Optimal. Leaf size=21 \[ -3+e^{-3+\frac {9}{x}}-e^{\frac {2}{5}+x}+x \]
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Rubi [A] time = 0.05, antiderivative size = 20, normalized size of antiderivative = 0.95, number of steps used = 6, number of rules used = 3, integrand size = 37, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.081, Rules used = {14, 2194, 2209} \begin {gather*} x+e^{\frac {9}{x}-3}-e^{x+\frac {2}{5}} \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 2194
Rule 2209
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-e^{\frac {2}{5}+x}+\frac {-9 e^{9/x}+e^3 x^2}{e^3 x^2}\right ) \, dx\\ &=\frac {\int \frac {-9 e^{9/x}+e^3 x^2}{x^2} \, dx}{e^3}-\int e^{\frac {2}{5}+x} \, dx\\ &=-e^{\frac {2}{5}+x}+\frac {\int \left (e^3-\frac {9 e^{9/x}}{x^2}\right ) \, dx}{e^3}\\ &=-e^{\frac {2}{5}+x}+x-\frac {9 \int \frac {e^{9/x}}{x^2} \, dx}{e^3}\\ &=e^{-3+\frac {9}{x}}-e^{\frac {2}{5}+x}+x\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.02, size = 20, normalized size = 0.95 \begin {gather*} e^{-3+\frac {9}{x}}-e^{\frac {2}{5}+x}+x \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.68, size = 17, normalized size = 0.81 \begin {gather*} x - e^{\left (x + \frac {2}{5}\right )} + e^{\left (-\frac {3 \, {\left (x - 3\right )}}{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 16, normalized size = 0.76 \begin {gather*} x - e^{\left (x + \frac {2}{5}\right )} + e^{\left (\frac {9}{x} - 3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 18, normalized size = 0.86
method | result | size |
default | \(x -{\mathrm e}^{x} {\mathrm e}^{\frac {2}{5}}+{\mathrm e}^{\frac {9}{x}} {\mathrm e}^{-3}\) | \(18\) |
risch | \(x -{\mathrm e}^{x +\frac {2}{5}}+{\mathrm e}^{-\frac {3 \left (x -3\right )}{x}}\) | \(18\) |
norman | \(\frac {x^{2}+x \,{\mathrm e}^{\frac {-3 x +9}{x}}-x \,{\mathrm e}^{x +\frac {2}{5}}}{x}\) | \(28\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.37, size = 16, normalized size = 0.76 \begin {gather*} x - e^{\left (x + \frac {2}{5}\right )} + e^{\left (\frac {9}{x} - 3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.16, size = 17, normalized size = 0.81 \begin {gather*} x+{\mathrm {e}}^{-3}\,{\mathrm {e}}^{9/x}-{\mathrm {e}}^{2/5}\,{\mathrm {e}}^x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.28, size = 15, normalized size = 0.71 \begin {gather*} x + e^{\frac {9 - 3 x}{x}} - e^{x + \frac {2}{5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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