Integrand size = 25, antiderivative size = 25 \[ \int \frac {1}{\left (a+b \left (F^{g (e+f x)}\right )^n\right )^2 (c+d x)} \, dx=\text {Int}\left (\frac {1}{\left (a+b \left (F^{e g+f g x}\right )^n\right )^2 (c+d x)},x\right ) \]
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Not integrable
Time = 0.09 (sec) , antiderivative size = 25, 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 = {} \[ \int \frac {1}{\left (a+b \left (F^{g (e+f x)}\right )^n\right )^2 (c+d x)} \, dx=\int \frac {1}{\left (a+b \left (F^{g (e+f x)}\right )^n\right )^2 (c+d x)} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {1}{\left (a+b \left (F^{e g+f g x}\right )^n\right )^2 (c+d x)} \, dx \\ \end{align*}
Not integrable
Time = 0.79 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.08 \[ \int \frac {1}{\left (a+b \left (F^{g (e+f x)}\right )^n\right )^2 (c+d x)} \, dx=\int \frac {1}{\left (a+b \left (F^{g (e+f x)}\right )^n\right )^2 (c+d x)} \, dx \]
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Not integrable
Time = 0.09 (sec) , antiderivative size = 25, normalized size of antiderivative = 1.00
\[\int \frac {1}{{\left (a +b \left (F^{g \left (f x +e \right )}\right )^{n}\right )}^{2} \left (d x +c \right )}d x\]
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Not integrable
Time = 0.26 (sec) , antiderivative size = 67, normalized size of antiderivative = 2.68 \[ \int \frac {1}{\left (a+b \left (F^{g (e+f x)}\right )^n\right )^2 (c+d x)} \, dx=\int { \frac {1}{{\left ({\left (F^{{\left (f x + e\right )} g}\right )}^{n} b + a\right )}^{2} {\left (d x + c\right )}} \,d x } \]
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Not integrable
Time = 3.95 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.96 \[ \int \frac {1}{\left (a+b \left (F^{g (e+f x)}\right )^n\right )^2 (c+d x)} \, dx=\int \frac {1}{\left (a + b \left (F^{e g + f g x}\right )^{n}\right )^{2} \left (c + d x\right )}\, dx \]
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Not integrable
Time = 0.27 (sec) , antiderivative size = 192, normalized size of antiderivative = 7.68 \[ \int \frac {1}{\left (a+b \left (F^{g (e+f x)}\right )^n\right )^2 (c+d x)} \, dx=\int { \frac {1}{{\left ({\left (F^{{\left (f x + e\right )} g}\right )}^{n} b + a\right )}^{2} {\left (d x + c\right )}} \,d x } \]
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Not integrable
Time = 0.39 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.08 \[ \int \frac {1}{\left (a+b \left (F^{g (e+f x)}\right )^n\right )^2 (c+d x)} \, dx=\int { \frac {1}{{\left ({\left (F^{{\left (f x + e\right )} g}\right )}^{n} b + a\right )}^{2} {\left (d x + c\right )}} \,d x } \]
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Not integrable
Time = 0.17 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.08 \[ \int \frac {1}{\left (a+b \left (F^{g (e+f x)}\right )^n\right )^2 (c+d x)} \, dx=\int \frac {1}{{\left (a+b\,{\left (F^{g\,\left (e+f\,x\right )}\right )}^n\right )}^2\,\left (c+d\,x\right )} \,d x \]
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