Integrand size = 16, antiderivative size = 16 \[ \int \frac {\tanh ^3(e+f x)}{c+d x} \, dx=\text {Int}\left (\frac {\tanh ^3(e+f x)}{c+d x},x\right ) \]
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Not integrable
Time = 0.03 (sec) , antiderivative size = 16, 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 = {} \[ \int \frac {\tanh ^3(e+f x)}{c+d x} \, dx=\int \frac {\tanh ^3(e+f x)}{c+d x} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {\tanh ^3(e+f x)}{c+d x} \, dx \\ \end{align*}
Not integrable
Time = 26.72 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int \frac {\tanh ^3(e+f x)}{c+d x} \, dx=\int \frac {\tanh ^3(e+f x)}{c+d x} \, dx \]
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Not integrable
Time = 0.05 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.00
\[\int \frac {\tanh \left (f x +e \right )^{3}}{d x +c}d x\]
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Not integrable
Time = 0.24 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int \frac {\tanh ^3(e+f x)}{c+d x} \, dx=\int { \frac {\tanh \left (f x + e\right )^{3}}{d x + c} \,d x } \]
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Not integrable
Time = 0.42 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.88 \[ \int \frac {\tanh ^3(e+f x)}{c+d x} \, dx=\int \frac {\tanh ^{3}{\left (e + f x \right )}}{c + d x}\, dx \]
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Not integrable
Time = 0.37 (sec) , antiderivative size = 303, normalized size of antiderivative = 18.94 \[ \int \frac {\tanh ^3(e+f x)}{c+d x} \, dx=\int { \frac {\tanh \left (f x + e\right )^{3}}{d x + c} \,d x } \]
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Not integrable
Time = 0.35 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int \frac {\tanh ^3(e+f x)}{c+d x} \, dx=\int { \frac {\tanh \left (f x + e\right )^{3}}{d x + c} \,d x } \]
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Not integrable
Time = 1.71 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int \frac {\tanh ^3(e+f x)}{c+d x} \, dx=\int \frac {{\mathrm {tanh}\left (e+f\,x\right )}^3}{c+d\,x} \,d x \]
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