Integrand size = 18, antiderivative size = 18 \[ \int (c+d x)^m (a+a \tanh (e+f x)) \, dx=\text {Int}\left ((c+d x)^m (a+a \tanh (e+f x)),x\right ) \]
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Not integrable
Time = 0.02 (sec) , antiderivative size = 18, 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 = {} \[ \int (c+d x)^m (a+a \tanh (e+f x)) \, dx=\int (c+d x)^m (a+a \tanh (e+f x)) \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int (c+d x)^m (a+a \tanh (e+f x)) \, dx \\ \end{align*}
Not integrable
Time = 16.54 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.11 \[ \int (c+d x)^m (a+a \tanh (e+f x)) \, dx=\int (c+d x)^m (a+a \tanh (e+f x)) \, dx \]
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Not integrable
Time = 0.04 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.00
\[\int \left (d x +c \right )^{m} \left (a +a \tanh \left (f x +e \right )\right )d x\]
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Not integrable
Time = 0.24 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.11 \[ \int (c+d x)^m (a+a \tanh (e+f x)) \, dx=\int { {\left (a \tanh \left (f x + e\right ) + a\right )} {\left (d x + c\right )}^{m} \,d x } \]
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Not integrable
Time = 1.55 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.33 \[ \int (c+d x)^m (a+a \tanh (e+f x)) \, dx=a \left (\int \left (c + d x\right )^{m} \tanh {\left (e + f x \right )}\, dx + \int \left (c + d x\right )^{m}\, dx\right ) \]
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Not integrable
Time = 0.30 (sec) , antiderivative size = 68, normalized size of antiderivative = 3.78 \[ \int (c+d x)^m (a+a \tanh (e+f x)) \, dx=\int { {\left (a \tanh \left (f x + e\right ) + a\right )} {\left (d x + c\right )}^{m} \,d x } \]
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Not integrable
Time = 0.27 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.11 \[ \int (c+d x)^m (a+a \tanh (e+f x)) \, dx=\int { {\left (a \tanh \left (f x + e\right ) + a\right )} {\left (d x + c\right )}^{m} \,d x } \]
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Not integrable
Time = 1.94 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.11 \[ \int (c+d x)^m (a+a \tanh (e+f x)) \, dx=\int \left (a+a\,\mathrm {tanh}\left (e+f\,x\right )\right )\,{\left (c+d\,x\right )}^m \,d x \]
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