Optimal. Leaf size=25 \[ e^{-x+\frac {9 \left (5+\frac {x}{5}+e^{5+x} x\right )}{x}} \]
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Rubi [A] time = 0.48, antiderivative size = 27, normalized size of antiderivative = 1.08, number of steps used = 1, number of rules used = 1, integrand size = 48, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.021, Rules used = {6706} \begin {gather*} e^{\frac {-5 x^2+45 e^{x+5} x+9 x+225}{5 x}} \end {gather*}
Antiderivative was successfully verified.
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Rule 6706
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=e^{\frac {225+9 x+45 e^{5+x} x-5 x^2}{5 x}}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.21, size = 21, normalized size = 0.84 \begin {gather*} e^{\frac {9}{5}+9 e^{5+x}+\frac {45}{x}-x} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.55, size = 23, normalized size = 0.92 \begin {gather*} e^{\left (-\frac {5 \, x^{2} - 45 \, x e^{\left (x + 5\right )} - 9 \, x - 225}{5 \, x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.19, size = 17, normalized size = 0.68 \begin {gather*} e^{\left (-x + \frac {45}{x} + 9 \, e^{\left (x + 5\right )} + \frac {9}{5}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.12, size = 24, normalized size = 0.96
method | result | size |
norman | \({\mathrm e}^{\frac {45 x \,{\mathrm e}^{5+x}-5 x^{2}+9 x +225}{5 x}}\) | \(24\) |
risch | \({\mathrm e}^{-\frac {-45 x \,{\mathrm e}^{5+x}+5 x^{2}-9 x -225}{5 x}}\) | \(24\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.42, size = 17, normalized size = 0.68 \begin {gather*} e^{\left (-x + \frac {45}{x} + 9 \, e^{\left (x + 5\right )} + \frac {9}{5}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 9.30, size = 20, normalized size = 0.80 \begin {gather*} {\mathrm {e}}^{9\,{\mathrm {e}}^5\,{\mathrm {e}}^x}\,{\mathrm {e}}^{-x}\,{\mathrm {e}}^{9/5}\,{\mathrm {e}}^{45/x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.19, size = 20, normalized size = 0.80 \begin {gather*} e^{\frac {- x^{2} + 9 x e^{x + 5} + \frac {9 x}{5} + 45}{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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