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

Optimal. Leaf size=15 \[ \text {Int}\left (\frac {\coth ^2(a+b x)}{x^2},x\right ) \]

[Out]

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

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Rubi [A]  time = 0.03, 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 = {} \[ \int \frac {\coth ^2(a+b x)}{x^2} \, dx \]

Verification is Not applicable to the result.

[In]

Int[Coth[a + b*x]^2/x^2,x]

[Out]

Defer[Int][Coth[a + b*x]^2/x^2, x]

Rubi steps

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

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Mathematica [A]  time = 0.92, size = 0, normalized size = 0.00 \[ \int \frac {\coth ^2(a+b x)}{x^2} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[Coth[a + b*x]^2/x^2,x]

[Out]

Integrate[Coth[a + b*x]^2/x^2, x]

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fricas [A]  time = 0.41, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\cosh \left (b x + a\right )^{2} \operatorname {csch}\left (b x + a\right )^{2}}{x^{2}}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maple [A]  time = 0.59, size = 0, normalized size = 0.00 \[ \int \frac {\left (\cosh ^{2}\left (b x +a \right )\right ) \mathrm {csch}\left (b x +a \right )^{2}}{x^{2}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maxima [A]  time = 0.00, size = 0, normalized size = 0.00 \[ -\frac {b x e^{\left (2 \, b x + 2 \, a\right )} - b x + 2}{b x^{2} e^{\left (2 \, b x + 2 \, a\right )} - b x^{2}} + 2 \, \int \frac {1}{b x^{3} e^{\left (b x + a\right )} + b x^{3}}\,{d x} - 2 \, \int \frac {1}{b x^{3} e^{\left (b x + a\right )} - b x^{3}}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-(b*x*e^(2*b*x + 2*a) - b*x + 2)/(b*x^2*e^(2*b*x + 2*a) - b*x^2) + 2*integrate(1/(b*x^3*e^(b*x + a) + b*x^3),
x) - 2*integrate(1/(b*x^3*e^(b*x + a) - b*x^3), x)

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mupad [A]  time = 0.00, size = -1, normalized size = -0.07 \[ \int \frac {{\mathrm {cosh}\left (a+b\,x\right )}^2}{x^2\,{\mathrm {sinh}\left (a+b\,x\right )}^2} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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