Optimal. Leaf size=27 \[ -2-\left (3+e^{16 e^{-\frac {2 \left (-5+x^2\right )}{x}}}\right )^2+5 x \]
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Rubi [A] time = 1.10, antiderivative size = 25, normalized size of antiderivative = 0.93, number of steps used = 3, number of rules used = 2, integrand size = 82, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.024, Rules used = {6742, 6686} \begin {gather*} 5 x-\left (e^{16 e^{\frac {10}{x}-2 x}}+3\right )^2 \end {gather*}
Antiderivative was successfully verified.
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Rule 6686
Rule 6742
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (5+\frac {64 \exp \left (16 e^{-\frac {2 \left (-5+x^2\right )}{x}}-\frac {2 \left (-5+x^2\right )}{x}\right ) \left (3+e^{16 e^{\frac {10}{x}-2 x}}\right ) \left (5+x^2\right )}{x^2}\right ) \, dx\\ &=5 x+64 \int \frac {\exp \left (16 e^{-\frac {2 \left (-5+x^2\right )}{x}}-\frac {2 \left (-5+x^2\right )}{x}\right ) \left (3+e^{16 e^{\frac {10}{x}-2 x}}\right ) \left (5+x^2\right )}{x^2} \, dx\\ &=-\left (3+e^{16 e^{\frac {10}{x}-2 x}}\right )^2+5 x\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.33, size = 38, normalized size = 1.41 \begin {gather*} -6 e^{16 e^{\frac {10}{x}-2 x}}-e^{32 e^{\frac {10}{x}-2 x}}+5 x \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.84, size = 36, normalized size = 1.33 \begin {gather*} 5 \, x - e^{\left (32 \, e^{\left (-\frac {2 \, {\left (x^{2} - 5\right )}}{x}\right )}\right )} - 6 \, e^{\left (16 \, e^{\left (-\frac {2 \, {\left (x^{2} - 5\right )}}{x}\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {{\left (5 \, x^{2} e^{\left (\frac {2 \, {\left (x^{2} - 5\right )}}{x}\right )} + 64 \, {\left (x^{2} + 5\right )} e^{\left (32 \, e^{\left (-\frac {2 \, {\left (x^{2} - 5\right )}}{x}\right )}\right )} + 192 \, {\left (x^{2} + 5\right )} e^{\left (16 \, e^{\left (-\frac {2 \, {\left (x^{2} - 5\right )}}{x}\right )}\right )}\right )} e^{\left (-\frac {2 \, {\left (x^{2} - 5\right )}}{x}\right )}}{x^{2}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.14, size = 37, normalized size = 1.37
method | result | size |
risch | \(-{\mathrm e}^{32 \,{\mathrm e}^{-\frac {2 \left (x^{2}-5\right )}{x}}}+5 x -6 \,{\mathrm e}^{16 \,{\mathrm e}^{-\frac {2 \left (x^{2}-5\right )}{x}}}\) | \(37\) |
norman | \(\frac {\left (5 x^{2} {\mathrm e}^{\frac {2 x^{2}-10}{x}}-x \,{\mathrm e}^{\frac {2 x^{2}-10}{x}} {\mathrm e}^{32 \,{\mathrm e}^{-\frac {2 \left (x^{2}-5\right )}{x}}}-6 \,{\mathrm e}^{\frac {2 x^{2}-10}{x}} {\mathrm e}^{16 \,{\mathrm e}^{-\frac {2 \left (x^{2}-5\right )}{x}}} x \right ) {\mathrm e}^{-\frac {2 \left (x^{2}-5\right )}{x}}}{x}\) | \(97\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.48, size = 34, normalized size = 1.26 \begin {gather*} 5 \, x - e^{\left (32 \, e^{\left (-2 \, x + \frac {10}{x}\right )}\right )} - 6 \, e^{\left (16 \, e^{\left (-2 \, x + \frac {10}{x}\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.28, size = 34, normalized size = 1.26 \begin {gather*} 5\,x-6\,{\mathrm {e}}^{16\,{\mathrm {e}}^{-2\,x}\,{\mathrm {e}}^{10/x}}-{\mathrm {e}}^{32\,{\mathrm {e}}^{-2\,x}\,{\mathrm {e}}^{10/x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.39, size = 31, normalized size = 1.15 \begin {gather*} 5 x - e^{32 e^{- \frac {2 \left (x^{2} - 5\right )}{x}}} - 6 e^{16 e^{- \frac {2 \left (x^{2} - 5\right )}{x}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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