Integrand size = 20, antiderivative size = 20 \[ \int \frac {\sqrt {b \tanh (e+f x)}}{c+d x} \, dx=\text {Int}\left (\frac {\sqrt {b \tanh (e+f x)}}{c+d x},x\right ) \]
[Out]
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 = {} \[ \int \frac {\sqrt {b \tanh (e+f x)}}{c+d x} \, dx=\int \frac {\sqrt {b \tanh (e+f x)}}{c+d x} \, dx \]
[In]
[Out]
Rubi steps \begin{align*} \text {integral}& = \int \frac {\sqrt {b \tanh (e+f x)}}{c+d x} \, dx \\ \end{align*}
Not integrable
Time = 2.01 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int \frac {\sqrt {b \tanh (e+f x)}}{c+d x} \, dx=\int \frac {\sqrt {b \tanh (e+f x)}}{c+d x} \, dx \]
[In]
[Out]
Not integrable
Time = 0.04 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.90
\[\int \frac {\sqrt {b \tanh \left (f x +e \right )}}{d x +c}d x\]
[In]
[Out]
Exception generated. \[ \int \frac {\sqrt {b \tanh (e+f x)}}{c+d x} \, dx=\text {Exception raised: TypeError} \]
[In]
[Out]
Not integrable
Time = 0.71 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.85 \[ \int \frac {\sqrt {b \tanh (e+f x)}}{c+d x} \, dx=\int \frac {\sqrt {b \tanh {\left (e + f x \right )}}}{c + d x}\, dx \]
[In]
[Out]
Not integrable
Time = 0.33 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.00 \[ \int \frac {\sqrt {b \tanh (e+f x)}}{c+d x} \, dx=\int { \frac {\sqrt {b \tanh \left (f x + e\right )}}{d x + c} \,d x } \]
[In]
[Out]
Not integrable
Time = 0.27 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.00 \[ \int \frac {\sqrt {b \tanh (e+f x)}}{c+d x} \, dx=\int { \frac {\sqrt {b \tanh \left (f x + e\right )}}{d x + c} \,d x } \]
[In]
[Out]
Not integrable
Time = 1.71 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.00 \[ \int \frac {\sqrt {b \tanh (e+f x)}}{c+d x} \, dx=\int \frac {\sqrt {b\,\mathrm {tanh}\left (e+f\,x\right )}}{c+d\,x} \,d x \]
[In]
[Out]