Integrand size = 20, antiderivative size = 20 \[ \int \frac {1}{(c+d x)^2 (a+a \cosh (e+f x))^2} \, dx=\text {Int}\left (\frac {1}{(c+d x)^2 (a+a \cosh (e+f x))^2},x\right ) \]
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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 = {} \[ \int \frac {1}{(c+d x)^2 (a+a \cosh (e+f x))^2} \, dx=\int \frac {1}{(c+d x)^2 (a+a \cosh (e+f x))^2} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {1}{(c+d x)^2 (a+a \cosh (e+f x))^2} \, dx \\ \end{align*}
Not integrable
Time = 22.76 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int \frac {1}{(c+d x)^2 (a+a \cosh (e+f x))^2} \, dx=\int \frac {1}{(c+d x)^2 (a+a \cosh (e+f x))^2} \, dx \]
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Not integrable
Time = 0.10 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.00
\[\int \frac {1}{\left (d x +c \right )^{2} \left (a +a \cosh \left (f x +e \right )\right )^{2}}d x\]
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Not integrable
Time = 0.26 (sec) , antiderivative size = 99, normalized size of antiderivative = 4.95 \[ \int \frac {1}{(c+d x)^2 (a+a \cosh (e+f x))^2} \, dx=\int { \frac {1}{{\left (d x + c\right )}^{2} {\left (a \cosh \left (f x + e\right ) + a\right )}^{2}} \,d x } \]
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Not integrable
Time = 4.46 (sec) , antiderivative size = 105, normalized size of antiderivative = 5.25 \[ \int \frac {1}{(c+d x)^2 (a+a \cosh (e+f x))^2} \, dx=\frac {\int \frac {1}{c^{2} \cosh ^{2}{\left (e + f x \right )} + 2 c^{2} \cosh {\left (e + f x \right )} + c^{2} + 2 c d x \cosh ^{2}{\left (e + f x \right )} + 4 c d x \cosh {\left (e + f x \right )} + 2 c d x + d^{2} x^{2} \cosh ^{2}{\left (e + f x \right )} + 2 d^{2} x^{2} \cosh {\left (e + f x \right )} + d^{2} x^{2}}\, dx}{a^{2}} \]
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Not integrable
Time = 0.63 (sec) , antiderivative size = 710, normalized size of antiderivative = 35.50 \[ \int \frac {1}{(c+d x)^2 (a+a \cosh (e+f x))^2} \, dx=\int { \frac {1}{{\left (d x + c\right )}^{2} {\left (a \cosh \left (f x + e\right ) + a\right )}^{2}} \,d x } \]
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Not integrable
Time = 0.42 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int \frac {1}{(c+d x)^2 (a+a \cosh (e+f x))^2} \, dx=\int { \frac {1}{{\left (d x + c\right )}^{2} {\left (a \cosh \left (f x + e\right ) + a\right )}^{2}} \,d x } \]
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Not integrable
Time = 2.45 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int \frac {1}{(c+d x)^2 (a+a \cosh (e+f x))^2} \, dx=\int \frac {1}{{\left (a+a\,\mathrm {cosh}\left (e+f\,x\right )\right )}^2\,{\left (c+d\,x\right )}^2} \,d x \]
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