Integrand size = 32, antiderivative size = 32 \[ \int \frac {(f+g x)^2}{A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )} \, dx=\text {Int}\left (\frac {(f+g x)^2}{A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )},x\right ) \]
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Not integrable
Time = 0.02 (sec) , antiderivative size = 32, 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 = {} \[ \int \frac {(f+g x)^2}{A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )} \, dx=\int \frac {(f+g x)^2}{A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {(f+g x)^2}{A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )} \, dx \\ \end{align*}
Not integrable
Time = 0.17 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.06 \[ \int \frac {(f+g x)^2}{A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )} \, dx=\int \frac {(f+g x)^2}{A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )} \, dx \]
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Not integrable
Time = 0.06 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.00
\[\int \frac {\left (g x +f \right )^{2}}{A +B \ln \left (e \left (\frac {b x +a}{d x +c}\right )^{n}\right )}d x\]
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Not integrable
Time = 0.28 (sec) , antiderivative size = 43, normalized size of antiderivative = 1.34 \[ \int \frac {(f+g x)^2}{A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )} \, dx=\int { \frac {{\left (g x + f\right )}^{2}}{B \log \left (e \left (\frac {b x + a}{d x + c}\right )^{n}\right ) + A} \,d x } \]
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Not integrable
Time = 28.90 (sec) , antiderivative size = 31, normalized size of antiderivative = 0.97 \[ \int \frac {(f+g x)^2}{A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )} \, dx=\int \frac {\left (f + g x\right )^{2}}{A + B \log {\left (e \left (\frac {a}{c + d x} + \frac {b x}{c + d x}\right )^{n} \right )}}\, dx \]
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Not integrable
Time = 0.43 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.06 \[ \int \frac {(f+g x)^2}{A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )} \, dx=\int { \frac {{\left (g x + f\right )}^{2}}{B \log \left (e \left (\frac {b x + a}{d x + c}\right )^{n}\right ) + A} \,d x } \]
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Not integrable
Time = 26.49 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.06 \[ \int \frac {(f+g x)^2}{A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )} \, dx=\int { \frac {{\left (g x + f\right )}^{2}}{B \log \left (e \left (\frac {b x + a}{d x + c}\right )^{n}\right ) + A} \,d x } \]
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Not integrable
Time = 0.72 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.06 \[ \int \frac {(f+g x)^2}{A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )} \, dx=\int \frac {{\left (f+g\,x\right )}^2}{A+B\,\ln \left (e\,{\left (\frac {a+b\,x}{c+d\,x}\right )}^n\right )} \,d x \]
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