Integrand size = 20, antiderivative size = 20 \[ \int \frac {(a+b \tanh (e+f x))^3}{c+d x} \, dx=\text {Int}\left (\frac {(a+b \tanh (e+f x))^3}{c+d x},x\right ) \]
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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 = {} \[ \int \frac {(a+b \tanh (e+f x))^3}{c+d x} \, dx=\int \frac {(a+b \tanh (e+f x))^3}{c+d x} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {(a+b \tanh (e+f x))^3}{c+d x} \, dx \\ \end{align*}
Not integrable
Time = 32.80 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int \frac {(a+b \tanh (e+f x))^3}{c+d x} \, dx=\int \frac {(a+b \tanh (e+f x))^3}{c+d x} \, dx \]
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Not integrable
Time = 0.30 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.00
\[\int \frac {\left (a +b \tanh \left (f x +e \right )\right )^{3}}{d x +c}d x\]
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Not integrable
Time = 0.28 (sec) , antiderivative size = 52, normalized size of antiderivative = 2.60 \[ \int \frac {(a+b \tanh (e+f x))^3}{c+d x} \, dx=\int { \frac {{\left (b \tanh \left (f x + e\right ) + a\right )}^{3}}{d x + c} \,d x } \]
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Not integrable
Time = 1.40 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.85 \[ \int \frac {(a+b \tanh (e+f x))^3}{c+d x} \, dx=\int \frac {\left (a + b \tanh {\left (e + f x \right )}\right )^{3}}{c + d x}\, dx \]
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Not integrable
Time = 0.56 (sec) , antiderivative size = 455, normalized size of antiderivative = 22.75 \[ \int \frac {(a+b \tanh (e+f x))^3}{c+d x} \, dx=\int { \frac {{\left (b \tanh \left (f x + e\right ) + a\right )}^{3}}{d x + c} \,d x } \]
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Not integrable
Time = 0.41 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int \frac {(a+b \tanh (e+f x))^3}{c+d x} \, dx=\int { \frac {{\left (b \tanh \left (f x + e\right ) + a\right )}^{3}}{d x + c} \,d x } \]
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Not integrable
Time = 1.94 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int \frac {(a+b \tanh (e+f x))^3}{c+d x} \, dx=\int \frac {{\left (a+b\,\mathrm {tanh}\left (e+f\,x\right )\right )}^3}{c+d\,x} \,d x \]
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