Optimal. Leaf size=18 \[ 4+x-x^2+\log (2-x \log (5 x)) \]
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Rubi [F] time = 0.26, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {-1+4 x+\left (1+x-2 x^2\right ) \log (5 x)}{-2+x \log (5 x)} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {1+x-2 x^2}{x}+\frac {2+x}{x (-2+x \log (5 x))}\right ) \, dx\\ &=\int \frac {1+x-2 x^2}{x} \, dx+\int \frac {2+x}{x (-2+x \log (5 x))} \, dx\\ &=\int \left (1+\frac {1}{x}-2 x\right ) \, dx+\int \left (\frac {1}{-2+x \log (5 x)}+\frac {2}{x (-2+x \log (5 x))}\right ) \, dx\\ &=x-x^2+\log (x)+2 \int \frac {1}{x (-2+x \log (5 x))} \, dx+\int \frac {1}{-2+x \log (5 x)} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.05, size = 17, normalized size = 0.94 \begin {gather*} x-x^2+\log (2-x \log (5 x)) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.64, size = 24, normalized size = 1.33 \begin {gather*} -x^{2} + x + \log \left (5 \, x\right ) + \log \left (\frac {x \log \left (5 \, x\right ) - 2}{x}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.26, size = 17, normalized size = 0.94 \begin {gather*} -x^{2} + x + \log \left (-x \log \left (5 \, x\right ) + 2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 17, normalized size = 0.94
method | result | size |
norman | \(-x^{2}+x +\ln \left (x \ln \left (5 x \right )-2\right )\) | \(17\) |
risch | \(\ln \relax (x )+x -x^{2}+\ln \left (\ln \left (5 x \right )-\frac {2}{x}\right )\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.83, size = 24, normalized size = 1.33 \begin {gather*} -x^{2} + x + \log \relax (x) + \log \left (\frac {x \log \relax (5) + x \log \relax (x) - 2}{x}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.34, size = 23, normalized size = 1.28 \begin {gather*} \ln \left (x\,\ln \left (5\,x\right )-2\right )+\frac {x^2-x^3}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.16, size = 17, normalized size = 0.94 \begin {gather*} - x^{2} + x + \log {\relax (x )} + \log {\left (\log {\left (5 x \right )} - \frac {2}{x} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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