3.1.24 \(\int \frac {x^4}{(a+b \text {csch}(c+d x^2))^2} \, dx\) [24]

Optimal. Leaf size=21 \[ \text {Int}\left (\frac {x^4}{\left (a+b \text {csch}\left (c+d x^2\right )\right )^2},x\right ) \]

[Out]

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

________________________________________________________________________________________

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

Verification is not applicable to the result.

[In]

Int[x^4/(a + b*Csch[c + d*x^2])^2,x]

[Out]

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

Rubi steps

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

________________________________________________________________________________________

Mathematica [A]
time = 119.71, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {x^4}{\left (a+b \text {csch}\left (c+d x^2\right )\right )^2} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

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

________________________________________________________________________________________

Maple [A]
time = 1.85, size = 0, normalized size = 0.00 \[\int \frac {x^{4}}{\left (a +b \,\mathrm {csch}\left (d \,x^{2}+c \right )\right )^{2}}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

________________________________________________________________________________________

Maxima [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-1/5*((a^3*d*e^(2*c) + a*b^2*d*e^(2*c))*x^5*e^(2*d*x^2) - 5*a*b^2*x^3 - (a^3*d + a*b^2*d)*x^5 + (5*b^3*x^3*e^c
+ 2*(a^2*b*d*e^c + b^3*d*e^c)*x^5)*e^(d*x^2))/(a^5*d + a^3*b^2*d - (a^5*d*e^(2*c) + a^3*b^2*d*e^(2*c))*e^(2*d
*x^2) - 2*(a^4*b*d*e^c + a^2*b^3*d*e^c)*e^(d*x^2)) - integrate((3*a*b^2*x^2 - (3*b^3*x^2*e^c + 2*(2*a^2*b*d*e^
c + b^3*d*e^c)*x^4)*e^(d*x^2))/(a^5*d + a^3*b^2*d - (a^5*d*e^(2*c) + a^3*b^2*d*e^(2*c))*e^(2*d*x^2) - 2*(a^4*b
*d*e^c + a^2*b^3*d*e^c)*e^(d*x^2)), x)

________________________________________________________________________________________

Fricas [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

________________________________________________________________________________________

Sympy [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {x^{4}}{\left (a + b \operatorname {csch}{\left (c + d x^{2} \right )}\right )^{2}}\, dx \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

________________________________________________________________________________________

Giac [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

________________________________________________________________________________________

Mupad [A]
time = 0.00, size = -1, normalized size = -0.05 \begin {gather*} \int \frac {x^4}{{\left (a+\frac {b}{\mathrm {sinh}\left (d\,x^2+c\right )}\right )}^2} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x^4/(a + b/sinh(c + d*x^2))^2,x)

[Out]

int(x^4/(a + b/sinh(c + d*x^2))^2, x)

________________________________________________________________________________________