3.17 \(\int \frac{x^4}{a+b \text{csch}(c+d x^2)} \, dx\)

Optimal. Leaf size=20 \[ \text{Unintegrable}\left (\frac{x^4}{a+b \text{csch}\left (c+d x^2\right )},x\right ) \]

[Out]

Unintegrable[x^4/(a + b*Csch[c + d*x^2]), x]

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Rubi [A]  time = 0.0292243, 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 = {} \[ \int \frac{x^4}{a+b \text{csch}\left (c+d x^2\right )} \, dx \]

Verification is Not applicable to the result.

[In]

Int[x^4/(a + b*Csch[c + d*x^2]),x]

[Out]

Defer[Int][x^4/(a + b*Csch[c + d*x^2]), x]

Rubi steps

\begin{align*} \int \frac{x^4}{a+b \text{csch}\left (c+d x^2\right )} \, dx &=\int \frac{x^4}{a+b \text{csch}\left (c+d x^2\right )} \, dx\\ \end{align*}

Mathematica [A]  time = 9.007, size = 0, normalized size = 0. \[ \int \frac{x^4}{a+b \text{csch}\left (c+d x^2\right )} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[x^4/(a + b*Csch[c + d*x^2]),x]

[Out]

Integrate[x^4/(a + b*Csch[c + d*x^2]), x]

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Maple [A]  time = 0.055, size = 0, normalized size = 0. \begin{align*} \int{\frac{{x}^{4}}{a+b{\rm csch} \left (d{x}^{2}+c\right )}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x^4/(a+b*csch(d*x^2+c)),x)

[Out]

int(x^4/(a+b*csch(d*x^2+c)),x)

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Maxima [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \frac{x^{5}}{5 \, a} - 2 \, b \int \frac{x^{4} e^{\left (d x^{2} + c\right )}}{a^{2} e^{\left (2 \, d x^{2} + 2 \, c\right )} + 2 \, a b e^{\left (d x^{2} + c\right )} - a^{2}}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^4/(a+b*csch(d*x^2+c)),x, algorithm="maxima")

[Out]

1/5*x^5/a - 2*b*integrate(x^4*e^(d*x^2 + c)/(a^2*e^(2*d*x^2 + 2*c) + 2*a*b*e^(d*x^2 + c) - a^2), x)

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Fricas [A]  time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{x^{4}}{b \operatorname{csch}\left (d x^{2} + c\right ) + a}, x\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^4/(a+b*csch(d*x^2+c)),x, algorithm="fricas")

[Out]

integral(x^4/(b*csch(d*x^2 + c) + a), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x**4/(a+b*csch(d*x**2+c)),x)

[Out]

Integral(x**4/(a + b*csch(c + d*x**2)), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^4/(a+b*csch(d*x^2+c)),x, algorithm="giac")

[Out]

integrate(x^4/(b*csch(d*x^2 + c) + a), x)