3.526 \(\int \frac {\text {csch}^3(a+b x) \text {sech}^3(a+b x)}{x} \, dx\)

Optimal. Leaf size=20 \[ 8 \text {Int}\left (\frac {\text {csch}^3(2 a+2 b x)}{x},x\right ) \]

[Out]

8*Unintegrable(csch(2*b*x+2*a)^3/x,x)

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Rubi [A]  time = 0.07, 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 = {} \[ \int \frac {\text {csch}^3(a+b x) \text {sech}^3(a+b x)}{x} \, dx \]

Verification is Not applicable to the result.

[In]

Int[(Csch[a + b*x]^3*Sech[a + b*x]^3)/x,x]

[Out]

8*Defer[Int][Csch[2*a + 2*b*x]^3/x, x]

Rubi steps

\begin {align*} \int \frac {\text {csch}^3(a+b x) \text {sech}^3(a+b x)}{x} \, dx &=8 \int \frac {\text {csch}^3(2 a+2 b x)}{x} \, dx\\ \end {align*}

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Mathematica [A]  time = 60.73, size = 0, normalized size = 0.00 \[ \int \frac {\text {csch}^3(a+b x) \text {sech}^3(a+b x)}{x} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

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fricas [A]  time = 0.42, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\operatorname {csch}\left (b x + a\right )^{3} \operatorname {sech}\left (b x + a\right )^{3}}{x}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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giac [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\operatorname {csch}\left (b x + a\right )^{3} \operatorname {sech}\left (b x + a\right )^{3}}{x}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maple [A]  time = 1.56, size = 0, normalized size = 0.00 \[ \int \frac {\mathrm {csch}\left (b x +a \right )^{3} \mathrm {sech}\left (b x +a \right )^{3}}{x}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maxima [A]  time = 0.00, size = 0, normalized size = 0.00 \[ -\frac {2 \, {\left ({\left (2 \, b x e^{\left (6 \, a\right )} - e^{\left (6 \, a\right )}\right )} e^{\left (6 \, b x\right )} + {\left (2 \, b x e^{\left (2 \, a\right )} + e^{\left (2 \, a\right )}\right )} e^{\left (2 \, b x\right )}\right )}}{b^{2} x^{2} e^{\left (8 \, b x + 8 \, a\right )} - 2 \, b^{2} x^{2} e^{\left (4 \, b x + 4 \, a\right )} + b^{2} x^{2}} - 64 \, \int \frac {2 \, b^{2} x^{2} - 1}{32 \, {\left (b^{2} x^{3} e^{\left (2 \, b x + 2 \, a\right )} + b^{2} x^{3}\right )}}\,{d x} + 64 \, \int \frac {2 \, b^{2} x^{2} - 1}{64 \, {\left (b^{2} x^{3} e^{\left (b x + a\right )} + b^{2} x^{3}\right )}}\,{d x} - 64 \, \int \frac {2 \, b^{2} x^{2} - 1}{64 \, {\left (b^{2} x^{3} e^{\left (b x + a\right )} - b^{2} x^{3}\right )}}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-2*((2*b*x*e^(6*a) - e^(6*a))*e^(6*b*x) + (2*b*x*e^(2*a) + e^(2*a))*e^(2*b*x))/(b^2*x^2*e^(8*b*x + 8*a) - 2*b^
2*x^2*e^(4*b*x + 4*a) + b^2*x^2) - 64*integrate(1/32*(2*b^2*x^2 - 1)/(b^2*x^3*e^(2*b*x + 2*a) + b^2*x^3), x) +
64*integrate(1/64*(2*b^2*x^2 - 1)/(b^2*x^3*e^(b*x + a) + b^2*x^3), x) - 64*integrate(1/64*(2*b^2*x^2 - 1)/(b^
2*x^3*e^(b*x + a) - b^2*x^3), x)

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mupad [A]  time = 0.00, size = -1, normalized size = -0.05 \[ \int \frac {1}{x\,{\mathrm {cosh}\left (a+b\,x\right )}^3\,{\mathrm {sinh}\left (a+b\,x\right )}^3} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(x*cosh(a + b*x)^3*sinh(a + b*x)^3),x)

[Out]

int(1/(x*cosh(a + b*x)^3*sinh(a + b*x)^3), x)

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sympy [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\operatorname {csch}^{3}{\left (a + b x \right )} \operatorname {sech}^{3}{\left (a + b x \right )}}{x}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(csch(b*x+a)**3*sech(b*x+a)**3/x,x)

[Out]

Integral(csch(a + b*x)**3*sech(a + b*x)**3/x, x)

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