\(\int \text {csch}^2(a+b x) F(c,d,\coth (a+b x),r,s) \, dx\) [1017]

Optimal result

Integrand size = 20, antiderivative size = 20 \[ \int \text {csch}^2(a+b x) F(c,d,\coth (a+b x),r,s) \, dx=\text {Int}\left (\text {csch}^2(a+b x) F(c,d,\coth (a+b x),r,s),x\right ) \]

[Out]

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

Rubi [N/A]

Not integrable

Time = 0.02 (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 = {} \[ \int \text {csch}^2(a+b x) F(c,d,\coth (a+b x),r,s) \, dx=\int \text {csch}^2(a+b x) F(c,d,\coth (a+b x),r,s) \, dx \]

[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*} \text {integral}& = -\frac {\text {Subst}(\int F(c,d,x,r,s) \, dx,x,\coth (a+b x))}{b} \\ \end{align*}

Mathematica [N/A]

Not integrable

Time = 0.09 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int \text {csch}^2(a+b x) F(c,d,\coth (a+b x),r,s) \, dx=\int \text {csch}^2(a+b x) F(c,d,\coth (a+b x),r,s) \, dx \]

[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]

Maple [N/A] (verified)

Not integrable

Time = 0.03 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.00

\[\int \operatorname {csch}\left (b x +a \right )^{2} F \left (c , d , \coth \left (b x +a \right ), r , s\right )d x\]

[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)

Fricas [N/A]

Not integrable

Time = 0.26 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int \text {csch}^2(a+b x) F(c,d,\coth (a+b x),r,s) \, dx=\int { F\left (c, d, \coth \left (b x + a\right ), r, s\right ) \operatorname {csch}\left (b x + a\right )^{2} \,d x } \]

[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)

Sympy [N/A]

Not integrable

Time = 3.17 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.85 \[ \int \text {csch}^2(a+b x) F(c,d,\coth (a+b x),r,s) \, dx=\int F{\left (c,d,\coth {\left (a + b x \right )},r,s \right )} \operatorname {csch}^{2}{\left (a + b x \right )}\, dx \]

[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)

Maxima [N/A]

Not integrable

Time = 0.29 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int \text {csch}^2(a+b x) F(c,d,\coth (a+b x),r,s) \, dx=\int { F\left (c, d, \coth \left (b x + a\right ), r, s\right ) \operatorname {csch}\left (b x + a\right )^{2} \,d x } \]

[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)

Giac [N/A]

Not integrable

Time = 0.27 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int \text {csch}^2(a+b x) F(c,d,\coth (a+b x),r,s) \, dx=\int { F\left (c, d, \coth \left (b x + a\right ), r, s\right ) \operatorname {csch}\left (b x + a\right )^{2} \,d x } \]

[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)

Mupad [N/A]

Not integrable

Time = 2.43 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int \text {csch}^2(a+b x) F(c,d,\coth (a+b x),r,s) \, dx=\int \frac {F\left (c,d,\mathrm {coth}\left (a+b\,x\right ),r,s\right )}{{\mathrm {sinh}\left (a+b\,x\right )}^2} \,d x \]

[In]

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

[Out]

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