Integrand size = 20, antiderivative size = 20 \[ \int (c+d x)^m (a+a \tanh (e+f x))^2 \, dx=\text {Int}\left ((c+d x)^m (a+a \tanh (e+f x))^2,x\right ) \]
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Not integrable
Time = 0.03 (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 = {} \[ \int (c+d x)^m (a+a \tanh (e+f x))^2 \, dx=\int (c+d x)^m (a+a \tanh (e+f x))^2 \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int (c+d x)^m (a+a \tanh (e+f x))^2 \, dx \\ \end{align*}
Not integrable
Time = 27.84 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int (c+d x)^m (a+a \tanh (e+f x))^2 \, dx=\int (c+d x)^m (a+a \tanh (e+f x))^2 \, dx \]
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Not integrable
Time = 0.05 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.00
\[\int \left (d x +c \right )^{m} \left (a +a \tanh \left (f x +e \right )\right )^{2}d x\]
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Not integrable
Time = 0.24 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.85 \[ \int (c+d x)^m (a+a \tanh (e+f x))^2 \, dx=\int { {\left (a \tanh \left (f x + e\right ) + a\right )}^{2} {\left (d x + c\right )}^{m} \,d x } \]
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Not integrable
Time = 2.28 (sec) , antiderivative size = 44, normalized size of antiderivative = 2.20 \[ \int (c+d x)^m (a+a \tanh (e+f x))^2 \, dx=a^{2} \left (\int 2 \left (c + d x\right )^{m} \tanh {\left (e + f x \right )}\, dx + \int \left (c + d x\right )^{m} \tanh ^{2}{\left (e + f x \right )}\, dx + \int \left (c + d x\right )^{m}\, dx\right ) \]
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Not integrable
Time = 0.48 (sec) , antiderivative size = 122, normalized size of antiderivative = 6.10 \[ \int (c+d x)^m (a+a \tanh (e+f x))^2 \, dx=\int { {\left (a \tanh \left (f x + e\right ) + a\right )}^{2} {\left (d x + c\right )}^{m} \,d x } \]
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Not integrable
Time = 0.30 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int (c+d x)^m (a+a \tanh (e+f x))^2 \, dx=\int { {\left (a \tanh \left (f x + e\right ) + a\right )}^{2} {\left (d x + c\right )}^{m} \,d x } \]
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Not integrable
Time = 1.96 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int (c+d x)^m (a+a \tanh (e+f x))^2 \, dx=\int {\left (a+a\,\mathrm {tanh}\left (e+f\,x\right )\right )}^2\,{\left (c+d\,x\right )}^m \,d x \]
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