Optimal. Leaf size=20 \[ -2+(7-x)^2+\frac {4}{x}+x-x \log (x) \]
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Rubi [A] time = 0.02, antiderivative size = 17, normalized size of antiderivative = 0.85, number of steps used = 5, number of rules used = 2, integrand size = 23, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.087, Rules used = {14, 2295} \begin {gather*} x^2-13 x+\frac {4}{x}-x \log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 2295
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {2 \left (-2-7 x^2+x^3\right )}{x^2}-\log (x)\right ) \, dx\\ &=2 \int \frac {-2-7 x^2+x^3}{x^2} \, dx-\int \log (x) \, dx\\ &=x-x \log (x)+2 \int \left (-7-\frac {2}{x^2}+x\right ) \, dx\\ &=\frac {4}{x}-13 x+x^2-x \log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 17, normalized size = 0.85 \begin {gather*} \frac {4}{x}-13 x+x^2-x \log (x) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.54, size = 21, normalized size = 1.05 \begin {gather*} \frac {x^{3} - x^{2} \log \relax (x) - 13 \, x^{2} + 4}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 17, normalized size = 0.85 \begin {gather*} x^{2} - x \log \relax (x) - 13 \, x + \frac {4}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 18, normalized size = 0.90
method | result | size |
default | \(-13 x -x \ln \relax (x )+x^{2}+\frac {4}{x}\) | \(18\) |
risch | \(-x \ln \relax (x )+\frac {x^{3}-13 x^{2}+4}{x}\) | \(21\) |
norman | \(\frac {4+x^{3}-13 x^{2}-x^{2} \ln \relax (x )}{x}\) | \(22\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.46, size = 17, normalized size = 0.85 \begin {gather*} x^{2} - x \log \relax (x) - 13 \, x + \frac {4}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.66, size = 16, normalized size = 0.80 \begin {gather*} \frac {4}{x}-x\,\left (\ln \relax (x)+13\right )+x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 14, normalized size = 0.70 \begin {gather*} x^{2} - x \log {\relax (x )} - 13 x + \frac {4}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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