Optimal. Leaf size=20 \[ \log \left (2 e^{-2+\frac {4}{6+x-\log (4+x)}}\right ) \]
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Rubi [A] time = 0.12, antiderivative size = 13, normalized size of antiderivative = 0.65, number of steps used = 3, number of rules used = 3, integrand size = 46, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.065, Rules used = {6688, 12, 6686} \begin {gather*} \frac {4}{x-\log (x+4)+6} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6686
Rule 6688
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {4 (-3-x)}{(4+x) (6+x-\log (4+x))^2} \, dx\\ &=4 \int \frac {-3-x}{(4+x) (6+x-\log (4+x))^2} \, dx\\ &=\frac {4}{6+x-\log (4+x)}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 13, normalized size = 0.65 \begin {gather*} \frac {4}{6+x-\log (4+x)} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.83, size = 13, normalized size = 0.65 \begin {gather*} \frac {4}{x - \log \left (x + 4\right ) + 6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.18, size = 13, normalized size = 0.65 \begin {gather*} \frac {4}{x - \log \left (x + 4\right ) + 6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 14, normalized size = 0.70
method | result | size |
norman | \(\frac {4}{x +6-\ln \left (4+x \right )}\) | \(14\) |
risch | \(\frac {4}{x +6-\ln \left (4+x \right )}\) | \(14\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.41, size = 13, normalized size = 0.65 \begin {gather*} \frac {4}{x - \log \left (x + 4\right ) + 6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.47, size = 13, normalized size = 0.65 \begin {gather*} \frac {4}{x-\ln \left (x+4\right )+6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 10, normalized size = 0.50 \begin {gather*} - \frac {4}{- x + \log {\left (x + 4 \right )} - 6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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