Integrand size = 25, antiderivative size = 25 \[ \int \frac {(c+d x)^m}{a+b \left (F^{g (e+f x)}\right )^n} \, dx=\text {Int}\left (\frac {(c+d x)^m}{a+b \left (F^{e g+f g x}\right )^n},x\right ) \]
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Not integrable
Time = 0.07 (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 = {} \[ \int \frac {(c+d x)^m}{a+b \left (F^{g (e+f x)}\right )^n} \, dx=\int \frac {(c+d x)^m}{a+b \left (F^{g (e+f x)}\right )^n} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {(c+d x)^m}{a+b \left (F^{e g+f g x}\right )^n} \, dx \\ \end{align*}
Not integrable
Time = 0.45 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.08 \[ \int \frac {(c+d x)^m}{a+b \left (F^{g (e+f x)}\right )^n} \, dx=\int \frac {(c+d x)^m}{a+b \left (F^{g (e+f x)}\right )^n} \, dx \]
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Not integrable
Time = 0.02 (sec) , antiderivative size = 25, normalized size of antiderivative = 1.00
\[\int \frac {\left (d x +c \right )^{m}}{a +b \left (F^{g \left (f x +e \right )}\right )^{n}}d x\]
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Not integrable
Time = 0.24 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.12 \[ \int \frac {(c+d x)^m}{a+b \left (F^{g (e+f x)}\right )^n} \, dx=\int { \frac {{\left (d x + c\right )}^{m}}{{\left (F^{{\left (f x + e\right )} g}\right )}^{n} b + a} \,d x } \]
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Not integrable
Time = 3.41 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.88 \[ \int \frac {(c+d x)^m}{a+b \left (F^{g (e+f x)}\right )^n} \, dx=\int \frac {\left (c + d x\right )^{m}}{a + b \left (F^{e g + f g x}\right )^{n}}\, dx \]
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Not integrable
Time = 0.25 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.04 \[ \int \frac {(c+d x)^m}{a+b \left (F^{g (e+f x)}\right )^n} \, dx=\int { \frac {{\left (d x + c\right )}^{m}}{{\left (F^{{\left (f x + e\right )} g}\right )}^{n} b + a} \,d x } \]
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Not integrable
Time = 0.39 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.08 \[ \int \frac {(c+d x)^m}{a+b \left (F^{g (e+f x)}\right )^n} \, dx=\int { \frac {{\left (d x + c\right )}^{m}}{{\left (F^{{\left (f x + e\right )} g}\right )}^{n} b + a} \,d x } \]
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Not integrable
Time = 0.13 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.08 \[ \int \frac {(c+d x)^m}{a+b \left (F^{g (e+f x)}\right )^n} \, dx=\int \frac {{\left (c+d\,x\right )}^m}{a+b\,{\left (F^{g\,\left (e+f\,x\right )}\right )}^n} \,d x \]
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