Integrand size = 20, antiderivative size = 20 \[ \int F(c,d,\tanh (a+b x),r,s) \text {sech}^2(a+b x) \, dx=\text {Int}\left (F(c,d,\tanh (a+b x),r,s) \text {sech}^2(a+b x),x\right ) \]
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Not integrable
Time = 0.01 (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 = {} \[ \int F(c,d,\tanh (a+b x),r,s) \text {sech}^2(a+b x) \, dx=\int F(c,d,\tanh (a+b x),r,s) \text {sech}^2(a+b x) \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \frac {\text {Subst}(\int F(c,d,x,r,s) \, dx,x,\tanh (a+b x))}{b} \\ \end{align*}
Not integrable
Time = 0.09 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int F(c,d,\tanh (a+b x),r,s) \text {sech}^2(a+b x) \, dx=\int F(c,d,\tanh (a+b x),r,s) \text {sech}^2(a+b x) \, dx \]
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Not integrable
Time = 0.03 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.00
\[\int F \left (c , d , \tanh \left (b x +a \right ), r , s\right ) \operatorname {sech}\left (b x +a \right )^{2}d x\]
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Not integrable
Time = 0.25 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int F(c,d,\tanh (a+b x),r,s) \text {sech}^2(a+b x) \, dx=\int { F\left (c, d, \tanh \left (b x + a\right ), r, s\right ) \operatorname {sech}\left (b x + a\right )^{2} \,d x } \]
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Not integrable
Time = 0.82 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.85 \[ \int F(c,d,\tanh (a+b x),r,s) \text {sech}^2(a+b x) \, dx=\int F{\left (c,d,\tanh {\left (a + b x \right )},r,s \right )} \operatorname {sech}^{2}{\left (a + b x \right )}\, dx \]
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Not integrable
Time = 0.29 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int F(c,d,\tanh (a+b x),r,s) \text {sech}^2(a+b x) \, dx=\int { F\left (c, d, \tanh \left (b x + a\right ), r, s\right ) \operatorname {sech}\left (b x + a\right )^{2} \,d x } \]
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Not integrable
Time = 0.26 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int F(c,d,\tanh (a+b x),r,s) \text {sech}^2(a+b x) \, dx=\int { F\left (c, d, \tanh \left (b x + a\right ), r, s\right ) \operatorname {sech}\left (b x + a\right )^{2} \,d x } \]
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Not integrable
Time = 2.44 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int F(c,d,\tanh (a+b x),r,s) \text {sech}^2(a+b x) \, dx=\int \frac {F\left (c,d,\mathrm {tanh}\left (a+b\,x\right ),r,s\right )}{{\mathrm {cosh}\left (a+b\,x\right )}^2} \,d x \]
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