### 3.1017 $$\int \text{csch}^2(a+b x) F(c,d,\coth (a+b x),r,s) \, dx$$

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

[Out]

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

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Rubi [A]  time = 0.0218718, 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 = {} $\int \text{csch}^2(a+b x) F(c,d,\coth (a+b x),r,s) \, dx$

Veriﬁcation is Not applicable to the result.

[In]

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

[Out]

-(Defer[Subst][Defer[Int][F[c, d, x, r, s], x], x, Coth[a + b*x]]/b)

Rubi steps

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

Mathematica [A]  time = 0.0698806, size = 0, normalized size = 0. $\int \text{csch}^2(a+b x) F(c,d,\coth (a+b x),r,s) \, dx$

Veriﬁcation is Not applicable to the result.

[In]

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

[Out]

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

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

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(csch(b*x+a)**2*F(c,d,coth(b*x+a),r,s),x)

[Out]

Integral(F(c, d, coth(a + b*x), r, s)*csch(a + b*x)**2, x)

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

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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