Optimal. Leaf size=24 \[ e^3+x+\frac {4+e^{e^2}}{-16 x+(4+x)^2} \]
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Rubi [A] time = 0.04, antiderivative size = 17, normalized size of antiderivative = 0.71, number of steps used = 2, number of rules used = 1, integrand size = 36, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.028, Rules used = {2074} \begin {gather*} x+\frac {4+e^{e^2}}{(4-x)^2} \end {gather*}
Antiderivative was successfully verified.
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Rule 2074
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (1-\frac {2 \left (4+e^{e^2}\right )}{(-4+x)^3}\right ) \, dx\\ &=\frac {4+e^{e^2}}{(4-x)^2}+x\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.02, size = 15, normalized size = 0.62 \begin {gather*} \frac {4+e^{e^2}}{(-4+x)^2}+x \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.60, size = 27, normalized size = 1.12 \begin {gather*} \frac {x^{3} - 8 \, x^{2} + 16 \, x + e^{\left (e^{2}\right )} + 4}{x^{2} - 8 \, x + 16} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.18, size = 13, normalized size = 0.54 \begin {gather*} x + \frac {e^{\left (e^{2}\right )} + 4}{{\left (x - 4\right )}^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 17, normalized size = 0.71
method | result | size |
default | \(x -\frac {-8-2 \,{\mathrm e}^{{\mathrm e}^{2}}}{2 \left (x -4\right )^{2}}\) | \(17\) |
norman | \(\frac {x^{3}+{\mathrm e}^{{\mathrm e}^{2}}-48 x +132}{\left (x -4\right )^{2}}\) | \(18\) |
gosper | \(\frac {x^{3}+{\mathrm e}^{{\mathrm e}^{2}}-48 x +132}{x^{2}-8 x +16}\) | \(23\) |
risch | \(x +\frac {{\mathrm e}^{{\mathrm e}^{2}}}{x^{2}-8 x +16}+\frac {4}{x^{2}-8 x +16}\) | \(29\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 18, normalized size = 0.75 \begin {gather*} x + \frac {e^{\left (e^{2}\right )} + 4}{x^{2} - 8 \, x + 16} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.06, size = 13, normalized size = 0.54 \begin {gather*} x+\frac {{\mathrm {e}}^{{\mathrm {e}}^2}+4}{{\left (x-4\right )}^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.16, size = 15, normalized size = 0.62 \begin {gather*} x + \frac {4 + e^{e^{2}}}{x^{2} - 8 x + 16} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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