Optimal. Leaf size=22 \[ 5+e^5+x+\frac {7-\log \left (e^{2 x}\right )}{6+x} \]
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Rubi [A] time = 0.01, antiderivative size = 9, normalized size of antiderivative = 0.41, number of steps used = 3, number of rules used = 2, integrand size = 19, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.105, Rules used = {27, 683} \begin {gather*} x+\frac {19}{x+6} \end {gather*}
Antiderivative was successfully verified.
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Rule 27
Rule 683
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {17+12 x+x^2}{(6+x)^2} \, dx\\ &=\int \left (1-\frac {19}{(6+x)^2}\right ) \, dx\\ &=x+\frac {19}{6+x}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 9, normalized size = 0.41 \begin {gather*} x+\frac {19}{6+x} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.61, size = 14, normalized size = 0.64 \begin {gather*} \frac {x^{2} + 6 \, x + 19}{x + 6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.22, size = 9, normalized size = 0.41 \begin {gather*} x + \frac {19}{x + 6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.31, size = 10, normalized size = 0.45
method | result | size |
default | \(x +\frac {19}{x +6}\) | \(10\) |
risch | \(x +\frac {19}{x +6}\) | \(10\) |
gosper | \(\frac {x^{2}-17}{x +6}\) | \(12\) |
norman | \(\frac {x^{2}-17}{x +6}\) | \(12\) |
meijerg | \(-\frac {55 x}{36 \left (1+\frac {x}{6}\right )}+\frac {x \left (\frac {x}{2}+6\right )}{\frac {x}{2}+3}\) | \(27\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.39, size = 9, normalized size = 0.41 \begin {gather*} x + \frac {19}{x + 6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 9, normalized size = 0.41 \begin {gather*} x+\frac {19}{x+6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.07, size = 5, normalized size = 0.23 \begin {gather*} x + \frac {19}{x + 6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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