3.36 \(\int \frac{\text{csch}^3(a+b x)}{c+d x} \, dx\)

Optimal. Leaf size=18 \[ \text{Unintegrable}\left (\frac{\text{csch}^3(a+b x)}{c+d x},x\right ) \]

[Out]

Unintegrable[Csch[a + b*x]^3/(c + d*x), x]

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Rubi [A]  time = 0.0396201, 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 = {} \[ \int \frac{\text{csch}^3(a+b x)}{c+d x} \, dx \]

Verification is Not applicable to the result.

[In]

Int[Csch[a + b*x]^3/(c + d*x),x]

[Out]

Defer[Int][Csch[a + b*x]^3/(c + d*x), x]

Rubi steps

\begin{align*} \int \frac{\text{csch}^3(a+b x)}{c+d x} \, dx &=\int \frac{\text{csch}^3(a+b x)}{c+d x} \, dx\\ \end{align*}

Mathematica [A]  time = 74.2687, size = 0, normalized size = 0. \[ \int \frac{\text{csch}^3(a+b x)}{c+d x} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[Csch[a + b*x]^3/(c + d*x),x]

[Out]

Integrate[Csch[a + b*x]^3/(c + d*x), x]

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Maple [A]  time = 0.484, size = 0, normalized size = 0. \begin{align*} \int{\frac{ \left ({\rm csch} \left (bx+a\right ) \right ) ^{3}}{dx+c}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(csch(b*x+a)^3/(d*x+c),x)

[Out]

int(csch(b*x+a)^3/(d*x+c),x)

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Maxima [A]  time = 0., size = 0, normalized size = 0. \begin{align*} -\frac{{\left (b d x e^{\left (3 \, a\right )} +{\left (b c - d\right )} e^{\left (3 \, a\right )}\right )} e^{\left (3 \, b x\right )} +{\left (b d x e^{a} +{\left (b c + d\right )} e^{a}\right )} e^{\left (b x\right )}}{b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2} +{\left (b^{2} d^{2} x^{2} e^{\left (4 \, a\right )} + 2 \, b^{2} c d x e^{\left (4 \, a\right )} + b^{2} c^{2} e^{\left (4 \, a\right )}\right )} e^{\left (4 \, b x\right )} - 2 \,{\left (b^{2} d^{2} x^{2} e^{\left (2 \, a\right )} + 2 \, b^{2} c d x e^{\left (2 \, a\right )} + b^{2} c^{2} e^{\left (2 \, a\right )}\right )} e^{\left (2 \, b x\right )}} - 8 \, \int \frac{b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2} - 2 \, d^{2}}{16 \,{\left (b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3} +{\left (b^{2} d^{3} x^{3} e^{a} + 3 \, b^{2} c d^{2} x^{2} e^{a} + 3 \, b^{2} c^{2} d x e^{a} + b^{2} c^{3} e^{a}\right )} e^{\left (b x\right )}\right )}}\,{d x} - 8 \, \int -\frac{b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2} - 2 \, d^{2}}{16 \,{\left (b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3} -{\left (b^{2} d^{3} x^{3} e^{a} + 3 \, b^{2} c d^{2} x^{2} e^{a} + 3 \, b^{2} c^{2} d x e^{a} + b^{2} c^{3} e^{a}\right )} e^{\left (b x\right )}\right )}}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(csch(b*x+a)^3/(d*x+c),x, algorithm="maxima")

[Out]

-((b*d*x*e^(3*a) + (b*c - d)*e^(3*a))*e^(3*b*x) + (b*d*x*e^a + (b*c + d)*e^a)*e^(b*x))/(b^2*d^2*x^2 + 2*b^2*c*
d*x + b^2*c^2 + (b^2*d^2*x^2*e^(4*a) + 2*b^2*c*d*x*e^(4*a) + b^2*c^2*e^(4*a))*e^(4*b*x) - 2*(b^2*d^2*x^2*e^(2*
a) + 2*b^2*c*d*x*e^(2*a) + b^2*c^2*e^(2*a))*e^(2*b*x)) - 8*integrate(1/16*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2
- 2*d^2)/(b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3 + (b^2*d^3*x^3*e^a + 3*b^2*c*d^2*x^2*e^a +
3*b^2*c^2*d*x*e^a + b^2*c^3*e^a)*e^(b*x)), x) - 8*integrate(-1/16*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2 - 2*d^2
)/(b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3 - (b^2*d^3*x^3*e^a + 3*b^2*c*d^2*x^2*e^a + 3*b^2*c^
2*d*x*e^a + b^2*c^3*e^a)*e^(b*x)), 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 )^{3}}{d x + c}, x\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(csch(b*x+a)^3/(d*x+c),x, algorithm="fricas")

[Out]

integral(csch(b*x + a)^3/(d*x + c), x)

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Sympy [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\operatorname{csch}^{3}{\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)**3/(d*x+c),x)

[Out]

Integral(csch(a + b*x)**3/(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 )^{3}}{d x + c}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(csch(b*x+a)^3/(d*x+c),x, algorithm="giac")

[Out]

integrate(csch(b*x + a)^3/(d*x + c), x)