3.3.25 \(\int \frac {\coth ^{-1}(1+d+d \coth (a+b x))}{x} \, dx\) [225]

Optimal. Leaf size=19 \[ \text {Int}\left (\frac {\coth ^{-1}(1+d+d \coth (a+b x))}{x},x\right ) \]

[Out]

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

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Rubi [A]
time = 0.07, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {\coth ^{-1}(1+d+d \coth (a+b x))}{x} \, dx \end {gather*}

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*}

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Mathematica [A]
time = 2.45, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\coth ^{-1}(1+d+d \coth (a+b x))}{x} \, dx \end {gather*}

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 = 0.22, size = 0, normalized size = 0.00 \[\int \frac {\mathrm {arccoth}\left (1+d +d \coth \left (b x +a \right )\right )}{x}\, dx\]

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 = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}

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 = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

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 = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\operatorname {acoth}{\left (d \coth {\left (a + b x \right )} + d + 1 \right )}}{x}\, dx \end {gather*}

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 = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

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)

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Mupad [A]
time = 0.00, size = -1, normalized size = -0.05 \begin {gather*} \int \frac {\mathrm {acoth}\left (d+d\,\mathrm {coth}\left (a+b\,x\right )+1\right )}{x} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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