Optimal. Leaf size=26 \[ \frac {1}{26} e^{-3+\frac {1}{x}-x}+\frac {(1-x)^2}{x} \]
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Rubi [A]
time = 0.15, antiderivative size = 19, normalized size of antiderivative = 0.73, number of steps
used = 6, number of rules used = 3, integrand size = 38, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.079, Rules used = {12, 14, 6838}
\begin {gather*} x+\frac {1}{26} e^{-x+\frac {1}{x}-3}+\frac {1}{x} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rule 6838
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{26} \int \frac {-26+26 x^2+e^{\frac {1-3 x-x^2}{x}} \left (-1-x^2\right )}{x^2} \, dx\\ &=\frac {1}{26} \int \left (\frac {26 \left (-1+x^2\right )}{x^2}-\frac {e^{-3+\frac {1}{x}-x} \left (1+x^2\right )}{x^2}\right ) \, dx\\ &=-\left (\frac {1}{26} \int \frac {e^{-3+\frac {1}{x}-x} \left (1+x^2\right )}{x^2} \, dx\right )+\int \frac {-1+x^2}{x^2} \, dx\\ &=\frac {1}{26} e^{-3+\frac {1}{x}-x}+\int \left (1-\frac {1}{x^2}\right ) \, dx\\ &=\frac {1}{26} e^{-3+\frac {1}{x}-x}+\frac {1}{x}+x\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.03, size = 19, normalized size = 0.73 \begin {gather*} \frac {1}{26} e^{-3+\frac {1}{x}-x}+\frac {1}{x}+x \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.77, size = 22, normalized size = 0.85
method | result | size |
risch | \(x +\frac {1}{x}+\frac {{\mathrm e}^{-\frac {x^{2}+3 x -1}{x}}}{26}\) | \(22\) |
norman | \(\frac {1+x^{2}+\frac {x \,{\mathrm e}^{\frac {-x^{2}-3 x +1}{x}}}{26}}{x}\) | \(28\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.35, size = 16, normalized size = 0.62 \begin {gather*} x + \frac {1}{x} + \frac {1}{26} \, e^{\left (-x + \frac {1}{x} - 3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 28, normalized size = 1.08 \begin {gather*} \frac {26 \, x^{2} + x e^{\left (-\frac {x^{2} + 3 \, x - 1}{x}\right )} + 26}{26 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.06, size = 17, normalized size = 0.65 \begin {gather*} x + \frac {e^{\frac {- x^{2} - 3 x + 1}{x}}}{26} + \frac {1}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.42, size = 28, normalized size = 1.08 \begin {gather*} \frac {26 \, x^{2} + x e^{\left (-\frac {x^{2} + 3 \, x - 1}{x}\right )} + 26}{26 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 3.34, size = 17, normalized size = 0.65 \begin {gather*} x+\frac {1}{x}+\frac {{\mathrm {e}}^{-x}\,{\mathrm {e}}^{1/x}\,{\mathrm {e}}^{-3}}{26} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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