Optimal. Leaf size=31 \[ \text {Int}\left (\frac {\log (x) \log ^3\left (\frac {a+b x}{x (b c-a d)}\right )}{x},x\right ) \]
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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 = {} \[ \int \frac {\log (x) \log ^3\left (\frac {a+b x}{(b c-a d) x}\right )}{x} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {\log (x) \log ^3\left (\frac {a+b x}{(b c-a d) x}\right )}{x} \, dx &=\int \frac {\log (x) \log ^3\left (\frac {a+b x}{(b c-a d) x}\right )}{x} \, dx\\ \end {align*}
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Mathematica [A] time = 5.10, size = 0, normalized size = 0.00 \[ \int \frac {\log (x) \log ^3\left (\frac {a+b x}{(b c-a d) x}\right )}{x} \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 1.50, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\log \relax (x) \log \left (\frac {b x + a}{{\left (b c - a d\right )} x}\right )^{3}}{x}, x\right ) \]
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 \[ \int \frac {\log \relax (x) \log \left (\frac {b x + a}{{\left (b c - a d\right )} x}\right )^{3}}{x}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.42, size = 0, normalized size = 0.00 \[ \int \frac {\ln \relax (x ) \ln \left (\frac {b x +a}{\left (-a d +b c \right ) x}\right )^{3}}{x}\, dx \]
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 \[ \frac {1}{2} \, \log \left (b x + a\right )^{3} \log \relax (x)^{2} - \int \frac {2 \, {\left (b x + a\right )} \log \relax (x)^{4} + 6 \, {\left (b x \log \left (b c - a d\right ) + a \log \left (b c - a d\right )\right )} \log \relax (x)^{3} + 3 \, {\left ({\left (3 \, b x + 2 \, a\right )} \log \relax (x)^{2} + 2 \, {\left (b x \log \left (b c - a d\right ) + a \log \left (b c - a d\right )\right )} \log \relax (x)\right )} \log \left (b x + a\right )^{2} + 6 \, {\left (b x \log \left (b c - a d\right )^{2} + a \log \left (b c - a d\right )^{2}\right )} \log \relax (x)^{2} - 6 \, {\left ({\left (b x + a\right )} \log \relax (x)^{3} + 2 \, {\left (b x \log \left (b c - a d\right ) + a \log \left (b c - a d\right )\right )} \log \relax (x)^{2} + {\left (b x \log \left (b c - a d\right )^{2} + a \log \left (b c - a d\right )^{2}\right )} \log \relax (x)\right )} \log \left (b x + a\right ) + 2 \, {\left (b x \log \left (b c - a d\right )^{3} + a \log \left (b c - a d\right )^{3}\right )} \log \relax (x)}{2 \, {\left (b x^{2} + a x\right )}}\,{d x} \]
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 \[ \int \frac {{\ln \left (-\frac {a+b\,x}{x\,\left (a\,d-b\,c\right )}\right )}^3\,\ln \relax (x)}{x} \,d x \]
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 \[ \frac {3 a \int \frac {\log {\relax (x )}^{2} \log {\left (\frac {a}{- a d x + b c x} + \frac {b x}{- a d x + b c x} \right )}^{2}}{a x + b x^{2}}\, dx}{2} + \frac {\log {\relax (x )}^{2} \log {\left (\frac {a + b x}{x \left (- a d + b c\right )} \right )}^{3}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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