Integrand size = 20, antiderivative size = 20 \[ \int \frac {1}{(c+d x) (b \tanh (e+f x))^{3/2}} \, dx=\text {Int}\left (\frac {1}{(c+d x) (b \tanh (e+f x))^{3/2}},x\right ) \]
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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 = {} \[ \int \frac {1}{(c+d x) (b \tanh (e+f x))^{3/2}} \, dx=\int \frac {1}{(c+d x) (b \tanh (e+f x))^{3/2}} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {1}{(c+d x) (b \tanh (e+f x))^{3/2}} \, dx \\ \end{align*}
Not integrable
Time = 21.46 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int \frac {1}{(c+d x) (b \tanh (e+f x))^{3/2}} \, dx=\int \frac {1}{(c+d x) (b \tanh (e+f x))^{3/2}} \, dx \]
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Not integrable
Time = 0.04 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.90
\[\int \frac {1}{\left (d x +c \right ) \left (b \tanh \left (f x +e \right )\right )^{\frac {3}{2}}}d x\]
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Exception generated. \[ \int \frac {1}{(c+d x) (b \tanh (e+f x))^{3/2}} \, dx=\text {Exception raised: TypeError} \]
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Not integrable
Time = 1.14 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.95 \[ \int \frac {1}{(c+d x) (b \tanh (e+f x))^{3/2}} \, dx=\int \frac {1}{\left (b \tanh {\left (e + f x \right )}\right )^{\frac {3}{2}} \left (c + d x\right )}\, dx \]
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Not integrable
Time = 0.46 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.00 \[ \int \frac {1}{(c+d x) (b \tanh (e+f x))^{3/2}} \, dx=\int { \frac {1}{{\left (d x + c\right )} \left (b \tanh \left (f x + e\right )\right )^{\frac {3}{2}}} \,d x } \]
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Not integrable
Time = 0.39 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.00 \[ \int \frac {1}{(c+d x) (b \tanh (e+f x))^{3/2}} \, dx=\int { \frac {1}{{\left (d x + c\right )} \left (b \tanh \left (f x + e\right )\right )^{\frac {3}{2}}} \,d x } \]
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Not integrable
Time = 1.97 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.00 \[ \int \frac {1}{(c+d x) (b \tanh (e+f x))^{3/2}} \, dx=\int \frac {1}{{\left (b\,\mathrm {tanh}\left (e+f\,x\right )\right )}^{3/2}\,\left (c+d\,x\right )} \,d x \]
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