3.520 \(\int \frac {\text {csch}^3(a+b x) \text {sech}^2(a+b x)}{x^2} \, dx\)

Optimal. Leaf size=23 \[ \text {Int}\left (\frac {\text {csch}^3(a+b x) \text {sech}^2(a+b x)}{x^2},x\right ) \]

[Out]

CannotIntegrate(csch(b*x+a)^3*sech(b*x+a)^2/x^2,x)

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Rubi [A]  time = 0.33, 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 = {} \[ \int \frac {\text {csch}^3(a+b x) \text {sech}^2(a+b x)}{x^2} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

Rubi steps

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

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Mathematica [A]  time = 46.12, size = 0, normalized size = 0.00 \[ \int \frac {\text {csch}^3(a+b x) \text {sech}^2(a+b x)}{x^2} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

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fricas [A]  time = 0.42, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\operatorname {csch}\left (b x + a\right )^{3} \operatorname {sech}\left (b x + a\right )^{2}}{x^{2}}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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giac [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \mathit {sage}_{0} x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

sage0*x

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maple [A]  time = 1.39, size = 0, normalized size = 0.00 \[ \int \frac {\mathrm {csch}\left (b x +a \right )^{3} \mathrm {sech}\left (b x +a \right )^{2}}{x^{2}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maxima [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \frac {2 \, b x e^{\left (3 \, b x + 3 \, a\right )} - {\left (3 \, b x e^{\left (5 \, a\right )} - 2 \, e^{\left (5 \, a\right )}\right )} e^{\left (5 \, b x\right )} - {\left (3 \, b x e^{a} + 2 \, e^{a}\right )} e^{\left (b x\right )}}{b^{2} x^{3} e^{\left (6 \, b x + 6 \, a\right )} - b^{2} x^{3} e^{\left (4 \, b x + 4 \, a\right )} - b^{2} x^{3} e^{\left (2 \, b x + 2 \, a\right )} + b^{2} x^{3}} - 32 \, \int \frac {3 \, {\left (b^{2} x^{2} - 2\right )}}{64 \, {\left (b^{2} x^{4} e^{\left (b x + a\right )} + b^{2} x^{4}\right )}}\,{d x} - 32 \, \int \frac {3 \, {\left (b^{2} x^{2} - 2\right )}}{64 \, {\left (b^{2} x^{4} e^{\left (b x + a\right )} - b^{2} x^{4}\right )}}\,{d x} - 32 \, \int \frac {e^{\left (b x + a\right )}}{8 \, {\left (b x^{3} e^{\left (2 \, b x + 2 \, a\right )} + b x^{3}\right )}}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

(2*b*x*e^(3*b*x + 3*a) - (3*b*x*e^(5*a) - 2*e^(5*a))*e^(5*b*x) - (3*b*x*e^a + 2*e^a)*e^(b*x))/(b^2*x^3*e^(6*b*
x + 6*a) - b^2*x^3*e^(4*b*x + 4*a) - b^2*x^3*e^(2*b*x + 2*a) + b^2*x^3) - 32*integrate(3/64*(b^2*x^2 - 2)/(b^2
*x^4*e^(b*x + a) + b^2*x^4), x) - 32*integrate(3/64*(b^2*x^2 - 2)/(b^2*x^4*e^(b*x + a) - b^2*x^4), x) - 32*int
egrate(1/8*e^(b*x + a)/(b*x^3*e^(2*b*x + 2*a) + b*x^3), x)

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mupad [A]  time = 0.00, size = -1, normalized size = -0.04 \[ \int \frac {1}{x^2\,{\mathrm {cosh}\left (a+b\,x\right )}^2\,{\mathrm {sinh}\left (a+b\,x\right )}^3} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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sympy [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\operatorname {csch}^{3}{\left (a + b x \right )} \operatorname {sech}^{2}{\left (a + b x \right )}}{x^{2}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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