Optimal. Leaf size=23 \[ x+\log \left (\frac {e^{\frac {4 \left (4+4 x^2\right )}{x}}}{(4+x)^2}\right ) \]
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Rubi [A] time = 0.04, antiderivative size = 15, normalized size of antiderivative = 0.65, number of steps used = 3, number of rules used = 2, integrand size = 27, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.074, Rules used = {1593, 1620} \begin {gather*} 17 x+\frac {16}{x}-2 \log (x+4) \end {gather*}
Antiderivative was successfully verified.
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Rule 1593
Rule 1620
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-64-16 x+66 x^2+17 x^3}{x^2 (4+x)} \, dx\\ &=\int \left (17-\frac {16}{x^2}-\frac {2}{4+x}\right ) \, dx\\ &=\frac {16}{x}+17 x-2 \log (4+x)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 15, normalized size = 0.65 \begin {gather*} \frac {16}{x}+17 x-2 \log (4+x) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.65, size = 18, normalized size = 0.78 \begin {gather*} \frac {17 \, x^{2} - 2 \, x \log \left (x + 4\right ) + 16}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 16, normalized size = 0.70 \begin {gather*} 17 \, x + \frac {16}{x} - 2 \, \log \left ({\left | x + 4 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.44, size = 16, normalized size = 0.70
method | result | size |
default | \(17 x +\frac {16}{x}-2 \ln \left (4+x \right )\) | \(16\) |
risch | \(17 x +\frac {16}{x}-2 \ln \left (4+x \right )\) | \(16\) |
meijerg | \(-2 \ln \left (1+\frac {x}{4}\right )+\frac {16}{x}+17 x\) | \(18\) |
norman | \(\frac {17 x^{2}+16}{x}-2 \ln \left (4+x \right )\) | \(19\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 15, normalized size = 0.65 \begin {gather*} 17 \, x + \frac {16}{x} - 2 \, \log \left (x + 4\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.05, size = 15, normalized size = 0.65 \begin {gather*} 17\,x-2\,\ln \left (x+4\right )+\frac {16}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.08, size = 12, normalized size = 0.52 \begin {gather*} 17 x - 2 \log {\left (x + 4 \right )} + \frac {16}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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