Optimal. Leaf size=17 \[ x^2+\frac {3}{5} (-3+6 x+\log (4+x)) \]
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Rubi [A] time = 0.01, antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {698} \begin {gather*} x^2+\frac {18 x}{5}+\frac {3}{5} \log (x+4) \end {gather*}
Antiderivative was successfully verified.
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Rule 698
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {18}{5}+2 x+\frac {3}{5 (4+x)}\right ) \, dx\\ &=\frac {18 x}{5}+x^2+\frac {3}{5} \log (4+x)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 22, normalized size = 1.29 \begin {gather*} \frac {1}{5} \left (-8+18 x+5 x^2+3 \log (5 (4+x))\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.48, size = 13, normalized size = 0.76 \begin {gather*} x^{2} + \frac {18}{5} \, x + \frac {3}{5} \, \log \left (x + 4\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.14, size = 14, normalized size = 0.82 \begin {gather*} x^{2} + \frac {18}{5} \, x + \frac {3}{5} \, \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 = 0.08, size = 14, normalized size = 0.82
method | result | size |
default | \(x^{2}+\frac {18 x}{5}+\frac {3 \ln \left (4+x \right )}{5}\) | \(14\) |
risch | \(x^{2}+\frac {18 x}{5}+\frac {3 \ln \left (4+x \right )}{5}\) | \(14\) |
norman | \(x^{2}+\frac {18 x}{5}+\frac {3 \ln \left (20+5 x \right )}{5}\) | \(16\) |
meijerg | \(\frac {3 \ln \left (1+\frac {x}{4}\right )}{5}-\frac {4 x \left (-\frac {3 x}{4}+6\right )}{3}+\frac {58 x}{5}\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.37, size = 13, normalized size = 0.76 \begin {gather*} x^{2} + \frac {18}{5} \, x + \frac {3}{5} \, \log \left (x + 4\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.94, size = 13, normalized size = 0.76 \begin {gather*} \frac {18\,x}{5}+\frac {3\,\ln \left (x+4\right )}{5}+x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.07, size = 15, normalized size = 0.88 \begin {gather*} x^{2} + \frac {18 x}{5} + \frac {3 \log {\left (x + 4 \right )}}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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