### 3.472 $$\int \frac{\text{csch}(a+b x) \text{sech}(a+b x)}{x^2} \, dx$$

Optimal. Leaf size=17 $2 \text{Unintegrable}\left (\frac{\text{csch}(2 a+2 b x)}{x^2},x\right )$

[Out]

2*Unintegrable[Csch[2*a + 2*b*x]/x^2, x]

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Rubi [A]  time = 0.0372738, 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 = {} $\int \frac{\text{csch}(a+b x) \text{sech}(a+b x)}{x^2} \, dx$

Veriﬁcation is Not applicable to the result.

[In]

Int[(Csch[a + b*x]*Sech[a + b*x])/x^2,x]

[Out]

2*Defer[Int][Csch[2*a + 2*b*x]/x^2, x]

Rubi steps

\begin{align*} \int \frac{\text{csch}(a+b x) \text{sech}(a+b x)}{x^2} \, dx &=2 \int \frac{\text{csch}(2 a+2 b x)}{x^2} \, dx\\ \end{align*}

Mathematica [A]  time = 15.6595, size = 0, normalized size = 0. $\int \frac{\text{csch}(a+b x) \text{sech}(a+b x)}{x^2} \, dx$

Veriﬁcation is Not applicable to the result.

[In]

Integrate[(Csch[a + b*x]*Sech[a + b*x])/x^2,x]

[Out]

Integrate[(Csch[a + b*x]*Sech[a + b*x])/x^2, x]

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Maple [A]  time = 0.064, size = 0, normalized size = 0. \begin{align*} \int{\frac{{\rm csch} \left (bx+a\right ){\rm sech} \left (bx+a\right )}{{x}^{2}}}\, dx \end{align*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int(csch(b*x+a)*sech(b*x+a)/x^2,x)

[Out]

int(csch(b*x+a)*sech(b*x+a)/x^2,x)

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

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(csch(b*x+a)*sech(b*x+a)/x^2,x, algorithm="maxima")

[Out]

integrate(csch(b*x + a)*sech(b*x + a)/x^2, x)

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

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(csch(b*x+a)*sech(b*x+a)/x^2,x, algorithm="fricas")

[Out]

integral(csch(b*x + a)*sech(b*x + a)/x^2, x)

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

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(csch(b*x+a)*sech(b*x+a)/x**2,x)

[Out]

Integral(csch(a + b*x)*sech(a + b*x)/x**2, x)

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

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(csch(b*x+a)*sech(b*x+a)/x^2,x, algorithm="giac")

[Out]

integrate(csch(b*x + a)*sech(b*x + a)/x^2, x)