Optimal. Leaf size=25 \[ \frac {e^{9 (-4+x)^2 x^2}}{(-4+x) (2+\log (\log (4)))} \]
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Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(77\) vs. \(2(25)=50\).
time = 0.29, antiderivative size = 77, normalized size of antiderivative = 3.08, number of steps
used = 1, number of rules used = 1, integrand size = 63, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.016, Rules used = {2326}
\begin {gather*} -\frac {e^{9 x^4-72 x^3+144 x^2} \left (-x^4+10 x^3-32 x^2+32 x\right )}{\left (x^3-6 x^2+8 x\right ) \left (2 x^2+\left (x^2-8 x+16\right ) \log (\log (4))-16 x+32\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 2326
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\frac {e^{144 x^2-72 x^3+9 x^4} \left (32 x-32 x^2+10 x^3-x^4\right )}{\left (8 x-6 x^2+x^3\right ) \left (32-16 x+2 x^2+\left (16-8 x+x^2\right ) \log (\log (4))\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.14, size = 25, normalized size = 1.00 \begin {gather*} \frac {e^{9 (-4+x)^2 x^2}}{(-4+x) (2+\log (\log (4)))} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 1.65, size = 27, normalized size = 1.08
method | result | size |
risch | \(\frac {{\mathrm e}^{9 \left (x -4\right )^{2} x^{2}}}{\left (\ln \left (2\right )+\ln \left (\ln \left (2\right )\right )+2\right ) \left (x -4\right )}\) | \(27\) |
norman | \(\frac {{\mathrm e}^{9 x^{4}-72 x^{3}+144 x^{2}}}{\left (\ln \left (2\right )+\ln \left (\ln \left (2\right )\right )+2\right ) \left (x -4\right )}\) | \(33\) |
gosper | \(\frac {{\mathrm e}^{9 x^{4}-72 x^{3}+144 x^{2}}}{x \ln \left (2 \ln \left (2\right )\right )-4 \ln \left (2 \ln \left (2\right )\right )+2 x -8}\) | \(40\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.57, size = 40, normalized size = 1.60 \begin {gather*} \frac {e^{\left (9 \, x^{4} - 72 \, x^{3} + 144 \, x^{2}\right )}}{x {\left (\log \left (2\right ) + \log \left (\log \left (2\right )\right ) + 2\right )} - 4 \, \log \left (2\right ) - 4 \, \log \left (\log \left (2\right )\right ) - 8} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 34, normalized size = 1.36 \begin {gather*} \frac {e^{\left (9 \, x^{4} - 72 \, x^{3} + 144 \, x^{2}\right )}}{{\left (x - 4\right )} \log \left (2 \, \log \left (2\right )\right ) + 2 \, x - 8} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.10, size = 44, normalized size = 1.76 \begin {gather*} \frac {e^{9 x^{4} - 72 x^{3} + 144 x^{2}}}{x \log {\left (\log {\left (2 \right )} \right )} + x \log {\left (2 \right )} + 2 x - 8 - 4 \log {\left (2 \right )} - 4 \log {\left (\log {\left (2 \right )} \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 43, normalized size = 1.72 \begin {gather*} \frac {e^{\left (9 \, x^{4} - 72 \, x^{3} + 144 \, x^{2}\right )}}{x \log \left (2\right ) + x \log \left (\log \left (2\right )\right ) + 2 \, x - 4 \, \log \left (2\right ) - 4 \, \log \left (\log \left (2\right )\right ) - 8} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [F]
time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int -\frac {{\mathrm {e}}^{9\,x^4-72\,x^3+144\,x^2}\,\left (-36\,x^4+360\,x^3-1152\,x^2+1152\,x+1\right )}{\ln \left (2\,\ln \left (2\right )\right )\,\left (x^2-8\,x+16\right )-16\,x+2\,x^2+32} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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