Optimal. Leaf size=18 \[ \frac {1}{10} \left (-e^{2-\frac {2}{x}+x}+x\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.13, antiderivative size = 20, normalized size of antiderivative = 1.11, number of steps
used = 4, number of rules used = 3, integrand size = 33, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {12, 14, 6838}
\begin {gather*} \frac {x}{10}-\frac {1}{10} e^{x-\frac {2}{x}+2} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 14
Rule 6838
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{10} \int \frac {x^2+e^{\frac {-2+2 x+x^2}{x}} \left (-2-x^2\right )}{x^2} \, dx\\ &=\frac {1}{10} \int \left (1-\frac {e^{2-\frac {2}{x}+x} \left (2+x^2\right )}{x^2}\right ) \, dx\\ &=\frac {x}{10}-\frac {1}{10} \int \frac {e^{2-\frac {2}{x}+x} \left (2+x^2\right )}{x^2} \, dx\\ &=-\frac {1}{10} e^{2-\frac {2}{x}+x}+\frac {x}{10}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.05, size = 18, normalized size = 1.00 \begin {gather*} \frac {1}{10} \left (-e^{2-\frac {2}{x}+x}+x\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 1.27, size = 20, normalized size = 1.11
method | result | size |
risch | \(\frac {x}{10}-\frac {{\mathrm e}^{\frac {x^{2}+2 x -2}{x}}}{10}\) | \(20\) |
norman | \(\frac {\frac {x^{2}}{10}-\frac {x \,{\mathrm e}^{\frac {x^{2}+2 x -2}{x}}}{10}}{x}\) | \(27\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.31, size = 15, normalized size = 0.83 \begin {gather*} \frac {1}{10} \, x - \frac {1}{10} \, e^{\left (x - \frac {2}{x} + 2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.35, size = 19, normalized size = 1.06 \begin {gather*} \frac {1}{10} \, x - \frac {1}{10} \, e^{\left (\frac {x^{2} + 2 \, x - 2}{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.09, size = 15, normalized size = 0.83 \begin {gather*} \frac {x}{10} - \frac {e^{\frac {x^{2} + 2 x - 2}{x}}}{10} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.40, size = 19, normalized size = 1.06 \begin {gather*} \frac {1}{10} \, x - \frac {1}{10} \, e^{\left (\frac {x^{2} + 2 \, x - 2}{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 5.84, size = 16, normalized size = 0.89 \begin {gather*} \frac {x}{10}-\frac {{\mathrm {e}}^2\,{\mathrm {e}}^{-\frac {2}{x}}\,{\mathrm {e}}^x}{10} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________