### 3.1016 $$\int F(c,d,\tanh (a+b x),r,s) \text{sech}^2(a+b x) \, dx$$

Optimal. Leaf size=22 $\text{CannotIntegrate}\left (\text{sech}^2(a+b x) F(c,d,\tanh (a+b x),r,s),x\right )$

[Out]

CannotIntegrate[F[c, d, Tanh[a + b*x], r, s]*Sech[a + b*x]^2, x]

________________________________________________________________________________________

Rubi [A]  time = 0.0200352, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, $$\frac{\text{number of rules}}{\text{integrand size}}$$ = 0., Rules used = {} $\int F(c,d,\tanh (a+b x),r,s) \text{sech}^2(a+b x) \, dx$

Veriﬁcation is Not applicable to the result.

[In]

Int[F[c, d, Tanh[a + b*x], r, s]*Sech[a + b*x]^2,x]

[Out]

Defer[Subst][Defer[Int][F[c, d, x, r, s], x], x, Tanh[a + b*x]]/b

Rubi steps

\begin{align*} \int F(c,d,\tanh (a+b x),r,s) \text{sech}^2(a+b x) \, dx &=\frac{\operatorname{Subst}(\int F(c,d,x,r,s) \, dx,x,\tanh (a+b x))}{b}\\ \end{align*}

Mathematica [A]  time = 0.0757455, size = 0, normalized size = 0. $\int F(c,d,\tanh (a+b x),r,s) \text{sech}^2(a+b x) \, dx$

Veriﬁcation is Not applicable to the result.

[In]

Integrate[F[c, d, Tanh[a + b*x], r, s]*Sech[a + b*x]^2,x]

[Out]

Integrate[F[c, d, Tanh[a + b*x], r, s]*Sech[a + b*x]^2, x]

________________________________________________________________________________________

Maple [A]  time = 0.026, size = 0, normalized size = 0. \begin{align*} \int F \left ( c,d,\tanh \left ( bx+a \right ) ,r,s \right ) \left ({\rm sech} \left (bx+a\right ) \right ) ^{2}\, dx \end{align*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int(F(c,d,tanh(b*x+a),r,s)*sech(b*x+a)^2,x)

[Out]

int(F(c,d,tanh(b*x+a),r,s)*sech(b*x+a)^2,x)

________________________________________________________________________________________

Maxima [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int F\left (c, d, \tanh \left (b x + a\right ), r, s\right ) \operatorname{sech}\left (b x + a\right )^{2}\,{d x} \end{align*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(F(c,d,tanh(b*x+a),r,s)*sech(b*x+a)^2,x, algorithm="maxima")

[Out]

integrate(F(c, d, tanh(b*x + a), r, s)*sech(b*x + a)^2, x)

________________________________________________________________________________________

Fricas [A]  time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (F\left (c, d, \tanh \left (b x + a\right ), r, s\right ) \operatorname{sech}\left (b x + a\right )^{2}, x\right ) \end{align*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(F(c,d,tanh(b*x+a),r,s)*sech(b*x+a)^2,x, algorithm="fricas")

[Out]

integral(F(c, d, tanh(b*x + a), r, s)*sech(b*x + a)^2, x)

________________________________________________________________________________________

Sympy [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int F{\left (c,d,\tanh{\left (a + b x \right )},r,s \right )} \operatorname{sech}^{2}{\left (a + b x \right )}\, dx \end{align*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(F(c,d,tanh(b*x+a),r,s)*sech(b*x+a)**2,x)

[Out]

Integral(F(c, d, tanh(a + b*x), r, s)*sech(a + b*x)**2, x)

________________________________________________________________________________________

Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int F\left (c, d, \tanh \left (b x + a\right ), r, s\right ) \operatorname{sech}\left (b x + a\right )^{2}\,{d x} \end{align*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(F(c,d,tanh(b*x+a),r,s)*sech(b*x+a)^2,x, algorithm="giac")

[Out]

integrate(F(c, d, tanh(b*x + a), r, s)*sech(b*x + a)^2, x)