Integrand size = 18, antiderivative size = 18 \[ \int \frac {a+b \tanh (e+f x)}{c+d x} \, dx=\text {Int}\left (\frac {a+b \tanh (e+f x)}{c+d x},x\right ) \]
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Not integrable
Time = 0.02 (sec) , antiderivative size = 18, 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 = {} \[ \int \frac {a+b \tanh (e+f x)}{c+d x} \, dx=\int \frac {a+b \tanh (e+f x)}{c+d x} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {a+b \tanh (e+f x)}{c+d x} \, dx \\ \end{align*}
Not integrable
Time = 2.93 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.11 \[ \int \frac {a+b \tanh (e+f x)}{c+d x} \, dx=\int \frac {a+b \tanh (e+f x)}{c+d x} \, dx \]
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Not integrable
Time = 0.05 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.00
\[\int \frac {a +b \tanh \left (f x +e \right )}{d x +c}d x\]
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Not integrable
Time = 0.24 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.11 \[ \int \frac {a+b \tanh (e+f x)}{c+d x} \, dx=\int { \frac {b \tanh \left (f x + e\right ) + a}{d x + c} \,d x } \]
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Not integrable
Time = 0.81 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.83 \[ \int \frac {a+b \tanh (e+f x)}{c+d x} \, dx=\int \frac {a + b \tanh {\left (e + f x \right )}}{c + d x}\, dx \]
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Not integrable
Time = 0.24 (sec) , antiderivative size = 56, normalized size of antiderivative = 3.11 \[ \int \frac {a+b \tanh (e+f x)}{c+d x} \, dx=\int { \frac {b \tanh \left (f x + e\right ) + a}{d x + c} \,d x } \]
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Not integrable
Time = 0.26 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.11 \[ \int \frac {a+b \tanh (e+f x)}{c+d x} \, dx=\int { \frac {b \tanh \left (f x + e\right ) + a}{d x + c} \,d x } \]
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Not integrable
Time = 1.76 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.11 \[ \int \frac {a+b \tanh (e+f x)}{c+d x} \, dx=\int \frac {a+b\,\mathrm {tanh}\left (e+f\,x\right )}{c+d\,x} \,d x \]
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