Optimal. Leaf size=27 \[ -5+\frac {e^{4+2 e^{\frac {1}{4-x}}+16 \log ^2(x)}}{x^2} \]
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Rubi [B] time = 1.14, antiderivative size = 83, normalized size of antiderivative = 3.07, number of steps used = 3, number of rules used = 3, integrand size = 73, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.041, Rules used = {1594, 27, 2288} \begin {gather*} \frac {e^{2 e^{\frac {1}{4-x}}+16 \log ^2(x)+4} \left (16 \left (x^2-8 x+16\right ) \log (x)+e^{\frac {1}{4-x}} x\right )}{(4-x)^2 x^3 \left (\frac {e^{\frac {1}{4-x}}}{(4-x)^2}+\frac {16 \log (x)}{x}\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 27
Rule 1594
Rule 2288
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{4+2 e^{-\frac {1}{-4+x}}+16 \log ^2(x)} \left (-32+16 x+2 e^{-\frac {1}{-4+x}} x-2 x^2+\left (512-256 x+32 x^2\right ) \log (x)\right )}{x^3 \left (16-8 x+x^2\right )} \, dx\\ &=\int \frac {e^{4+2 e^{-\frac {1}{-4+x}}+16 \log ^2(x)} \left (-32+16 x+2 e^{-\frac {1}{-4+x}} x-2 x^2+\left (512-256 x+32 x^2\right ) \log (x)\right )}{(-4+x)^2 x^3} \, dx\\ &=\frac {e^{4+2 e^{\frac {1}{4-x}}+16 \log ^2(x)} \left (e^{\frac {1}{4-x}} x+16 \left (16-8 x+x^2\right ) \log (x)\right )}{(4-x)^2 x^3 \left (\frac {e^{\frac {1}{4-x}}}{(4-x)^2}+\frac {16 \log (x)}{x}\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 1.07, size = 25, normalized size = 0.93 \begin {gather*} \frac {e^{4+2 e^{-\frac {1}{-4+x}}+16 \log ^2(x)}}{x^2} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.81, size = 23, normalized size = 0.85 \begin {gather*} \frac {e^{\left (16 \, \log \relax (x)^{2} + 2 \, e^{\left (-\frac {1}{x - 4}\right )} + 4\right )}}{x^{2}} \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 {2 \, {\left (x^{2} - x e^{\left (-\frac {1}{x - 4}\right )} - 16 \, {\left (x^{2} - 8 \, x + 16\right )} \log \relax (x) - 8 \, x + 16\right )} e^{\left (16 \, \log \relax (x)^{2} + 2 \, e^{\left (-\frac {1}{x - 4}\right )} + 4\right )}}{x^{5} - 8 \, x^{4} + 16 \, x^{3}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 24, normalized size = 0.89
method | result | size |
risch | \(\frac {{\mathrm e}^{2 \,{\mathrm e}^{-\frac {1}{x -4}}+4+16 \ln \relax (x )^{2}}}{x^{2}}\) | \(24\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.42, size = 23, normalized size = 0.85 \begin {gather*} \frac {e^{\left (16 \, \log \relax (x)^{2} + 2 \, e^{\left (-\frac {1}{x - 4}\right )} + 4\right )}}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 7.54, size = 24, normalized size = 0.89 \begin {gather*} \frac {{\mathrm {e}}^{16\,{\ln \relax (x)}^2}\,{\mathrm {e}}^4\,{\mathrm {e}}^{2\,{\mathrm {e}}^{-\frac {1}{x-4}}}}{x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 1.09, size = 22, normalized size = 0.81 \begin {gather*} \frac {e^{4 + 2 e^{- \frac {1}{x - 4}}} e^{16 \log {\relax (x )}^{2}}}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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