Optimal. Leaf size=30 \[ e^{1-e^x-e^{\log ^2(-2+x)}+2 x+\log ^2\left ((-4+x)^2\right )} \]
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Rubi [A] time = 4.55, antiderivative size = 33, normalized size of antiderivative = 1.10, number of steps used = 1, number of rules used = 1, integrand size = 101, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.010, Rules used = {6706} \begin {gather*} e^{\log ^2\left (x^2-8 x+16\right )-e^x+2 x-e^{\log ^2(x-2)}+1} \end {gather*}
Antiderivative was successfully verified.
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Rule 6706
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\exp \left (1-e^x-e^{\log ^2(-2+x)}+2 x+\log ^2\left (16-8 x+x^2\right )\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.26, size = 30, normalized size = 1.00 \begin {gather*} e^{1-e^x-e^{\log ^2(-2+x)}+2 x+\log ^2\left ((-4+x)^2\right )} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.57, size = 30, normalized size = 1.00 \begin {gather*} e^{\left (\log \left (x^{2} - 8 \, x + 16\right )^{2} + 2 \, x - e^{\left (\log \left (x - 2\right )^{2}\right )} - e^{x} + 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.29, size = 30, normalized size = 1.00 \begin {gather*} e^{\left (\log \left (x^{2} - 8 \, x + 16\right )^{2} + 2 \, x - e^{\left (\log \left (x - 2\right )^{2}\right )} - e^{x} + 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [C] time = 0.64, size = 175, normalized size = 5.83
method | result | size |
risch | \(\left (x -4\right )^{-4 i \pi \,\mathrm {csgn}\left (i \left (x -4\right )^{2}\right )} \left (x -4\right )^{4 i \pi \,\mathrm {csgn}\left (i \left (x -4\right )\right )} {\mathrm e}^{-{\mathrm e}^{\ln \left (x -2\right )^{2}}+4 \ln \left (x -4\right )^{2}+1-\frac {\pi ^{2} \mathrm {csgn}\left (i \left (x -4\right )^{2}\right )^{6}}{4}+\pi ^{2} \mathrm {csgn}\left (i \left (x -4\right )^{2}\right )^{5} \mathrm {csgn}\left (i \left (x -4\right )\right )-\frac {3 \pi ^{2} \mathrm {csgn}\left (i \left (x -4\right )^{2}\right )^{4} \mathrm {csgn}\left (i \left (x -4\right )\right )^{2}}{2}+\pi ^{2} \mathrm {csgn}\left (i \left (x -4\right )^{2}\right )^{3} \mathrm {csgn}\left (i \left (x -4\right )\right )^{3}-\frac {\pi ^{2} \mathrm {csgn}\left (i \left (x -4\right )^{2}\right )^{2} \mathrm {csgn}\left (i \left (x -4\right )\right )^{4}}{4}-{\mathrm e}^{x}+2 x}\) | \(175\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.55, size = 27, normalized size = 0.90 \begin {gather*} e^{\left (4 \, \log \left (x - 4\right )^{2} + 2 \, x - e^{\left (\log \left (x - 2\right )^{2}\right )} - e^{x} + 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.27, size = 34, normalized size = 1.13 \begin {gather*} {\mathrm {e}}^{2\,x}\,{\mathrm {e}}^{{\ln \left (x^2-8\,x+16\right )}^2}\,\mathrm {e}\,{\mathrm {e}}^{-{\mathrm {e}}^x}\,{\mathrm {e}}^{-{\mathrm {e}}^{{\ln \left (x-2\right )}^2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 3.85, size = 29, normalized size = 0.97 \begin {gather*} e^{2 x - e^{x} - e^{\log {\left (x - 2 \right )}^{2}} + \log {\left (x^{2} - 8 x + 16 \right )}^{2} + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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