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

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

[Out]

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

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Rubi [A]  time = 0.04, 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 = {} \[ \int \frac {\text {csch}^2(a+b x)}{c+d x} \, dx \]

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*}

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Mathematica [A]  time = 17.00, size = 0, normalized size = 0.00 \[ \int \frac {\text {csch}^2(a+b x)}{c+d x} \, dx \]

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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fricas [A]  time = 0.48, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\operatorname {csch}\left (b x + a\right )^{2}}{d x + c}, x\right ) \]

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

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)

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maple [A]  time = 0.10, size = 0, normalized size = 0.00 \[ \int \frac {\mathrm {csch}\left (b x +a \right )^{2}}{d x +c}\, dx \]

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 = 0.00, size = 0, normalized size = 0.00 \[ 4 \, d \int \frac {1}{4 \, {\left (b d^{2} x^{2} + 2 \, b c d x + b c^{2} + {\left (b d^{2} x^{2} e^{a} + 2 \, b c d x e^{a} + b c^{2} e^{a}\right )} e^{\left (b x\right )}\right )}}\,{d x} - 4 \, d \int -\frac {1}{4 \, {\left (b d^{2} x^{2} + 2 \, b c d x + b c^{2} - {\left (b d^{2} x^{2} e^{a} + 2 \, b c d x e^{a} + b c^{2} e^{a}\right )} e^{\left (b x\right )}\right )}}\,{d x} + \frac {2}{b d x + b c - {\left (b d x e^{\left (2 \, a\right )} + b c e^{\left (2 \, a\right )}\right )} e^{\left (2 \, b x\right )}} \]

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(sinh(a + b*x)^2*(c + d*x)),x)

[Out]

int(1/(sinh(a + b*x)^2*(c + d*x)), x)

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

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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