3.222 \(\int \frac{\text{csch}^3(c+d x)}{(e+f x)^2 (a+i a \sinh (c+d x))} \, dx\)
Optimal. Leaf size=33 \[ \text{Unintegrable}\left (\frac{\text{csch}^3(c+d x)}{(e+f x)^2 (a+i a \sinh (c+d x))},x\right ) \]
[Out]
Unintegrable[Csch[c + d*x]^3/((e + f*x)^2*(a + I*a*Sinh[c + d*x])), x]
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Rubi [A] time = 0.0739772, antiderivative size = 0, normalized size of antiderivative = 0.,
number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {}
\[ \int \frac{\text{csch}^3(c+d x)}{(e+f x)^2 (a+i a \sinh (c+d x))} \, dx \]
Verification is Not applicable to the result.
[In]
Int[Csch[c + d*x]^3/((e + f*x)^2*(a + I*a*Sinh[c + d*x])),x]
[Out]
Defer[Int][Csch[c + d*x]^3/((e + f*x)^2*(a + I*a*Sinh[c + d*x])), x]
Rubi steps
\begin{align*} \int \frac{\text{csch}^3(c+d x)}{(e+f x)^2 (a+i a \sinh (c+d x))} \, dx &=\int \frac{\text{csch}^3(c+d x)}{(e+f x)^2 (a+i a \sinh (c+d x))} \, dx\\ \end{align*}
Mathematica [F] time = 180.047, size = 0, normalized size = 0. \[ \text{\$Aborted} \]
Verification is Not applicable to the result.
[In]
Integrate[Csch[c + d*x]^3/((e + f*x)^2*(a + I*a*Sinh[c + d*x])),x]
[Out]
$Aborted
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Maple [A] time = 2.257, size = 0, normalized size = 0. \begin{align*} \int{\frac{ \left ({\rm csch} \left (dx+c\right ) \right ) ^{3}}{ \left ( fx+e \right ) ^{2} \left ( a+ia\sinh \left ( dx+c \right ) \right ) }}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
int(csch(d*x+c)^3/(f*x+e)^2/(a+I*a*sinh(d*x+c)),x)
[Out]
int(csch(d*x+c)^3/(f*x+e)^2/(a+I*a*sinh(d*x+c)),x)
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Maxima [A] time = 0., size = 0, normalized size = 0. \begin{align*} \text{result too large to display} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(csch(d*x+c)^3/(f*x+e)^2/(a+I*a*sinh(d*x+c)),x, algorithm="maxima")
[Out]
-8*f*integrate(1/(-2*I*a*d*f^3*x^3 - 6*I*a*d*e*f^2*x^2 - 6*I*a*d*e^2*f*x - 2*I*a*d*e^3 + 2*(a*d*f^3*x^3*e^c +
3*a*d*e*f^2*x^2*e^c + 3*a*d*e^2*f*x*e^c + a*d*e^3*e^c)*e^(d*x)), x) - 8*(4*d*f*x + 4*d*e + (3*d*f*x*e^(4*c) +
(3*d*e - 2*f)*e^(4*c))*e^(4*d*x) + (-3*I*d*f*x*e^(3*c) + (-3*I*d*e + 2*I*f)*e^(3*c))*e^(3*d*x) - (5*d*f*x*e^(2
*c) + (5*d*e - 2*f)*e^(2*c))*e^(2*d*x) + (I*d*f*x*e^c + (I*d*e - 2*I*f)*e^c)*e^(d*x))/(-8*I*a*d^2*f^3*x^3 - 24
*I*a*d^2*e*f^2*x^2 - 24*I*a*d^2*e^2*f*x - 8*I*a*d^2*e^3 + 8*(a*d^2*f^3*x^3*e^(5*c) + 3*a*d^2*e*f^2*x^2*e^(5*c)
+ 3*a*d^2*e^2*f*x*e^(5*c) + a*d^2*e^3*e^(5*c))*e^(5*d*x) + (-8*I*a*d^2*f^3*x^3*e^(4*c) - 24*I*a*d^2*e*f^2*x^2
*e^(4*c) - 24*I*a*d^2*e^2*f*x*e^(4*c) - 8*I*a*d^2*e^3*e^(4*c))*e^(4*d*x) - 16*(a*d^2*f^3*x^3*e^(3*c) + 3*a*d^2
*e*f^2*x^2*e^(3*c) + 3*a*d^2*e^2*f*x*e^(3*c) + a*d^2*e^3*e^(3*c))*e^(3*d*x) + (16*I*a*d^2*f^3*x^3*e^(2*c) + 48
*I*a*d^2*e*f^2*x^2*e^(2*c) + 48*I*a*d^2*e^2*f*x*e^(2*c) + 16*I*a*d^2*e^3*e^(2*c))*e^(2*d*x) + 8*(a*d^2*f^3*x^3
*e^c + 3*a*d^2*e*f^2*x^2*e^c + 3*a*d^2*e^2*f*x*e^c + a*d^2*e^3*e^c)*e^(d*x)) - 8*integrate(1/16*(3*d^2*f^2*x^2
+ 3*d^2*e^2 + 4*I*d*e*f - 6*f^2 + (6*d^2*e*f + 4*I*d*f^2)*x)/(a*d^2*f^4*x^4 + 4*a*d^2*e*f^3*x^3 + 6*a*d^2*e^2
*f^2*x^2 + 4*a*d^2*e^3*f*x + a*d^2*e^4 + (a*d^2*f^4*x^4*e^c + 4*a*d^2*e*f^3*x^3*e^c + 6*a*d^2*e^2*f^2*x^2*e^c
+ 4*a*d^2*e^3*f*x*e^c + a*d^2*e^4*e^c)*e^(d*x)), x) - 8*integrate(-1/16*(3*d^2*f^2*x^2 + 3*d^2*e^2 - 4*I*d*e*f
- 6*f^2 + (6*d^2*e*f - 4*I*d*f^2)*x)/(a*d^2*f^4*x^4 + 4*a*d^2*e*f^3*x^3 + 6*a*d^2*e^2*f^2*x^2 + 4*a*d^2*e^3*f
*x + a*d^2*e^4 - (a*d^2*f^4*x^4*e^c + 4*a*d^2*e*f^3*x^3*e^c + 6*a*d^2*e^2*f^2*x^2*e^c + 4*a*d^2*e^3*f*x*e^c +
a*d^2*e^4*e^c)*e^(d*x)), x)
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Fricas [A] time = 0., size = 0, normalized size = 0. \begin{align*} \text{result too large to display} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(csch(d*x+c)^3/(f*x+e)^2/(a+I*a*sinh(d*x+c)),x, algorithm="fricas")
[Out]
-(4*d*f*x + 4*d*e + (3*d*f*x + 3*d*e - 2*f)*e^(4*d*x + 4*c) - (3*I*d*f*x + 3*I*d*e - 2*I*f)*e^(3*d*x + 3*c) -
(5*d*f*x + 5*d*e - 2*f)*e^(2*d*x + 2*c) - (-I*d*f*x - I*d*e + 2*I*f)*e^(d*x + c) - (-I*a*d^2*f^3*x^3 - 3*I*a*d
^2*e*f^2*x^2 - 3*I*a*d^2*e^2*f*x - I*a*d^2*e^3 + (a*d^2*f^3*x^3 + 3*a*d^2*e*f^2*x^2 + 3*a*d^2*e^2*f*x + a*d^2*
e^3)*e^(5*d*x + 5*c) + (-I*a*d^2*f^3*x^3 - 3*I*a*d^2*e*f^2*x^2 - 3*I*a*d^2*e^2*f*x - I*a*d^2*e^3)*e^(4*d*x + 4
*c) - 2*(a*d^2*f^3*x^3 + 3*a*d^2*e*f^2*x^2 + 3*a*d^2*e^2*f*x + a*d^2*e^3)*e^(3*d*x + 3*c) + (2*I*a*d^2*f^3*x^3
+ 6*I*a*d^2*e*f^2*x^2 + 6*I*a*d^2*e^2*f*x + 2*I*a*d^2*e^3)*e^(2*d*x + 2*c) + (a*d^2*f^3*x^3 + 3*a*d^2*e*f^2*x
^2 + 3*a*d^2*e^2*f*x + a*d^2*e^3)*e^(d*x + c))*integral((8*d*f^2*x + 8*d*e*f - (3*d^2*f^2*x^2 + 3*d^2*e^2 + 4*
d*e*f - 6*f^2 + 2*(3*d^2*e*f + 2*d*f^2)*x)*e^(2*d*x + 2*c) + (3*I*d^2*f^2*x^2 + 3*I*d^2*e^2 + 4*I*d*e*f - 6*I*
f^2 + (6*I*d^2*e*f + 4*I*d*f^2)*x)*e^(d*x + c))/(I*a*d^2*f^4*x^4 + 4*I*a*d^2*e*f^3*x^3 + 6*I*a*d^2*e^2*f^2*x^2
+ 4*I*a*d^2*e^3*f*x + I*a*d^2*e^4 + (a*d^2*f^4*x^4 + 4*a*d^2*e*f^3*x^3 + 6*a*d^2*e^2*f^2*x^2 + 4*a*d^2*e^3*f*
x + a*d^2*e^4)*e^(3*d*x + 3*c) + (-I*a*d^2*f^4*x^4 - 4*I*a*d^2*e*f^3*x^3 - 6*I*a*d^2*e^2*f^2*x^2 - 4*I*a*d^2*e
^3*f*x - I*a*d^2*e^4)*e^(2*d*x + 2*c) - (a*d^2*f^4*x^4 + 4*a*d^2*e*f^3*x^3 + 6*a*d^2*e^2*f^2*x^2 + 4*a*d^2*e^3
*f*x + a*d^2*e^4)*e^(d*x + c)), x))/(-I*a*d^2*f^3*x^3 - 3*I*a*d^2*e*f^2*x^2 - 3*I*a*d^2*e^2*f*x - I*a*d^2*e^3
+ (a*d^2*f^3*x^3 + 3*a*d^2*e*f^2*x^2 + 3*a*d^2*e^2*f*x + a*d^2*e^3)*e^(5*d*x + 5*c) + (-I*a*d^2*f^3*x^3 - 3*I*
a*d^2*e*f^2*x^2 - 3*I*a*d^2*e^2*f*x - I*a*d^2*e^3)*e^(4*d*x + 4*c) - 2*(a*d^2*f^3*x^3 + 3*a*d^2*e*f^2*x^2 + 3*
a*d^2*e^2*f*x + a*d^2*e^3)*e^(3*d*x + 3*c) + (2*I*a*d^2*f^3*x^3 + 6*I*a*d^2*e*f^2*x^2 + 6*I*a*d^2*e^2*f*x + 2*
I*a*d^2*e^3)*e^(2*d*x + 2*c) + (a*d^2*f^3*x^3 + 3*a*d^2*e*f^2*x^2 + 3*a*d^2*e^2*f*x + a*d^2*e^3)*e^(d*x + c))
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(csch(d*x+c)**3/(f*x+e)**2/(a+I*a*sinh(d*x+c)),x)
[Out]
Timed out
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Giac [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(csch(d*x+c)^3/(f*x+e)^2/(a+I*a*sinh(d*x+c)),x, algorithm="giac")
[Out]
Timed out