Optimal. Leaf size=17 \[ -4+x+\frac {2}{5} \log \left (-16-x^2+\log (x)\right ) \]
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Rubi [A] time = 0.33, antiderivative size = 16, normalized size of antiderivative = 0.94, number of steps used = 5, number of rules used = 4, integrand size = 37, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.108, Rules used = {6741, 12, 6742, 6684} \begin {gather*} \frac {2}{5} \log \left (x^2-\log (x)+16\right )+x \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6684
Rule 6741
Rule 6742
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-2+80 x+4 x^2+5 x^3-5 x \log (x)}{5 x \left (16+x^2-\log (x)\right )} \, dx\\ &=\frac {1}{5} \int \frac {-2+80 x+4 x^2+5 x^3-5 x \log (x)}{x \left (16+x^2-\log (x)\right )} \, dx\\ &=\frac {1}{5} \int \left (5+\frac {2 \left (-1+2 x^2\right )}{x \left (16+x^2-\log (x)\right )}\right ) \, dx\\ &=x+\frac {2}{5} \int \frac {-1+2 x^2}{x \left (16+x^2-\log (x)\right )} \, dx\\ &=x+\frac {2}{5} \log \left (16+x^2-\log (x)\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.12, size = 20, normalized size = 1.18 \begin {gather*} \frac {1}{5} \left (5 x+2 \log \left (16+x^2-\log (x)\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.66, size = 14, normalized size = 0.82 \begin {gather*} x + \frac {2}{5} \, \log \left (-x^{2} + \log \relax (x) - 16\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.25, size = 14, normalized size = 0.82 \begin {gather*} x + \frac {2}{5} \, \log \left (-x^{2} + \log \relax (x) - 16\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 15, normalized size = 0.88
method | result | size |
norman | \(x +\frac {2 \ln \left (x^{2}-\ln \relax (x )+16\right )}{5}\) | \(15\) |
risch | \(x +\frac {2 \ln \left (\ln \relax (x )-16-x^{2}\right )}{5}\) | \(15\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.39, size = 14, normalized size = 0.82 \begin {gather*} x + \frac {2}{5} \, \log \left (-x^{2} + \log \relax (x) - 16\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.78, size = 14, normalized size = 0.82 \begin {gather*} x+\frac {2\,\ln \left (x^2-\ln \relax (x)+16\right )}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.14, size = 14, normalized size = 0.82 \begin {gather*} x + \frac {2 \log {\left (- x^{2} + \log {\relax (x )} - 16 \right )}}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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