Optimal. Leaf size=24 \[ \log \left (4 \log \left (1+3 \left (625+\frac {1+e^{2 x}}{x}\right )+x^2\right )\right ) \]
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Rubi [A] time = 0.15, antiderivative size = 21, normalized size of antiderivative = 0.88, 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 = {6684} \begin {gather*} \log \left (\log \left (\frac {x^3+1876 x+3 e^{2 x}+3}{x}\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 6684
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\log \left (\log \left (\frac {3+3 e^{2 x}+1876 x+x^3}{x}\right )\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.42, size = 21, normalized size = 0.88 \begin {gather*} \log \left (\log \left (\frac {3+3 e^{2 x}+1876 x+x^3}{x}\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.65, size = 20, normalized size = 0.83 \begin {gather*} \log \left (\log \left (\frac {x^{3} + 1876 \, x + 3 \, e^{\left (2 \, x\right )} + 3}{x}\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.20, size = 20, normalized size = 0.83 \begin {gather*} \log \left (\log \left (\frac {x^{3} + 1876 \, x + 3 \, e^{\left (2 \, x\right )} + 3}{x}\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.12, size = 21, normalized size = 0.88
method | result | size |
norman | \(\ln \left (\ln \left (\frac {3 \,{\mathrm e}^{2 x}+x^{3}+1876 x +3}{x}\right )\right )\) | \(21\) |
risch | \(\ln \left (\ln \left (3 \,{\mathrm e}^{2 x}+x^{3}+1876 x +3\right )-\frac {i \left (\pi \,\mathrm {csgn}\left (\frac {i}{x}\right ) \mathrm {csgn}\left (i \left (3 \,{\mathrm e}^{2 x}+x^{3}+1876 x +3\right )\right ) \mathrm {csgn}\left (\frac {i \left (3 \,{\mathrm e}^{2 x}+x^{3}+1876 x +3\right )}{x}\right )-\pi \,\mathrm {csgn}\left (\frac {i}{x}\right ) \mathrm {csgn}\left (\frac {i \left (3 \,{\mathrm e}^{2 x}+x^{3}+1876 x +3\right )}{x}\right )^{2}-\pi \,\mathrm {csgn}\left (i \left (3 \,{\mathrm e}^{2 x}+x^{3}+1876 x +3\right )\right ) \mathrm {csgn}\left (\frac {i \left (3 \,{\mathrm e}^{2 x}+x^{3}+1876 x +3\right )}{x}\right )^{2}+\pi \mathrm {csgn}\left (\frac {i \left (3 \,{\mathrm e}^{2 x}+x^{3}+1876 x +3\right )}{x}\right )^{3}-2 i \ln \relax (x )\right )}{2}\right )\) | \(177\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.40, size = 21, normalized size = 0.88 \begin {gather*} \log \left (\log \left (x^{3} + 1876 \, x + 3 \, e^{\left (2 \, x\right )} + 3\right ) - \log \relax (x)\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 8.15, size = 20, normalized size = 0.83 \begin {gather*} \ln \left (\ln \left (\frac {1876\,x+3\,{\mathrm {e}}^{2\,x}+x^3+3}{x}\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.49, size = 19, normalized size = 0.79 \begin {gather*} \log {\left (\log {\left (\frac {x^{3} + 1876 x + 3 e^{2 x} + 3}{x} \right )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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