Integrand size = 31, antiderivative size = 31 \[ \int \frac {(f+g x)^2}{A+B \log \left (\frac {e (a+b x)^2}{(c+d x)^2}\right )} \, dx=\text {Int}\left (\frac {(f+g x)^2}{A+B \log \left (\frac {e (a+b x)^2}{(c+d x)^2}\right )},x\right ) \]
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Not integrable
Time = 0.02 (sec) , antiderivative size = 31, 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 = {} \[ \int \frac {(f+g x)^2}{A+B \log \left (\frac {e (a+b x)^2}{(c+d x)^2}\right )} \, dx=\int \frac {(f+g x)^2}{A+B \log \left (\frac {e (a+b x)^2}{(c+d x)^2}\right )} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {(f+g x)^2}{A+B \log \left (\frac {e (a+b x)^2}{(c+d x)^2}\right )} \, dx \\ \end{align*}
Not integrable
Time = 0.11 (sec) , antiderivative size = 33, normalized size of antiderivative = 1.06 \[ \int \frac {(f+g x)^2}{A+B \log \left (\frac {e (a+b x)^2}{(c+d x)^2}\right )} \, dx=\int \frac {(f+g x)^2}{A+B \log \left (\frac {e (a+b x)^2}{(c+d x)^2}\right )} \, dx \]
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Not integrable
Time = 0.75 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.00
\[\int \frac {\left (g x +f \right )^{2}}{A +B \ln \left (\frac {e \left (b x +a \right )^{2}}{\left (d x +c \right )^{2}}\right )}d x\]
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Not integrable
Time = 0.33 (sec) , antiderivative size = 65, normalized size of antiderivative = 2.10 \[ \int \frac {(f+g x)^2}{A+B \log \left (\frac {e (a+b x)^2}{(c+d x)^2}\right )} \, dx=\int { \frac {{\left (g x + f\right )}^{2}}{B \log \left (\frac {{\left (b x + a\right )}^{2} e}{{\left (d x + c\right )}^{2}}\right ) + A} \,d x } \]
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Not integrable
Time = 21.42 (sec) , antiderivative size = 85, normalized size of antiderivative = 2.74 \[ \int \frac {(f+g x)^2}{A+B \log \left (\frac {e (a+b x)^2}{(c+d x)^2}\right )} \, dx=\int \frac {\left (f + g x\right )^{2}}{A + B \log {\left (\frac {a^{2} e}{c^{2} + 2 c d x + d^{2} x^{2}} + \frac {2 a b e x}{c^{2} + 2 c d x + d^{2} x^{2}} + \frac {b^{2} e x^{2}}{c^{2} + 2 c d x + d^{2} x^{2}} \right )}}\, dx \]
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Not integrable
Time = 0.24 (sec) , antiderivative size = 33, normalized size of antiderivative = 1.06 \[ \int \frac {(f+g x)^2}{A+B \log \left (\frac {e (a+b x)^2}{(c+d x)^2}\right )} \, dx=\int { \frac {{\left (g x + f\right )}^{2}}{B \log \left (\frac {{\left (b x + a\right )}^{2} e}{{\left (d x + c\right )}^{2}}\right ) + A} \,d x } \]
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Not integrable
Time = 0.56 (sec) , antiderivative size = 33, normalized size of antiderivative = 1.06 \[ \int \frac {(f+g x)^2}{A+B \log \left (\frac {e (a+b x)^2}{(c+d x)^2}\right )} \, dx=\int { \frac {{\left (g x + f\right )}^{2}}{B \log \left (\frac {{\left (b x + a\right )}^{2} e}{{\left (d x + c\right )}^{2}}\right ) + A} \,d x } \]
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Not integrable
Time = 2.26 (sec) , antiderivative size = 33, normalized size of antiderivative = 1.06 \[ \int \frac {(f+g x)^2}{A+B \log \left (\frac {e (a+b x)^2}{(c+d x)^2}\right )} \, dx=\int \frac {{\left (f+g\,x\right )}^2}{A+B\,\ln \left (\frac {e\,{\left (a+b\,x\right )}^2}{{\left (c+d\,x\right )}^2}\right )} \,d x \]
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