Optimal. Leaf size=31 \[ \text {Int}\left (\frac {\log (x)}{x \log \left (\frac {a+b x}{x (b c-a d)}\right )},x\right ) \]
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Rubi [A] time = 0.02, 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 = {} \[ \int \frac {\log (x)}{x \log \left (\frac {a+b x}{(b c-a d) x}\right )} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {\log (x)}{x \log \left (\frac {a+b x}{(b c-a d) x}\right )} \, dx &=\int \frac {\log (x)}{x \log \left (\frac {a+b x}{(b c-a d) x}\right )} \, dx\\ \end {align*}
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Mathematica [A] time = 5.10, size = 0, normalized size = 0.00 \[ \int \frac {\log (x)}{x \log \left (\frac {a+b x}{(b c-a d) x}\right )} \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.59, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\log \relax (x)}{x \log \left (\frac {b x + a}{{\left (b c - a d\right )} x}\right )}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\log \relax (x)}{x \log \left (\frac {b x + a}{{\left (b c - a d\right )} x}\right )}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.14, size = 0, normalized size = 0.00 \[ \int \frac {\ln \relax (x )}{x \ln \left (\frac {b x +a}{\left (-a d +b c \right ) x}\right )}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\log \relax (x)}{x \log \left (\frac {b x + a}{{\left (b c - a d\right )} x}\right )}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [A] time = 0.00, size = -1, normalized size = -0.03 \[ \int \frac {\ln \relax (x)}{x\,\ln \left (-\frac {a+b\,x}{x\,\left (a\,d-b\,c\right )}\right )} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\log {\relax (x )}}{x \log {\left (\frac {a}{- a d x + b c x} + \frac {b x}{- a d x + b c x} \right )}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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