Integrand size = 20, antiderivative size = 20 \[ \int \frac {(c+d x)^m}{(a+a \cosh (e+f x))^2} \, dx=\text {Int}\left (\frac {(c+d x)^m}{(a+a \cosh (e+f x))^2},x\right ) \]
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Not integrable
Time = 0.04 (sec) , antiderivative size = 20, 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 = {} \[ \int \frac {(c+d x)^m}{(a+a \cosh (e+f x))^2} \, dx=\int \frac {(c+d x)^m}{(a+a \cosh (e+f x))^2} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {(c+d x)^m}{(a+a \cosh (e+f x))^2} \, dx \\ \end{align*}
Not integrable
Time = 7.28 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int \frac {(c+d x)^m}{(a+a \cosh (e+f x))^2} \, dx=\int \frac {(c+d x)^m}{(a+a \cosh (e+f x))^2} \, dx \]
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Not integrable
Time = 0.07 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.00
\[\int \frac {\left (d x +c \right )^{m}}{\left (a +a \cosh \left (f x +e \right )\right )^{2}}d x\]
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Not integrable
Time = 0.25 (sec) , antiderivative size = 39, normalized size of antiderivative = 1.95 \[ \int \frac {(c+d x)^m}{(a+a \cosh (e+f x))^2} \, dx=\int { \frac {{\left (d x + c\right )}^{m}}{{\left (a \cosh \left (f x + e\right ) + a\right )}^{2}} \,d x } \]
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Not integrable
Time = 10.95 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.45 \[ \int \frac {(c+d x)^m}{(a+a \cosh (e+f x))^2} \, dx=\frac {\int \frac {\left (c + d x\right )^{m}}{\cosh ^{2}{\left (e + f x \right )} + 2 \cosh {\left (e + f x \right )} + 1}\, dx}{a^{2}} \]
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Not integrable
Time = 0.33 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int \frac {(c+d x)^m}{(a+a \cosh (e+f x))^2} \, dx=\int { \frac {{\left (d x + c\right )}^{m}}{{\left (a \cosh \left (f x + e\right ) + a\right )}^{2}} \,d x } \]
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Not integrable
Time = 0.53 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int \frac {(c+d x)^m}{(a+a \cosh (e+f x))^2} \, dx=\int { \frac {{\left (d x + c\right )}^{m}}{{\left (a \cosh \left (f x + e\right ) + a\right )}^{2}} \,d x } \]
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Not integrable
Time = 1.80 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int \frac {(c+d x)^m}{(a+a \cosh (e+f x))^2} \, dx=\int \frac {{\left (c+d\,x\right )}^m}{{\left (a+a\,\mathrm {cosh}\left (e+f\,x\right )\right )}^2} \,d x \]
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