\(\int \frac {\text {csch}^2(a+b x)}{x} \, dx\) [8]

Optimal result

Integrand size = 12, antiderivative size = 12 \[ \int \frac {\text {csch}^2(a+b x)}{x} \, dx=\text {Int}\left (\frac {\text {csch}^2(a+b x)}{x},x\right ) \]

[Out]

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

Rubi [N/A]

Not integrable

Time = 0.02 (sec) , antiderivative size = 12, 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 = {} \[ \int \frac {\text {csch}^2(a+b x)}{x} \, dx=\int \frac {\text {csch}^2(a+b x)}{x} \, dx \]

[In]

Int[Csch[a + b*x]^2/x,x]

[Out]

Defer[Int][Csch[a + b*x]^2/x, x]

Rubi steps \begin{align*} \text {integral}& = \int \frac {\text {csch}^2(a+b x)}{x} \, dx \\ \end{align*}

Mathematica [N/A]

Not integrable

Time = 6.40 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int \frac {\text {csch}^2(a+b x)}{x} \, dx=\int \frac {\text {csch}^2(a+b x)}{x} \, dx \]

[In]

Integrate[Csch[a + b*x]^2/x,x]

[Out]

Integrate[Csch[a + b*x]^2/x, x]

Maple [N/A] (verified)

Not integrable

Time = 0.09 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00

\[\int \frac {\operatorname {csch}\left (b x +a \right )^{2}}{x}d x\]

[In]

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

[Out]

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

Fricas [N/A]

Not integrable

Time = 0.27 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int \frac {\text {csch}^2(a+b x)}{x} \, dx=\int { \frac {\operatorname {csch}\left (b x + a\right )^{2}}{x} \,d x } \]

[In]

integrate(csch(b*x+a)^2/x,x, algorithm="fricas")

[Out]

integral(csch(b*x + a)^2/x, x)

Sympy [N/A]

Not integrable

Time = 0.32 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.83 \[ \int \frac {\text {csch}^2(a+b x)}{x} \, dx=\int \frac {\operatorname {csch}^{2}{\left (a + b x \right )}}{x}\, dx \]

[In]

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

[Out]

Integral(csch(a + b*x)**2/x, x)

Maxima [N/A]

Not integrable

Time = 0.30 (sec) , antiderivative size = 73, normalized size of antiderivative = 6.08 \[ \int \frac {\text {csch}^2(a+b x)}{x} \, dx=\int { \frac {\operatorname {csch}\left (b x + a\right )^{2}}{x} \,d x } \]

[In]

integrate(csch(b*x+a)^2/x,x, algorithm="maxima")

[Out]

-2/(b*x*e^(2*b*x + 2*a) - b*x) + 4*integrate(1/4/(b*x^2*e^(b*x + a) + b*x^2), x) - 4*integrate(1/4/(b*x^2*e^(b
*x + a) - b*x^2), x)

Giac [N/A]

Not integrable

Time = 0.29 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int \frac {\text {csch}^2(a+b x)}{x} \, dx=\int { \frac {\operatorname {csch}\left (b x + a\right )^{2}}{x} \,d x } \]

[In]

integrate(csch(b*x+a)^2/x,x, algorithm="giac")

[Out]

integrate(csch(b*x + a)^2/x, x)

Mupad [N/A]

Not integrable

Time = 2.12 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int \frac {\text {csch}^2(a+b x)}{x} \, dx=\int \frac {1}{x\,{\mathrm {sinh}\left (a+b\,x\right )}^2} \,d x \]

[In]

int(1/(x*sinh(a + b*x)^2),x)

[Out]

int(1/(x*sinh(a + b*x)^2), x)