Integrand size = 32, antiderivative size = 32 \[ \int \frac {a g+b g x}{\left (A+B \log \left (\frac {e (c+d x)^2}{(a+b x)^2}\right )\right )^2} \, dx=\text {Int}\left (\frac {a g+b g x}{\left (A+B \log \left (\frac {e (c+d x)^2}{(a+b x)^2}\right )\right )^2},x\right ) \]
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Not integrable
Time = 0.01 (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 = {} \[ \int \frac {a g+b g x}{\left (A+B \log \left (\frac {e (c+d x)^2}{(a+b x)^2}\right )\right )^2} \, dx=\int \frac {a g+b g x}{\left (A+B \log \left (\frac {e (c+d x)^2}{(a+b x)^2}\right )\right )^2} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {a g+b g x}{\left (A+B \log \left (\frac {e (c+d x)^2}{(a+b x)^2}\right )\right )^2} \, dx \\ \end{align*}
Not integrable
Time = 0.24 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.06 \[ \int \frac {a g+b g x}{\left (A+B \log \left (\frac {e (c+d x)^2}{(a+b x)^2}\right )\right )^2} \, dx=\int \frac {a g+b g x}{\left (A+B \log \left (\frac {e (c+d x)^2}{(a+b x)^2}\right )\right )^2} \, dx \]
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Not integrable
Time = 0.74 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.00
\[\int \frac {b g x +a g}{{\left (A +B \ln \left (\frac {e \left (d x +c \right )^{2}}{\left (b x +a \right )^{2}}\right )\right )}^{2}}d x\]
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Not integrable
Time = 0.26 (sec) , antiderivative size = 107, normalized size of antiderivative = 3.34 \[ \int \frac {a g+b g x}{\left (A+B \log \left (\frac {e (c+d x)^2}{(a+b x)^2}\right )\right )^2} \, dx=\int { \frac {b g x + a g}{{\left (B \log \left (\frac {{\left (d x + c\right )}^{2} e}{{\left (b x + a\right )}^{2}}\right ) + A\right )}^{2}} \,d x } \]
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Not integrable
Time = 10.73 (sec) , antiderivative size = 559, normalized size of antiderivative = 17.47 \[ \int \frac {a g+b g x}{\left (A+B \log \left (\frac {e (c+d x)^2}{(a+b x)^2}\right )\right )^2} \, dx=\frac {- a^{2} c g - a^{2} d g x - 2 a b c g x - 2 a b d g x^{2} - b^{2} c g x^{2} - b^{2} d g x^{3}}{2 A B a d - 2 A B b c + \left (2 B^{2} a d - 2 B^{2} b c\right ) \log {\left (\frac {e \left (c + d x\right )^{2}}{\left (a + b x\right )^{2}} \right )}} + \frac {g \left (\int \frac {a^{2} d}{A + B \log {\left (\frac {c^{2} e}{a^{2} + 2 a b x + b^{2} x^{2}} + \frac {2 c d e x}{a^{2} + 2 a b x + b^{2} x^{2}} + \frac {d^{2} e x^{2}}{a^{2} + 2 a b x + b^{2} x^{2}} \right )}}\, dx + \int \frac {2 a b c}{A + B \log {\left (\frac {c^{2} e}{a^{2} + 2 a b x + b^{2} x^{2}} + \frac {2 c d e x}{a^{2} + 2 a b x + b^{2} x^{2}} + \frac {d^{2} e x^{2}}{a^{2} + 2 a b x + b^{2} x^{2}} \right )}}\, dx + \int \frac {2 b^{2} c x}{A + B \log {\left (\frac {c^{2} e}{a^{2} + 2 a b x + b^{2} x^{2}} + \frac {2 c d e x}{a^{2} + 2 a b x + b^{2} x^{2}} + \frac {d^{2} e x^{2}}{a^{2} + 2 a b x + b^{2} x^{2}} \right )}}\, dx + \int \frac {3 b^{2} d x^{2}}{A + B \log {\left (\frac {c^{2} e}{a^{2} + 2 a b x + b^{2} x^{2}} + \frac {2 c d e x}{a^{2} + 2 a b x + b^{2} x^{2}} + \frac {d^{2} e x^{2}}{a^{2} + 2 a b x + b^{2} x^{2}} \right )}}\, dx + \int \frac {4 a b d x}{A + B \log {\left (\frac {c^{2} e}{a^{2} + 2 a b x + b^{2} x^{2}} + \frac {2 c d e x}{a^{2} + 2 a b x + b^{2} x^{2}} + \frac {d^{2} e x^{2}}{a^{2} + 2 a b x + b^{2} x^{2}} \right )}}\, dx\right )}{2 B \left (a d - b c\right )} \]
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Not integrable
Time = 0.23 (sec) , antiderivative size = 234, normalized size of antiderivative = 7.31 \[ \int \frac {a g+b g x}{\left (A+B \log \left (\frac {e (c+d x)^2}{(a+b x)^2}\right )\right )^2} \, dx=\int { \frac {b g x + a g}{{\left (B \log \left (\frac {{\left (d x + c\right )}^{2} e}{{\left (b x + a\right )}^{2}}\right ) + A\right )}^{2}} \,d x } \]
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Not integrable
Time = 0.56 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.06 \[ \int \frac {a g+b g x}{\left (A+B \log \left (\frac {e (c+d x)^2}{(a+b x)^2}\right )\right )^2} \, dx=\int { \frac {b g x + a g}{{\left (B \log \left (\frac {{\left (d x + c\right )}^{2} e}{{\left (b x + a\right )}^{2}}\right ) + A\right )}^{2}} \,d x } \]
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Not integrable
Time = 11.96 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.06 \[ \int \frac {a g+b g x}{\left (A+B \log \left (\frac {e (c+d x)^2}{(a+b x)^2}\right )\right )^2} \, dx=\int \frac {a\,g+b\,g\,x}{{\left (A+B\,\ln \left (\frac {e\,{\left (c+d\,x\right )}^2}{{\left (a+b\,x\right )}^2}\right )\right )}^2} \,d x \]
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