3.1.37 \(\int \frac {\text {csch}^3(a+b x)}{(c+d x)^2} \, dx\) [37]

Optimal. Leaf size=19 \[ \text {Int}\left (\frac {\text {csch}^3(a+b x)}{(c+d x)^2},x\right ) \]

[Out]

Unintegrable(csch(b*x+a)^3/(d*x+c)^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 = {} \begin {gather*} \int \frac {\text {csch}^3(a+b x)}{(c+d x)^2} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[Csch[a + b*x]^3/(c + d*x)^2,x]

[Out]

Defer[Int][Csch[a + b*x]^3/(c + d*x)^2, x]

Rubi steps

\begin {align*} \int \frac {\text {csch}^3(a+b x)}{(c+d x)^2} \, dx &=\int \frac {\text {csch}^3(a+b x)}{(c+d x)^2} \, dx\\ \end {align*}

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Mathematica [A]
time = 55.69, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\text {csch}^3(a+b x)}{(c+d x)^2} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[Csch[a + b*x]^3/(c + d*x)^2,x]

[Out]

Integrate[Csch[a + b*x]^3/(c + d*x)^2, x]

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Maple [A]
time = 180.00, size = 0, normalized size = 0.00 \[\int \frac {\mathrm {csch}\left (b x +a \right )^{3}}{\left (d x +c \right )^{2}}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(csch(b*x+a)^3/(d*x+c)^2,x)

[Out]

int(csch(b*x+a)^3/(d*x+c)^2,x)

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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(csch(b*x+a)^3/(d*x+c)^2,x, algorithm="maxima")

[Out]

-((b*d*x*e^(3*a) + (b*c - 2*d)*e^(3*a))*e^(3*b*x) + (b*d*x*e^a + (b*c + 2*d)*e^a)*e^(b*x))/(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^(4*a) + 3*b^2*c*d^2*x^2*e^(4*a) + 3*b^2*c^2*d*x*e^(4*a)
+ b^2*c^3*e^(4*a))*e^(4*b*x) - 2*(b^2*d^3*x^3*e^(2*a) + 3*b^2*c*d^2*x^2*e^(2*a) + 3*b^2*c^2*d*x*e^(2*a) + b^2
*c^3*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 - 6*d^2)/(b^2*d^4*x^4 + 4*b^2
*c*d^3*x^3 + 6*b^2*c^2*d^2*x^2 + 4*b^2*c^3*d*x + b^2*c^4 + (b^2*d^4*x^4*e^a + 4*b^2*c*d^3*x^3*e^a + 6*b^2*c^2*
d^2*x^2*e^a + 4*b^2*c^3*d*x*e^a + b^2*c^4*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 - 6*d^2)/(b^2*d^4*x^4 + 4*b^2*c*d^3*x^3 + 6*b^2*c^2*d^2*x^2 + 4*b^2*c^3*d*x + b^2*c^4 - (b^2*d^4*x^4*e^
a + 4*b^2*c*d^3*x^3*e^a + 6*b^2*c^2*d^2*x^2*e^a + 4*b^2*c^3*d*x*e^a + b^2*c^4*e^a)*e^(b*x)), x)

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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(csch(b*x+a)^3/(d*x+c)^2,x, algorithm="fricas")

[Out]

integral(csch(b*x + a)^3/(d^2*x^2 + 2*c*d*x + c^2), x)

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Sympy [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\operatorname {csch}^{3}{\left (a + b x \right )}}{\left (c + d x\right )^{2}}\, dx \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(csch(b*x+a)**3/(d*x+c)**2,x)

[Out]

Integral(csch(a + b*x)**3/(c + d*x)**2, x)

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Giac [F(-1)] Timed out
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(csch(b*x+a)^3/(d*x+c)^2,x, algorithm="giac")

[Out]

Timed out

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Mupad [A]
time = 0.00, size = -1, normalized size = -0.05 \begin {gather*} \int \frac {1}{{\mathrm {sinh}\left (a+b\,x\right )}^3\,{\left (c+d\,x\right )}^2} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(sinh(a + b*x)^3*(c + d*x)^2),x)

[Out]

int(1/(sinh(a + b*x)^3*(c + d*x)^2), x)

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