Integrand size = 31, antiderivative size = 31 \[ \int \frac {1}{(f+g x) \left (A+B \log \left (\frac {e (a+b x)^2}{(c+d x)^2}\right )\right )^2} \, dx=\text {Int}\left (\frac {1}{(f+g x) \left (A+B \log \left (\frac {e (a+b x)^2}{(c+d x)^2}\right )\right )^2},x\right ) \]
[Out]
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 = {} \[ \int \frac {1}{(f+g x) \left (A+B \log \left (\frac {e (a+b x)^2}{(c+d x)^2}\right )\right )^2} \, dx=\int \frac {1}{(f+g x) \left (A+B \log \left (\frac {e (a+b x)^2}{(c+d x)^2}\right )\right )^2} \, dx \]
[In]
[Out]
Rubi steps \begin{align*} \text {integral}& = \int \frac {1}{(f+g x) \left (A+B \log \left (\frac {e (a+b x)^2}{(c+d x)^2}\right )\right )^2} \, dx \\ \end{align*}
Not integrable
Time = 0.28 (sec) , antiderivative size = 33, normalized size of antiderivative = 1.06 \[ \int \frac {1}{(f+g x) \left (A+B \log \left (\frac {e (a+b x)^2}{(c+d x)^2}\right )\right )^2} \, dx=\int \frac {1}{(f+g x) \left (A+B \log \left (\frac {e (a+b x)^2}{(c+d x)^2}\right )\right )^2} \, dx \]
[In]
[Out]
Not integrable
Time = 0.54 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.00
\[\int \frac {1}{\left (g x +f \right ) {\left (A +B \ln \left (\frac {e \left (b x +a \right )^{2}}{\left (d x +c \right )^{2}}\right )\right )}^{2}}d x\]
[In]
[Out]
Not integrable
Time = 0.31 (sec) , antiderivative size = 123, normalized size of antiderivative = 3.97 \[ \int \frac {1}{(f+g x) \left (A+B \log \left (\frac {e (a+b x)^2}{(c+d x)^2}\right )\right )^2} \, dx=\int { \frac {1}{{\left (g x + f\right )} {\left (B \log \left (\frac {{\left (b x + a\right )}^{2} e}{{\left (d x + c\right )}^{2}}\right ) + A\right )}^{2}} \,d x } \]
[In]
[Out]
Timed out. \[ \int \frac {1}{(f+g x) \left (A+B \log \left (\frac {e (a+b x)^2}{(c+d x)^2}\right )\right )^2} \, dx=\text {Timed out} \]
[In]
[Out]
Not integrable
Time = 0.23 (sec) , antiderivative size = 455, normalized size of antiderivative = 14.68 \[ \int \frac {1}{(f+g x) \left (A+B \log \left (\frac {e (a+b x)^2}{(c+d x)^2}\right )\right )^2} \, dx=\int { \frac {1}{{\left (g x + f\right )} {\left (B \log \left (\frac {{\left (b x + a\right )}^{2} e}{{\left (d x + c\right )}^{2}}\right ) + A\right )}^{2}} \,d x } \]
[In]
[Out]
Not integrable
Time = 0.76 (sec) , antiderivative size = 33, normalized size of antiderivative = 1.06 \[ \int \frac {1}{(f+g x) \left (A+B \log \left (\frac {e (a+b x)^2}{(c+d x)^2}\right )\right )^2} \, dx=\int { \frac {1}{{\left (g x + f\right )} {\left (B \log \left (\frac {{\left (b x + a\right )}^{2} e}{{\left (d x + c\right )}^{2}}\right ) + A\right )}^{2}} \,d x } \]
[In]
[Out]
Not integrable
Time = 8.00 (sec) , antiderivative size = 33, normalized size of antiderivative = 1.06 \[ \int \frac {1}{(f+g x) \left (A+B \log \left (\frac {e (a+b x)^2}{(c+d x)^2}\right )\right )^2} \, dx=\int \frac {1}{\left (f+g\,x\right )\,{\left (A+B\,\ln \left (\frac {e\,{\left (a+b\,x\right )}^2}{{\left (c+d\,x\right )}^2}\right )\right )}^2} \,d x \]
[In]
[Out]