3.230 \(\int \frac{\coth ^{-1}(1-d-d \coth (a+b x))}{x} \, dx\)

Optimal. Leaf size=21 \[ \text{CannotIntegrate}\left (\frac{\coth ^{-1}(d (-\coth (a+b x))-d+1)}{x},x\right ) \]

[Out]

CannotIntegrate[ArcCoth[1 - d - d*Coth[a + b*x]]/x, x]

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Rubi [A]  time = 0.0834828, 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 = {} \[ \int \frac{\coth ^{-1}(1-d-d \coth (a+b x))}{x} \, dx \]

Verification is Not applicable to the result.

[In]

Int[ArcCoth[1 - d - d*Coth[a + b*x]]/x,x]

[Out]

Defer[Int][ArcCoth[1 - d - d*Coth[a + b*x]]/x, x]

Rubi steps

\begin{align*} \int \frac{\coth ^{-1}(1-d-d \coth (a+b x))}{x} \, dx &=\int \frac{\coth ^{-1}(1-d-d \coth (a+b x))}{x} \, dx\\ \end{align*}

Mathematica [A]  time = 3.29888, size = 0, normalized size = 0. \[ \int \frac{\coth ^{-1}(1-d-d \coth (a+b x))}{x} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[ArcCoth[1 - d - d*Coth[a + b*x]]/x,x]

[Out]

Integrate[ArcCoth[1 - d - d*Coth[a + b*x]]/x, x]

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Maple [A]  time = 0.392, size = 0, normalized size = 0. \begin{align*} \int{\frac{{\rm arccoth} \left (1-d-d{\rm coth} \left (bx+a\right )\right )}{x}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(arccoth(1-d-d*coth(b*x+a))/x,x)

[Out]

int(arccoth(1-d-d*coth(b*x+a))/x,x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(arccoth(1-d-d*coth(b*x+a))/x,x, algorithm="maxima")

[Out]

-integrate(arccoth(d*coth(b*x + a) + d - 1)/x, x)

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Fricas [A]  time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (-\frac{\operatorname{arcoth}\left (d \coth \left (b x + a\right ) + d - 1\right )}{x}, x\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(arccoth(1-d-d*coth(b*x+a))/x,x, algorithm="fricas")

[Out]

integral(-arccoth(d*coth(b*x + a) + d - 1)/x, x)

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Sympy [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\operatorname{acoth}{\left (- d \coth{\left (a + b x \right )} - d + 1 \right )}}{x}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(acoth(1-d-d*coth(b*x+a))/x,x)

[Out]

Integral(acoth(-d*coth(a + b*x) - d + 1)/x, x)

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Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\operatorname{arcoth}\left (-d \coth \left (b x + a\right ) - d + 1\right )}{x}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(arccoth(1-d-d*coth(b*x+a))/x,x, algorithm="giac")

[Out]

integrate(arccoth(-d*coth(b*x + a) - d + 1)/x, x)