Integrand size = 30, antiderivative size = 30 \[ \int \frac {f+g x}{\left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2} \, dx=\text {Int}\left (\frac {f+g x}{\left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2},x\right ) \]
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Not integrable
Time = 0.01 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.00, number of steps used = 0, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \frac {f+g x}{\left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2} \, dx=\int \frac {f+g x}{\left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {f+g x}{\left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2} \, dx \\ \end{align*}
Not integrable
Time = 0.32 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.07 \[ \int \frac {f+g x}{\left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2} \, dx=\int \frac {f+g x}{\left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2} \, dx \]
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Not integrable
Time = 0.02 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.00
\[\int \frac {g x +f}{{\left (A +B \ln \left (e \left (\frac {b x +a}{d x +c}\right )^{n}\right )\right )}^{2}}d x\]
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Not integrable
Time = 0.26 (sec) , antiderivative size = 60, normalized size of antiderivative = 2.00 \[ \int \frac {f+g x}{\left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2} \, dx=\int { \frac {g x + f}{{\left (B \log \left (e \left (\frac {b x + a}{d x + c}\right )^{n}\right ) + A\right )}^{2}} \,d x } \]
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Not integrable
Time = 60.30 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.03 \[ \int \frac {f+g x}{\left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2} \, dx=\int \frac {f + g x}{\left (A + B \log {\left (e \left (\frac {a}{c + d x} + \frac {b x}{c + d x}\right )^{n} \right )}\right )^{2}}\, dx \]
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Not integrable
Time = 0.51 (sec) , antiderivative size = 249, normalized size of antiderivative = 8.30 \[ \int \frac {f+g x}{\left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2} \, dx=\int { \frac {g x + f}{{\left (B \log \left (e \left (\frac {b x + a}{d x + c}\right )^{n}\right ) + A\right )}^{2}} \,d x } \]
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Not integrable
Time = 0.78 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.07 \[ \int \frac {f+g x}{\left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2} \, dx=\int { \frac {g x + f}{{\left (B \log \left (e \left (\frac {b x + a}{d x + c}\right )^{n}\right ) + A\right )}^{2}} \,d x } \]
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Not integrable
Time = 0.82 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.07 \[ \int \frac {f+g x}{\left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2} \, dx=\int \frac {f+g\,x}{{\left (A+B\,\ln \left (e\,{\left (\frac {a+b\,x}{c+d\,x}\right )}^n\right )\right )}^2} \,d x \]
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