\(\int \frac {\coth ^{-1}(1-d-d \coth (a+b x))}{x} \, dx\) [230]

Optimal result

Integrand size = 19, antiderivative size = 19 \[ \int \frac {\coth ^{-1}(1-d-d \coth (a+b x))}{x} \, dx=\text {Int}\left (\frac {\coth ^{-1}(1-d-d \coth (a+b x))}{x},x\right ) \]

[Out]

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

Rubi [N/A]

Not integrable

Time = 0.07 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.00, number of steps used = 0, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \frac {\coth ^{-1}(1-d-d \coth (a+b x))}{x} \, dx=\int \frac {\coth ^{-1}(1-d-d \coth (a+b x))}{x} \, dx \]

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

Mathematica [N/A]

Not integrable

Time = 2.91 (sec) , antiderivative size = 21, normalized size of antiderivative = 1.11 \[ \int \frac {\coth ^{-1}(1-d-d \coth (a+b x))}{x} \, dx=\int \frac {\coth ^{-1}(1-d-d \coth (a+b x))}{x} \, dx \]

[In]

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

[Out]

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

Maple [N/A] (verified)

Not integrable

Time = 0.11 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.00

\[\int \frac {\operatorname {arccoth}\left (1-d -d \coth \left (b x +a \right )\right )}{x}d x\]

[In]

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

[Out]

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

Fricas [N/A]

Not integrable

Time = 0.25 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.00 \[ \int \frac {\coth ^{-1}(1-d-d \coth (a+b x))}{x} \, dx=\int { \frac {\operatorname {arcoth}\left (-d \coth \left (b x + a\right ) - d + 1\right )}{x} \,d x } \]

[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)

Sympy [N/A]

Not integrable

Time = 1.65 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.89 \[ \int \frac {\coth ^{-1}(1-d-d \coth (a+b x))}{x} \, dx=- \int \frac {\operatorname {acoth}{\left (d \coth {\left (a + b x \right )} + d - 1 \right )}}{x}\, dx \]

[In]

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

[Out]

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

Maxima [N/A]

Not integrable

Time = 1.00 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.05 \[ \int \frac {\coth ^{-1}(1-d-d \coth (a+b x))}{x} \, dx=\int { \frac {\operatorname {arcoth}\left (-d \coth \left (b x + a\right ) - d + 1\right )}{x} \,d x } \]

[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)

Giac [N/A]

Not integrable

Time = 0.35 (sec) , antiderivative size = 21, normalized size of antiderivative = 1.11 \[ \int \frac {\coth ^{-1}(1-d-d \coth (a+b x))}{x} \, dx=\int { \frac {\operatorname {arcoth}\left (-d \coth \left (b x + a\right ) - d + 1\right )}{x} \,d x } \]

[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)

Mupad [N/A]

Not integrable

Time = 4.46 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.00 \[ \int \frac {\coth ^{-1}(1-d-d \coth (a+b x))}{x} \, dx=\int -\frac {\mathrm {acoth}\left (d+d\,\mathrm {coth}\left (a+b\,x\right )-1\right )}{x} \,d x \]

[In]

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

[Out]

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