Optimal. Leaf size=17 \[ -4-3 x-\frac {x}{4+x}-\log (x) \]
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Rubi [A]
time = 0.03, antiderivative size = 15, normalized size of antiderivative = 0.88, number of steps
used = 4, number of rules used = 3, integrand size = 30, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {1608, 27, 1634}
\begin {gather*} -3 x+\frac {4}{x+4}-\log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 27
Rule 1608
Rule 1634
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-16-60 x-25 x^2-3 x^3}{x \left (16+8 x+x^2\right )} \, dx\\ &=\int \frac {-16-60 x-25 x^2-3 x^3}{x (4+x)^2} \, dx\\ &=\int \left (-3-\frac {1}{x}-\frac {4}{(4+x)^2}\right ) \, dx\\ &=-3 x+\frac {4}{4+x}-\log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 15, normalized size = 0.88 \begin {gather*} -3 x+\frac {4}{4+x}-\log (x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.04, size = 16, normalized size = 0.94
method | result | size |
default | \(-3 x +\frac {4}{4+x}-\ln \left (x \right )\) | \(16\) |
risch | \(-3 x +\frac {4}{4+x}-\ln \left (x \right )\) | \(16\) |
norman | \(\frac {-3 x^{2}+52}{4+x}-\ln \left (x \right )\) | \(19\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 15, normalized size = 0.88 \begin {gather*} -3 \, x + \frac {4}{x + 4} - \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.31, size = 23, normalized size = 1.35 \begin {gather*} -\frac {3 \, x^{2} + {\left (x + 4\right )} \log \left (x\right ) + 12 \, x - 4}{x + 4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 10, normalized size = 0.59 \begin {gather*} - 3 x - \log {\left (x \right )} + \frac {4}{x + 4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 16, normalized size = 0.94 \begin {gather*} -3 \, x + \frac {4}{x + 4} - \log \left ({\left | x \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.39, size = 15, normalized size = 0.88 \begin {gather*} \frac {4}{x+4}-\ln \left (x\right )-3\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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