x^{3}-2 \,{\mathrm e}^{x} x +11 x^{2}-10 \,{\mathrm e}^{x}+{\mathrm e}^{2 x}+10 x}}{x}\) | \(50\) |
norman | \(\frac {x^{2} {\mathrm e}^{2}-2 \,{\mathrm e}^{2} {\mathrm e}^{{\mathrm e}^{2 x}+\left (-2 x^{2}-2 x -10\right ) {\mathrm e}^{x}+x^{4}+2 x^{3}+11 x^{2}+10 x +25}}{x}\) | \(52\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [B] time = 0.51, size = 49, normalized size = 1.75 \begin {gather*} x e^{2} - \frac {2 \, e^{\left (x^{4} + 2 \, x^{3} - 2 \, x^{2} e^{x} + 11 \, x^{2} - 2 \, x e^{x} + 10 \, x + e^{\left (2 \, x\right )} - 10 \, e^{x} + 27\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.36, size = 56, normalized size = 2.00 \begin {gather*} x\,{\mathrm {e}}^2-\frac {2\,{\mathrm {e}}^{-2\,x\,{\mathrm {e}}^x}\,{\mathrm {e}}^{10\,x}\,{\mathrm {e}}^{x^4}\,{\mathrm {e}}^{27}\,{\mathrm {e}}^{-2\,x^2\,{\mathrm {e}}^x}\,{\mathrm {e}}^{2\,x^3}\,{\mathrm {e}}^{11\,x^2}\,{\mathrm {e}}^{{\mathrm {e}}^{2\,x}}\,{\mathrm {e}}^{-10\,{\mathrm {e}}^x}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [B] time = 0.28, size = 51, normalized size = 1.82 \begin {gather*} x e^{2} - \frac {2 e^{2} e^{x^{4} + 2 x^{3} + 11 x^{2} + 10 x + \left (- 2 x^{2} - 2 x - 10\right ) e^{x} + e^{2 x} + 25}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________