Optimal. Leaf size=30 \[ 5+e^x+\frac {1}{5} \left (e^4+e^{e^5-\frac {1+e}{2 x}+x}\right ) \]
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Rubi [F] time = 0.15, 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 {10 e^x x^2+e^{\frac {-1-e+2 e^5 x+2 x^2}{2 x}} \left (1+e+2 x^2\right )}{10 x^2} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{10} \int \frac {10 e^x x^2+e^{\frac {-1-e+2 e^5 x+2 x^2}{2 x}} \left (1+e+2 x^2\right )}{x^2} \, dx\\ &=\frac {1}{10} \int \left (10 e^x+2 e^{e^5-\frac {1+e}{2 x}+x}+\frac {e^{e^5-\frac {1+e}{2 x}+x} (1+e)}{x^2}\right ) \, dx\\ &=\frac {1}{5} \int e^{e^5-\frac {1+e}{2 x}+x} \, dx+\frac {1}{10} (1+e) \int \frac {e^{e^5-\frac {1+e}{2 x}+x}}{x^2} \, dx+\int e^x \, dx\\ &=e^x+\frac {1}{5} \int e^{e^5-\frac {1+e}{2 x}+x} \, dx+\frac {1}{10} (1+e) \int \frac {e^{e^5-\frac {1+e}{2 x}+x}}{x^2} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.14, size = 27, normalized size = 0.90 \begin {gather*} e^x+\frac {1}{5} e^{e^5+\frac {-1-e}{2 x}+x} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.61, size = 27, normalized size = 0.90 \begin {gather*} e^{x} + \frac {1}{5} \, e^{\left (\frac {2 \, x^{2} + 2 \, x e^{5} - e - 1}{2 \, x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.46, size = 27, normalized size = 0.90 \begin {gather*} e^{x} + \frac {1}{5} \, e^{\left (\frac {2 \, x^{2} + 2 \, x e^{5} - e - 1}{2 \, x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.09, size = 26, normalized size = 0.87
method | result | size |
risch | \({\mathrm e}^{x}+\frac {{\mathrm e}^{-\frac {-2 x \,{\mathrm e}^{5}+{\mathrm e}-2 x^{2}+1}{2 x}}}{5}\) | \(26\) |
norman | \(\frac {{\mathrm e}^{x} x +\frac {x \,{\mathrm e}^{\frac {2 x \,{\mathrm e}^{5}-{\mathrm e}+2 x^{2}-1}{2 x}}}{5}}{x}\) | \(35\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.74, size = 22, normalized size = 0.73 \begin {gather*} \frac {1}{5} \, e^{\left (x - \frac {e}{2 \, x} - \frac {1}{2 \, x} + e^{5}\right )} + e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.39, size = 22, normalized size = 0.73 \begin {gather*} \frac {{\mathrm {e}}^{x+{\mathrm {e}}^5-\frac {\mathrm {e}}{2\,x}-\frac {1}{2\,x}}}{5}+{\mathrm {e}}^x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.23, size = 24, normalized size = 0.80 \begin {gather*} e^{x} + \frac {e^{\frac {x^{2} + x e^{5} - \frac {e}{2} - \frac {1}{2}}{x}}}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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