Optimal. Leaf size=19 \[ \frac {4 e^{-5+\frac {25}{64 x}+2 x}}{x} \]
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Rubi [A] time = 0.24, antiderivative size = 35, normalized size of antiderivative = 1.84, number of steps used = 3, number of rules used = 3, integrand size = 41, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.073, Rules used = {12, 6688, 2288} \begin {gather*} -\frac {4 e^{2 x+\frac {25}{64 x}-5} \left (25-128 x^2\right )}{\left (128-\frac {25}{x^2}\right ) x^3} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2288
Rule 6688
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{16} \int \frac {e^{\frac {25-320 x+128 x^2-64 x \log (x)}{64 x}} \left (-25-64 x+128 x^2\right )}{x^2} \, dx\\ &=\frac {1}{16} \int \frac {e^{-5+\frac {25}{64 x}+2 x} \left (-25-64 x+128 x^2\right )}{x^3} \, dx\\ &=-\frac {4 e^{-5+\frac {25}{64 x}+2 x} \left (25-128 x^2\right )}{\left (128-\frac {25}{x^2}\right ) x^3}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.02, size = 19, normalized size = 1.00 \begin {gather*} \frac {4 e^{-5+\frac {25}{64 x}+2 x}}{x} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.94, size = 23, normalized size = 1.21 \begin {gather*} 4 \, e^{\left (\frac {128 \, x^{2} - 64 \, x \log \relax (x) - 320 \, x + 25}{64 \, x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 17, normalized size = 0.89 \begin {gather*} 4 \, e^{\left (2 \, x + \frac {25}{64 \, x} - \log \relax (x) - 5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.09, size = 22, normalized size = 1.16
method | result | size |
risch | \(\frac {4 \,{\mathrm e}^{\frac {128 x^{2}-320 x +25}{64 x}}}{x}\) | \(22\) |
gosper | \(4 \,{\mathrm e}^{-\frac {64 x \ln \relax (x )-128 x^{2}+320 x -25}{64 x}}\) | \(24\) |
norman | \(4 \,{\mathrm e}^{\frac {-64 x \ln \relax (x )+128 x^{2}-320 x +25}{64 x}}\) | \(24\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.41, size = 16, normalized size = 0.84 \begin {gather*} \frac {4 \, e^{\left (2 \, x + \frac {25}{64 \, x} - 5\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.63, size = 16, normalized size = 0.84 \begin {gather*} \frac {4\,{\mathrm {e}}^{2\,x+\frac {25}{64\,x}-5}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.34, size = 20, normalized size = 1.05 \begin {gather*} 4 e^{\frac {2 x^{2} - x \log {\relax (x )} - 5 x + \frac {25}{64}}{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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