Optimal. Leaf size=15 \[ x-\log \left (\frac {1}{x^3 (3+\log (x))}\right ) \]
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Rubi [A]
time = 0.14, antiderivative size = 11, normalized size of antiderivative = 0.73, number of steps
used = 7, number of rules used = 5, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.227, Rules used = {2641, 6874, 45,
2339, 29} \begin {gather*} x+3 \log (x)+\log (\log (x)+3) \end {gather*}
Antiderivative was successfully verified.
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Rule 29
Rule 45
Rule 2339
Rule 2641
Rule 6874
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {10+3 x+(3+x) \log (x)}{x (3+\log (x))} \, dx\\ &=\int \left (\frac {3+x}{x}+\frac {1}{x (3+\log (x))}\right ) \, dx\\ &=\int \frac {3+x}{x} \, dx+\int \frac {1}{x (3+\log (x))} \, dx\\ &=\int \left (1+\frac {3}{x}\right ) \, dx+\text {Subst}\left (\int \frac {1}{x} \, dx,x,3+\log (x)\right )\\ &=x+3 \log (x)+\log (3+\log (x))\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.04, size = 11, normalized size = 0.73 \begin {gather*} x+3 \log (x)+\log (3+\log (x)) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 2.77, size = 12, normalized size = 0.80
method | result | size |
default | \(x +\ln \left (3+\ln \left (x \right )\right )+3 \ln \left (x \right )\) | \(12\) |
norman | \(x +\ln \left (3+\ln \left (x \right )\right )+3 \ln \left (x \right )\) | \(12\) |
risch | \(x +\ln \left (3+\ln \left (x \right )\right )+3 \ln \left (x \right )\) | \(12\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 11, normalized size = 0.73 \begin {gather*} x + 3 \, \log \left (x\right ) + \log \left (\log \left (x\right ) + 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 11, normalized size = 0.73 \begin {gather*} x + 3 \, \log \left (x\right ) + \log \left (\log \left (x\right ) + 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.05, size = 12, normalized size = 0.80 \begin {gather*} x + 3 \log {\left (x \right )} + \log {\left (\log {\left (x \right )} + 3 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 11, normalized size = 0.73 \begin {gather*} x + 3 \, \log \left (x\right ) + \log \left (\log \left (x\right ) + 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 4.74, size = 11, normalized size = 0.73 \begin {gather*} x+\ln \left (\ln \left (x\right )+3\right )+3\,\ln \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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