Integrand size = 20, antiderivative size = 20 \[ \int \frac {(a+b \tanh (e+f x))^2}{c+d x} \, dx=\text {Int}\left (\frac {(a+b \tanh (e+f x))^2}{c+d x},x\right ) \]
[Out]
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 = {} \[ \int \frac {(a+b \tanh (e+f x))^2}{c+d x} \, dx=\int \frac {(a+b \tanh (e+f x))^2}{c+d x} \, dx \]
[In]
[Out]
Rubi steps \begin{align*} \text {integral}& = \int \frac {(a+b \tanh (e+f x))^2}{c+d x} \, dx \\ \end{align*}
Not integrable
Time = 26.59 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int \frac {(a+b \tanh (e+f x))^2}{c+d x} \, dx=\int \frac {(a+b \tanh (e+f x))^2}{c+d x} \, dx \]
[In]
[Out]
Not integrable
Time = 0.15 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.00
\[\int \frac {\left (a +b \tanh \left (f x +e \right )\right )^{2}}{d x +c}d x\]
[In]
[Out]
Not integrable
Time = 0.26 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.80 \[ \int \frac {(a+b \tanh (e+f x))^2}{c+d x} \, dx=\int { \frac {{\left (b \tanh \left (f x + e\right ) + a\right )}^{2}}{d x + c} \,d x } \]
[In]
[Out]
Not integrable
Time = 1.16 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.85 \[ \int \frac {(a+b \tanh (e+f x))^2}{c+d x} \, dx=\int \frac {\left (a + b \tanh {\left (e + f x \right )}\right )^{2}}{c + d x}\, dx \]
[In]
[Out]
Not integrable
Time = 0.38 (sec) , antiderivative size = 155, normalized size of antiderivative = 7.75 \[ \int \frac {(a+b \tanh (e+f x))^2}{c+d x} \, dx=\int { \frac {{\left (b \tanh \left (f x + e\right ) + a\right )}^{2}}{d x + c} \,d x } \]
[In]
[Out]
Not integrable
Time = 0.30 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int \frac {(a+b \tanh (e+f x))^2}{c+d x} \, dx=\int { \frac {{\left (b \tanh \left (f x + e\right ) + a\right )}^{2}}{d x + c} \,d x } \]
[In]
[Out]
Not integrable
Time = 1.98 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int \frac {(a+b \tanh (e+f x))^2}{c+d x} \, dx=\int \frac {{\left (a+b\,\mathrm {tanh}\left (e+f\,x\right )\right )}^2}{c+d\,x} \,d x \]
[In]
[Out]