3.31 \(\int \frac{\text{csch}^2(a+b x)}{c+d x} \, dx\)

Optimal. Leaf size=18 \[ \text{Unintegrable}\left (\frac{\text{csch}^2(a+b x)}{c+d x},x\right ) \]

[Out]

Unintegrable[Csch[a + b*x]^2/(c + d*x), x]

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Rubi [A]  time = 0.0403233, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ \int \frac{\text{csch}^2(a+b x)}{c+d x} \, dx \]

Verification is Not applicable to the result.

[In]

Int[Csch[a + b*x]^2/(c + d*x),x]

[Out]

Defer[Int][Csch[a + b*x]^2/(c + d*x), x]

Rubi steps

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

Mathematica [A]  time = 17.713, size = 0, normalized size = 0. \[ \int \frac{\text{csch}^2(a+b x)}{c+d x} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[Csch[a + b*x]^2/(c + d*x),x]

[Out]

Integrate[Csch[a + b*x]^2/(c + d*x), x]

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Maple [A]  time = 0.061, size = 0, normalized size = 0. \begin{align*} \int{\frac{ \left ({\rm csch} \left (bx+a\right ) \right ) ^{2}}{dx+c}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Maxima [A]  time = 0., size = 0, normalized size = 0. \begin{align*} 4 \, d \int \frac{1}{4 \,{\left (b d^{2} x^{2} + 2 \, b c d x + b c^{2} +{\left (b d^{2} x^{2} e^{a} + 2 \, b c d x e^{a} + b c^{2} e^{a}\right )} e^{\left (b x\right )}\right )}}\,{d x} - 4 \, d \int -\frac{1}{4 \,{\left (b d^{2} x^{2} + 2 \, b c d x + b c^{2} -{\left (b d^{2} x^{2} e^{a} + 2 \, b c d x e^{a} + b c^{2} e^{a}\right )} e^{\left (b x\right )}\right )}}\,{d x} + \frac{2}{b d x + b c -{\left (b d x e^{\left (2 \, a\right )} + b c e^{\left (2 \, a\right )}\right )} e^{\left (2 \, b x\right )}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Fricas [A]  time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{\operatorname{csch}\left (b x + a\right )^{2}}{d x + c}, x\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Sympy [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\operatorname{csch}^{2}{\left (a + b x \right )}}{c + d x}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\operatorname{csch}\left (b x + a\right )^{2}}{d x + c}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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