3.502 \(\int \frac {\text {csch}^3(c+d x) \text {sech}^3(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx\)
Optimal. Leaf size=39 \[ \text {Int}\left (\frac {\text {csch}^3(c+d x) \text {sech}^3(c+d x)}{(e+f x) (a+b \sinh (c+d x))},x\right ) \]
[Out]
Unintegrable(csch(d*x+c)^3*sech(d*x+c)^3/(f*x+e)/(a+b*sinh(d*x+c)),x)
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Rubi [A] time = 0.13, 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 =
{} \[ \int \frac {\text {csch}^3(c+d x) \text {sech}^3(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx \]
Verification is Not applicable to the result.
[In]
Int[(Csch[c + d*x]^3*Sech[c + d*x]^3)/((e + f*x)*(a + b*Sinh[c + d*x])),x]
[Out]
Defer[Int][(Csch[c + d*x]^3*Sech[c + d*x]^3)/((e + f*x)*(a + b*Sinh[c + d*x])), x]
Rubi steps
\begin {align*} \int \frac {\text {csch}^3(c+d x) \text {sech}^3(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx &=\int \frac {\text {csch}^3(c+d x) \text {sech}^3(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx\\ \end {align*}
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Mathematica [F] time = 180.00, size = 0, normalized size = 0.00 \[ \text {\$Aborted} \]
Verification is Not applicable to the result.
[In]
Integrate[(Csch[c + d*x]^3*Sech[c + d*x]^3)/((e + f*x)*(a + b*Sinh[c + d*x])),x]
[Out]
$Aborted
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fricas [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(csch(d*x+c)^3*sech(d*x+c)^3/(f*x+e)/(a+b*sinh(d*x+c)),x, algorithm="fricas")
[Out]
Timed out
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giac [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(csch(d*x+c)^3*sech(d*x+c)^3/(f*x+e)/(a+b*sinh(d*x+c)),x, algorithm="giac")
[Out]
Timed out
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maple [A] time = 4.63, size = 0, normalized size = 0.00 \[ \int \frac {\mathrm {csch}\left (d x +c \right )^{3} \mathrm {sech}\left (d x +c \right )^{3}}{\left (f x +e \right ) \left (a +b \sinh \left (d x +c \right )\right )}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
int(csch(d*x+c)^3*sech(d*x+c)^3/(f*x+e)/(a+b*sinh(d*x+c)),x)
[Out]
int(csch(d*x+c)^3*sech(d*x+c)^3/(f*x+e)/(a+b*sinh(d*x+c)),x)
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maxima [A] time = 0.00, size = 0, normalized size = 0.00 \[ \text {result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(csch(d*x+c)^3*sech(d*x+c)^3/(f*x+e)/(a+b*sinh(d*x+c)),x, algorithm="maxima")
[Out]
-(a*b^2*f - (2*b^3*d*e*e^(7*c) + (3*d*e - f)*a^2*b*e^(7*c) + (3*a^2*b*d*f*e^(7*c) + 2*b^3*d*f*e^(7*c))*x)*e^(7
*d*x) + (2*(2*d*e - f)*a^3*e^(6*c) + (2*d*e - f)*a*b^2*e^(6*c) + 2*(2*a^3*d*f*e^(6*c) + a*b^2*d*f*e^(6*c))*x)*
e^(6*d*x) - (2*b^3*d*e*e^(5*c) - (d*e - f)*a^2*b*e^(5*c) - (a^2*b*d*f*e^(5*c) - 2*b^3*d*f*e^(5*c))*x)*e^(5*d*x
) + (4*a*b^2*d*f*x*e^(4*c) + (4*d*e - f)*a*b^2*e^(4*c))*e^(4*d*x) + (2*b^3*d*e*e^(3*c) - (d*e + f)*a^2*b*e^(3*
c) - (a^2*b*d*f*e^(3*c) - 2*b^3*d*f*e^(3*c))*x)*e^(3*d*x) + (2*(2*d*e + f)*a^3*e^(2*c) + (2*d*e + f)*a*b^2*e^(
2*c) + 2*(2*a^3*d*f*e^(2*c) + a*b^2*d*f*e^(2*c))*x)*e^(2*d*x) + (2*b^3*d*e*e^c + (3*d*e + f)*a^2*b*e^c + (3*a^
2*b*d*f*e^c + 2*b^3*d*f*e^c)*x)*e^(d*x))/(a^4*d^2*e^2 + a^2*b^2*d^2*e^2 + (a^4*d^2*f^2 + a^2*b^2*d^2*f^2)*x^2
+ 2*(a^4*d^2*e*f + a^2*b^2*d^2*e*f)*x + (a^4*d^2*e^2*e^(8*c) + a^2*b^2*d^2*e^2*e^(8*c) + (a^4*d^2*f^2*e^(8*c)
+ a^2*b^2*d^2*f^2*e^(8*c))*x^2 + 2*(a^4*d^2*e*f*e^(8*c) + a^2*b^2*d^2*e*f*e^(8*c))*x)*e^(8*d*x) - 2*(a^4*d^2*e
^2*e^(4*c) + a^2*b^2*d^2*e^2*e^(4*c) + (a^4*d^2*f^2*e^(4*c) + a^2*b^2*d^2*f^2*e^(4*c))*x^2 + 2*(a^4*d^2*e*f*e^
(4*c) + a^2*b^2*d^2*e*f*e^(4*c))*x)*e^(4*d*x)) + 64*integrate(-1/32*(a*b^6*e^(d*x + c) - b^7)/(a^7*b*e + 2*a^5
*b^3*e + a^3*b^5*e + (a^7*b*f + 2*a^5*b^3*f + a^3*b^5*f)*x - (a^7*b*e*e^(2*c) + 2*a^5*b^3*e*e^(2*c) + a^3*b^5*
e*e^(2*c) + (a^7*b*f*e^(2*c) + 2*a^5*b^3*f*e^(2*c) + a^3*b^5*f*e^(2*c))*x)*e^(2*d*x) - 2*(a^8*e*e^c + 2*a^6*b^
2*e*e^c + a^4*b^4*e*e^c + (a^8*f*e^c + 2*a^6*b^2*f*e^c + a^4*b^4*f*e^c)*x)*e^(d*x)), x) - 64*integrate(1/64*(b
^2*d^2*e^2 + a*b*d*e*f - (2*d^2*e^2 - f^2)*a^2 - (2*a^2*d^2*f^2 - b^2*d^2*f^2)*x^2 - (4*a^2*d^2*e*f - 2*b^2*d^
2*e*f - a*b*d*f^2)*x)/(a^3*d^2*f^3*x^3 + 3*a^3*d^2*e*f^2*x^2 + 3*a^3*d^2*e^2*f*x + a^3*d^2*e^3 - (a^3*d^2*f^3*
x^3*e^c + 3*a^3*d^2*e*f^2*x^2*e^c + 3*a^3*d^2*e^2*f*x*e^c + a^3*d^2*e^3*e^c)*e^(d*x)), x) + 64*integrate(-1/64
*(b^2*d^2*e^2 - a*b*d*e*f - (2*d^2*e^2 - f^2)*a^2 - (2*a^2*d^2*f^2 - b^2*d^2*f^2)*x^2 - (4*a^2*d^2*e*f - 2*b^2
*d^2*e*f + a*b*d*f^2)*x)/(a^3*d^2*f^3*x^3 + 3*a^3*d^2*e*f^2*x^2 + 3*a^3*d^2*e^2*f*x + a^3*d^2*e^3 + (a^3*d^2*f
^3*x^3*e^c + 3*a^3*d^2*e*f^2*x^2*e^c + 3*a^3*d^2*e^2*f*x*e^c + a^3*d^2*e^3*e^c)*e^(d*x)), x) + 64*integrate(-1
/64*(2*(2*d^2*e^2 - f^2)*a^3 + 2*(3*d^2*e^2 - f^2)*a*b^2 + 2*(2*a^3*d^2*f^2 + 3*a*b^2*d^2*f^2)*x^2 + 4*(2*a^3*
d^2*e*f + 3*a*b^2*d^2*e*f)*x - ((3*d^2*e^2 - 2*f^2)*a^2*b*e^c + (5*d^2*e^2 - 2*f^2)*b^3*e^c + (3*a^2*b*d^2*f^2
*e^c + 5*b^3*d^2*f^2*e^c)*x^2 + 2*(3*a^2*b*d^2*e*f*e^c + 5*b^3*d^2*e*f*e^c)*x)*e^(d*x))/(a^4*d^2*e^3 + 2*a^2*b
^2*d^2*e^3 + b^4*d^2*e^3 + (a^4*d^2*f^3 + 2*a^2*b^2*d^2*f^3 + b^4*d^2*f^3)*x^3 + 3*(a^4*d^2*e*f^2 + 2*a^2*b^2*
d^2*e*f^2 + b^4*d^2*e*f^2)*x^2 + 3*(a^4*d^2*e^2*f + 2*a^2*b^2*d^2*e^2*f + b^4*d^2*e^2*f)*x + (a^4*d^2*e^3*e^(2
*c) + 2*a^2*b^2*d^2*e^3*e^(2*c) + b^4*d^2*e^3*e^(2*c) + (a^4*d^2*f^3*e^(2*c) + 2*a^2*b^2*d^2*f^3*e^(2*c) + b^4
*d^2*f^3*e^(2*c))*x^3 + 3*(a^4*d^2*e*f^2*e^(2*c) + 2*a^2*b^2*d^2*e*f^2*e^(2*c) + b^4*d^2*e*f^2*e^(2*c))*x^2 +
3*(a^4*d^2*e^2*f*e^(2*c) + 2*a^2*b^2*d^2*e^2*f*e^(2*c) + b^4*d^2*e^2*f*e^(2*c))*x)*e^(2*d*x)), x)
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mupad [A] time = 0.00, size = -1, normalized size = -0.03 \[ \int \frac {1}{{\mathrm {cosh}\left (c+d\,x\right )}^3\,{\mathrm {sinh}\left (c+d\,x\right )}^3\,\left (e+f\,x\right )\,\left (a+b\,\mathrm {sinh}\left (c+d\,x\right )\right )} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
int(1/(cosh(c + d*x)^3*sinh(c + d*x)^3*(e + f*x)*(a + b*sinh(c + d*x))),x)
[Out]
int(1/(cosh(c + d*x)^3*sinh(c + d*x)^3*(e + f*x)*(a + b*sinh(c + d*x))), x)
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sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(csch(d*x+c)**3*sech(d*x+c)**3/(f*x+e)/(a+b*sinh(d*x+c)),x)
[Out]
Timed out
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