3.403 \(\int \frac {\coth (a+b x)}{x^2} \, dx\)

Optimal. Leaf size=13 \[ \text {Int}\left (\frac {\coth (a+b x)}{x^2},x\right ) \]

[Out]

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

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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 = {} \[ \int \frac {\coth (a+b x)}{x^2} \, dx \]

Verification is Not applicable to the result.

[In]

Int[Coth[a + b*x]/x^2,x]

[Out]

Defer[Int][Coth[a + b*x]/x^2, x]

Rubi steps

\begin {align*} \int \frac {\coth (a+b x)}{x^2} \, dx &=\int \frac {\coth (a+b x)}{x^2} \, dx\\ \end {align*}

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Mathematica [A]  time = 0.87, size = 0, normalized size = 0.00 \[ \int \frac {\coth (a+b x)}{x^2} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[Coth[a + b*x]/x^2,x]

[Out]

Integrate[Coth[a + b*x]/x^2, x]

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fricas [A]  time = 0.45, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\cosh \left (b x + a\right ) \operatorname {csch}\left (b x + a\right )}{x^{2}}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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giac [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\cosh \left (b x + a\right ) \operatorname {csch}\left (b x + a\right )}{x^{2}}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maple [A]  time = 0.46, size = 0, normalized size = 0.00 \[ \int \frac {\cosh \left (b x +a \right ) \mathrm {csch}\left (b x +a \right )}{x^{2}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maxima [A]  time = 0.00, size = 0, normalized size = 0.00 \[ -\frac {1}{x} - \int \frac {1}{x^{2} e^{\left (b x + a\right )} + x^{2}}\,{d x} + \int \frac {1}{x^{2} e^{\left (b x + a\right )} - x^{2}}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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mupad [A]  time = 0.00, size = -1, normalized size = -0.08 \[ \int \frac {\mathrm {cosh}\left (a+b\,x\right )}{x^2\,\mathrm {sinh}\left (a+b\,x\right )} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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sympy [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\cosh {\left (a + b x \right )} \operatorname {csch}{\left (a + b x \right )}}{x^{2}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Integral(cosh(a + b*x)*csch(a + b*x)/x**2, x)

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