Optimal. Leaf size=19 \[ \left (1+e^{11-\frac {2}{x}-x}-2 x\right ) x \]
________________________________________________________________________________________
Rubi [F] time = 0.30, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {x-4 x^2+e^{\frac {-2+11 x-x^2}{x}} \left (2+x-x^2\right )}{x} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (1-4 x-\frac {e^{11-\frac {2}{x}-x} (-2+x) (1+x)}{x}\right ) \, dx\\ &=x-2 x^2-\int \frac {e^{11-\frac {2}{x}-x} (-2+x) (1+x)}{x} \, dx\\ &=x-2 x^2-\int \left (-e^{11-\frac {2}{x}-x}-\frac {2 e^{11-\frac {2}{x}-x}}{x}+e^{11-\frac {2}{x}-x} x\right ) \, dx\\ &=x-2 x^2+2 \int \frac {e^{11-\frac {2}{x}-x}}{x} \, dx+\int e^{11-\frac {2}{x}-x} \, dx-\int e^{11-\frac {2}{x}-x} x \, dx\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.05, size = 19, normalized size = 1.00 \begin {gather*} \left (1+e^{11-\frac {2}{x}-x}-2 x\right ) x \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.54, size = 23, normalized size = 1.21 \begin {gather*} -2 \, x^{2} + x e^{\left (-\frac {x^{2} - 11 \, x + 2}{x}\right )} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.13, size = 23, normalized size = 1.21 \begin {gather*} -2 \, x^{2} + x e^{\left (-\frac {x^{2} - 11 \, x + 2}{x}\right )} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.16, size = 24, normalized size = 1.26
method | result | size |
risch | \(x +{\mathrm e}^{-\frac {x^{2}-11 x +2}{x}} x -2 x^{2}\) | \(24\) |
norman | \(x +x \,{\mathrm e}^{\frac {-x^{2}+11 x -2}{x}}-2 x^{2}\) | \(25\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.43, size = 20, normalized size = 1.05 \begin {gather*} -2 \, x^{2} + x e^{\left (-x - \frac {2}{x} + 11\right )} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 4.12, size = 21, normalized size = 1.11 \begin {gather*} x-2\,x^2+x\,{\mathrm {e}}^{-x}\,{\mathrm {e}}^{11}\,{\mathrm {e}}^{-\frac {2}{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.13, size = 19, normalized size = 1.00 \begin {gather*} - 2 x^{2} + x e^{\frac {- x^{2} + 11 x - 2}{x}} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________