### 3.437 $$\int \frac{\coth ^2(a+b x)}{x^2} \, dx$$

Optimal. Leaf size=14 $\text{Unintegrable}\left (\frac{\coth ^2(a+b x)}{x^2},x\right )$

[Out]

Unintegrable[Coth[a + b*x]^2/x^2, x]

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Rubi [A]  time = 0.0306246, 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 = {} $\int \frac{\coth ^2(a+b x)}{x^2} \, dx$

Veriﬁcation is Not applicable to the result.

[In]

Int[Coth[a + b*x]^2/x^2,x]

[Out]

Defer[Int][Coth[a + b*x]^2/x^2, x]

Rubi steps

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

Mathematica [A]  time = 0.890475, size = 0, normalized size = 0. $\int \frac{\coth ^2(a+b x)}{x^2} \, dx$

Veriﬁcation is Not applicable to the result.

[In]

Integrate[Coth[a + b*x]^2/x^2,x]

[Out]

Integrate[Coth[a + b*x]^2/x^2, x]

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Maple [A]  time = 0.095, size = 0, normalized size = 0. \begin{align*} \int{\frac{ \left ( \cosh \left ( bx+a \right ) \right ) ^{2} \left ({\rm csch} \left (bx+a\right ) \right ) ^{2}}{{x}^{2}}}\, dx \end{align*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Maxima [A]  time = 0., size = 0, normalized size = 0. \begin{align*} -\frac{b x e^{\left (2 \, b x + 2 \, a\right )} - b x + 2}{b x^{2} e^{\left (2 \, b x + 2 \, a\right )} - b x^{2}} + 2 \, \int \frac{1}{b x^{3} e^{\left (b x + a\right )} + b x^{3}}\,{d x} - 2 \, \int \frac{1}{b x^{3} e^{\left (b x + a\right )} - b x^{3}}\,{d x} \end{align*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-(b*x*e^(2*b*x + 2*a) - b*x + 2)/(b*x^2*e^(2*b*x + 2*a) - b*x^2) + 2*integrate(1/(b*x^3*e^(b*x + a) + b*x^3),
x) - 2*integrate(1/(b*x^3*e^(b*x + a) - b*x^3), x)

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

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Sympy [F(-1)]  time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Timed out

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

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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