### 3.436 $$\int \frac{\coth ^2(a+b x)}{x} \, dx$$

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

[Out]

Unintegrable[Coth[a + b*x]^2/x, x]

________________________________________________________________________________________

Rubi [A]  time = 0.0300103, 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 = {} $\int \frac{\coth ^2(a+b x)}{x} \, dx$

Veriﬁcation is Not applicable to the result.

[In]

Int[Coth[a + b*x]^2/x,x]

[Out]

Defer[Int][Coth[a + b*x]^2/x, x]

Rubi steps

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

Mathematica [A]  time = 0.378467, size = 0, normalized size = 0. $\int \frac{\coth ^2(a+b x)}{x} \, dx$

Veriﬁcation is Not applicable to the result.

[In]

Integrate[Coth[a + b*x]^2/x,x]

[Out]

Integrate[Coth[a + b*x]^2/x, x]

________________________________________________________________________________________

Maple [A]  time = 0.059, 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}}\, 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,x)

[Out]

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

________________________________________________________________________________________

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

[Out]

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

________________________________________________________________________________________

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}, 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,x, algorithm="fricas")

[Out]

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

________________________________________________________________________________________

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,x)

[Out]

Timed out

________________________________________________________________________________________

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}\,{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,x, algorithm="giac")

[Out]

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