Integrand size = 32, antiderivative size = 32 \[ \int \frac {1}{(f+g x)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )} \, dx=\text {Int}\left (\frac {1}{(f+g x)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )},x\right ) \]
[Out]
Not integrable
Time = 0.03 (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 = {} \[ \int \frac {1}{(f+g x)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )} \, dx=\int \frac {1}{(f+g x)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )} \, dx \]
[In]
[Out]
Rubi steps \begin{align*} \text {integral}& = \int \frac {1}{(f+g x)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )} \, dx \\ \end{align*}
Not integrable
Time = 0.53 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.06 \[ \int \frac {1}{(f+g x)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )} \, dx=\int \frac {1}{(f+g x)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )} \, dx \]
[In]
[Out]
Not integrable
Time = 0.07 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.00
\[\int \frac {1}{\left (g x +f \right )^{2} \left (A +B \ln \left (e \left (\frac {b x +a}{d x +c}\right )^{n}\right )\right )}d x\]
[In]
[Out]
Not integrable
Time = 0.25 (sec) , antiderivative size = 63, normalized size of antiderivative = 1.97 \[ \int \frac {1}{(f+g x)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )} \, dx=\int { \frac {1}{{\left (g x + f\right )}^{2} {\left (B \log \left (e \left (\frac {b x + a}{d x + c}\right )^{n}\right ) + A\right )}} \,d x } \]
[In]
[Out]
Timed out. \[ \int \frac {1}{(f+g x)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )} \, dx=\text {Timed out} \]
[In]
[Out]
Not integrable
Time = 0.34 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.06 \[ \int \frac {1}{(f+g x)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )} \, dx=\int { \frac {1}{{\left (g x + f\right )}^{2} {\left (B \log \left (e \left (\frac {b x + a}{d x + c}\right )^{n}\right ) + A\right )}} \,d x } \]
[In]
[Out]
Not integrable
Time = 26.96 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.06 \[ \int \frac {1}{(f+g x)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )} \, dx=\int { \frac {1}{{\left (g x + f\right )}^{2} {\left (B \log \left (e \left (\frac {b x + a}{d x + c}\right )^{n}\right ) + A\right )}} \,d x } \]
[In]
[Out]
Not integrable
Time = 0.69 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.06 \[ \int \frac {1}{(f+g x)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )} \, dx=\int \frac {1}{{\left (f+g\,x\right )}^2\,\left (A+B\,\ln \left (e\,{\left (\frac {a+b\,x}{c+d\,x}\right )}^n\right )\right )} \,d x \]
[In]
[Out]