### 3.402 $$\int \frac{\coth (a+b x)}{x} \, dx$$

Optimal. Leaf size=12 $\text{Unintegrable}\left (\frac{\coth (a+b x)}{x},x\right )$

[Out]

Unintegrable[Coth[a + b*x]/x, x]

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Rubi [A]  time = 0.0159891, 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 = {} $\int \frac{\coth (a+b x)}{x} \, dx$

Veriﬁcation is Not applicable to the result.

[In]

Int[Coth[a + b*x]/x,x]

[Out]

Defer[Int][Coth[a + b*x]/x, x]

Rubi steps

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

Mathematica [A]  time = 0.434758, size = 0, normalized size = 0. $\int \frac{\coth (a+b x)}{x} \, dx$

Veriﬁcation is Not applicable to the result.

[In]

Integrate[Coth[a + b*x]/x,x]

[Out]

Integrate[Coth[a + b*x]/x, x]

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Maple [A]  time = 0.061, size = 0, normalized size = 0. \begin{align*} \int{\frac{\cosh \left ( bx+a \right ){\rm csch} \left (bx+a\right )}{x}}\, dx \end{align*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-integrate(1/(x*e^(b*x + a) + x), x) + integrate(1/(x*e^(b*x + a) - x), x) + log(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 ) \operatorname{csch}\left (b x + a\right )}{x}, x\right ) \end{align*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Integral(cosh(a + b*x)*csch(a + b*x)/x, x)

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

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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