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] Leaf count is larger than twice the leaf count of optimal. \(83\) vs. \(2(27)=54\).
time = 1.21, 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 = {1608, 27, 2326}
\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 1608
Rule 2326
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 = 0.64, 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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Maple [A]
time = 0.17, size = 24, normalized size = 0.89
method | result | size |
risch | \(\frac {{\mathrm e}^{2 \,{\mathrm e}^{-\frac {1}{x -4}}+4+16 \ln \left (x \right )^{2}}}{x^{2}}\) | \(24\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.31, size = 23, normalized size = 0.85 \begin {gather*} \frac {e^{\left (16 \, \log \left (x\right )^{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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Fricas [A]
time = 0.37, size = 23, normalized size = 0.85 \begin {gather*} \frac {e^{\left (16 \, \log \left (x\right )^{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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Sympy [A]
time = 0.61, size = 22, normalized size = 0.81 \begin {gather*} \frac {e^{4 + 2 e^{- \frac {1}{x - 4}}} e^{16 \log {\left (x \right )}^{2}}}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 57 vs.
\(2 (25) = 50\).
time = 0.43, size = 57, normalized size = 2.11 \begin {gather*} \frac {e^{\left (\frac {64 \, x \log \left (x\right )^{2} + 8 \, x e^{\left (-\frac {1}{x - 4}\right )} - 256 \, \log \left (x\right )^{2} - x - 32 \, e^{\left (-\frac {1}{x - 4}\right )}}{4 \, {\left (x - 4\right )}} + \frac {1}{x - 4} + \frac {17}{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 \left (x\right )}^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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