Optimal. Leaf size=23 \[ -e^{\frac {3}{\log (1+\log (3 x))}}+x^3+\log (4+x) \]
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Rubi [A] time = 0.56, antiderivative size = 23, normalized size of antiderivative = 1.00, number of steps used = 7, number of rules used = 4, integrand size = 90, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.044, Rules used = {6688, 14, 1850, 6706} \begin {gather*} x^3-e^{\frac {3}{\log (\log (3 x)+1)}}+\log (x+4) \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 1850
Rule 6688
Rule 6706
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {\frac {x+12 x^3+3 x^4}{4+x}+\frac {3 e^{\frac {3}{\log (1+\log (3 x))}}}{(1+\log (3 x)) \log ^2(1+\log (3 x))}}{x} \, dx\\ &=\int \left (\frac {1+12 x^2+3 x^3}{4+x}+\frac {3 e^{\frac {3}{\log (1+\log (3 x))}}}{x (1+\log (3 x)) \log ^2(1+\log (3 x))}\right ) \, dx\\ &=3 \int \frac {e^{\frac {3}{\log (1+\log (3 x))}}}{x (1+\log (3 x)) \log ^2(1+\log (3 x))} \, dx+\int \frac {1+12 x^2+3 x^3}{4+x} \, dx\\ &=3 \operatorname {Subst}\left (\int \frac {e^{\frac {3}{\log (1+x)}}}{(1+x) \log ^2(1+x)} \, dx,x,\log (3 x)\right )+\int \left (3 x^2+\frac {1}{4+x}\right ) \, dx\\ &=-e^{\frac {3}{\log (1+\log (3 x))}}+x^3+\log (4+x)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.11, size = 23, normalized size = 1.00 \begin {gather*} -e^{\frac {3}{\log (1+\log (3 x))}}+x^3+\log (4+x) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.83, size = 22, normalized size = 0.96 \begin {gather*} x^{3} - e^{\left (\frac {3}{\log \left (\log \left (3 \, x\right ) + 1\right )}\right )} + \log \left (x + 4\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.60, size = 22, normalized size = 0.96 \begin {gather*} x^{3} - e^{\left (\frac {3}{\log \left (\log \left (3 \, x\right ) + 1\right )}\right )} + \log \left (x + 4\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 23, normalized size = 1.00
method | result | size |
risch | \(x^{3}+\ln \left (4+x \right )-{\mathrm e}^{\frac {3}{\ln \left (\ln \left (3 x \right )+1\right )}}\) | \(23\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.93, size = 47, normalized size = 2.04 \begin {gather*} x^{3} - \frac {x e^{\left (\frac {3}{\log \left (\log \relax (3) + \log \relax (x) + 1\right )}\right )}}{x + 4} - \frac {4 \, e^{\left (\frac {3}{\log \left (\log \relax (3) + \log \relax (x) + 1\right )}\right )}}{x + 4} + \log \left (x + 4\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.49, size = 22, normalized size = 0.96 \begin {gather*} \ln \left (x+4\right )-{\mathrm {e}}^{\frac {3}{\ln \left (\ln \left (3\,x\right )+1\right )}}+x^3 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.57, size = 19, normalized size = 0.83 \begin {gather*} x^{3} - e^{\frac {3}{\log {\left (\log {\left (3 x \right )} + 1 \right )}}} + \log {\left (x + 4 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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