3.5.2 \(\int \frac {\coth (a+b x)}{x} \, dx\) [402]

Optimal. Leaf size=13 \[ \text {Int}\left (\frac {\coth (a+b x)}{x},x\right ) \]

[Out]

Unintegrable(coth(b*x+a)/x,x)

________________________________________________________________________________________

Rubi [A]
time = 0.02, 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 (a+b x)}{x} \, dx \end {gather*}

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 = 0.32, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\coth (a+b x)}{x} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[Coth[a + b*x]/x,x]

[Out]

Integrate[Coth[a + b*x]/x, x]

________________________________________________________________________________________

Maple [A]
time = 0.98, size = 0, normalized size = 0.00 \[\int \frac {\cosh \left (b x +a \right ) \mathrm {csch}\left (b x +a \right )}{x}\, dx\]

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)

________________________________________________________________________________________

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(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)

________________________________________________________________________________________

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

[Out]

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

________________________________________________________________________________________

Sympy [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\cosh {\left (a + b x \right )} \operatorname {csch}{\left (a + b x \right )}}{x}\, dx \end {gather*}

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)

________________________________________________________________________________________

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

[Out]

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

________________________________________________________________________________________

Mupad [A]
time = 0.00, size = -1, normalized size = -0.08 \begin {gather*} \int \frac {\mathrm {cosh}\left (a+b\,x\right )}{x\,\mathrm {sinh}\left (a+b\,x\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

________________________________________________________________________________________