3.117 \(\int \frac{1}{(c+d x)^2 (a+i a \sinh (e+f x))^2} \, dx\)
Optimal. Leaf size=25 \[ \text{Unintegrable}\left (\frac{1}{(c+d x)^2 (a+i a \sinh (e+f x))^2},x\right ) \]
[Out]
Unintegrable[1/((c + d*x)^2*(a + I*a*Sinh[e + f*x])^2), x]
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Rubi [A] time = 0.0574974, 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 = {}
\[ \int \frac{1}{(c+d x)^2 (a+i a \sinh (e+f x))^2} \, dx \]
Verification is Not applicable to the result.
[In]
Int[1/((c + d*x)^2*(a + I*a*Sinh[e + f*x])^2),x]
[Out]
Defer[Int][1/((c + d*x)^2*(a + I*a*Sinh[e + f*x])^2), x]
Rubi steps
\begin{align*} \int \frac{1}{(c+d x)^2 (a+i a \sinh (e+f x))^2} \, dx &=\int \frac{1}{(c+d x)^2 (a+i a \sinh (e+f x))^2} \, dx\\ \end{align*}
Mathematica [A] time = 37.9065, size = 0, normalized size = 0. \[ \int \frac{1}{(c+d x)^2 (a+i a \sinh (e+f x))^2} \, dx \]
Verification is Not applicable to the result.
[In]
Integrate[1/((c + d*x)^2*(a + I*a*Sinh[e + f*x])^2),x]
[Out]
Integrate[1/((c + d*x)^2*(a + I*a*Sinh[e + f*x])^2), x]
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Maple [A] time = 1.103, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{ \left ( dx+c \right ) ^{2} \left ( a+ia\sinh \left ( fx+e \right ) \right ) ^{2}}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
int(1/(d*x+c)^2/(a+I*a*sinh(f*x+e))^2,x)
[Out]
int(1/(d*x+c)^2/(a+I*a*sinh(f*x+e))^2,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(1/(d*x+c)^2/(a+I*a*sinh(f*x+e))^2,x, algorithm="maxima")
[Out]
(-2*I*d^2*f^2*x^2 - 4*I*c*d*f^2*x - 2*I*c^2*f^2 + 12*I*d^2 + (4*I*d^2*f*x*e^(2*e) + 4*I*c*d*f*e^(2*e) - 12*I*d
^2*e^(2*e))*e^(2*f*x) + 2*(3*d^2*f^2*x^2*e^e + 3*c^2*f^2*e^e + 2*c*d*f*e^e - 12*d^2*e^e + 2*(3*c*d*f^2*e^e + d
^2*f*e^e)*x)*e^(f*x))/(3*I*a^2*d^4*f^3*x^4 + 12*I*a^2*c*d^3*f^3*x^3 + 18*I*a^2*c^2*d^2*f^3*x^2 + 12*I*a^2*c^3*
d*f^3*x + 3*I*a^2*c^4*f^3 + 3*(a^2*d^4*f^3*x^4*e^(3*e) + 4*a^2*c*d^3*f^3*x^3*e^(3*e) + 6*a^2*c^2*d^2*f^3*x^2*e
^(3*e) + 4*a^2*c^3*d*f^3*x*e^(3*e) + a^2*c^4*f^3*e^(3*e))*e^(3*f*x) + (-9*I*a^2*d^4*f^3*x^4*e^(2*e) - 36*I*a^2
*c*d^3*f^3*x^3*e^(2*e) - 54*I*a^2*c^2*d^2*f^3*x^2*e^(2*e) - 36*I*a^2*c^3*d*f^3*x*e^(2*e) - 9*I*a^2*c^4*f^3*e^(
2*e))*e^(2*f*x) - 9*(a^2*d^4*f^3*x^4*e^e + 4*a^2*c*d^3*f^3*x^3*e^e + 6*a^2*c^2*d^2*f^3*x^2*e^e + 4*a^2*c^3*d*f
^3*x*e^e + a^2*c^4*f^3*e^e)*e^(f*x)) - integrate(4*(d^3*f^2*x^2 + 2*c*d^2*f^2*x + c^2*d*f^2 - 12*d^3)/(3*a^2*d
^5*f^3*x^5 + 15*a^2*c*d^4*f^3*x^4 + 30*a^2*c^2*d^3*f^3*x^3 + 30*a^2*c^3*d^2*f^3*x^2 + 15*a^2*c^4*d*f^3*x + 3*a
^2*c^5*f^3 + (3*I*a^2*d^5*f^3*x^5*e^e + 15*I*a^2*c*d^4*f^3*x^4*e^e + 30*I*a^2*c^2*d^3*f^3*x^3*e^e + 30*I*a^2*c
^3*d^2*f^3*x^2*e^e + 15*I*a^2*c^4*d*f^3*x*e^e + 3*I*a^2*c^5*f^3*e^e)*e^(f*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(1/(d*x+c)^2/(a+I*a*sinh(f*x+e))^2,x, algorithm="fricas")
[Out]
(-2*I*d^2*f^2*x^2 - 4*I*c*d*f^2*x - 2*I*c^2*f^2 + 12*I*d^2 + (4*I*d^2*f*x + 4*I*c*d*f - 12*I*d^2)*e^(2*f*x + 2
*e) + 2*(3*d^2*f^2*x^2 + 3*c^2*f^2 + 2*c*d*f - 12*d^2 + 2*(3*c*d*f^2 + d^2*f)*x)*e^(f*x + e) + (3*I*a^2*d^4*f^
3*x^4 + 12*I*a^2*c*d^3*f^3*x^3 + 18*I*a^2*c^2*d^2*f^3*x^2 + 12*I*a^2*c^3*d*f^3*x + 3*I*a^2*c^4*f^3 + 3*(a^2*d^
4*f^3*x^4 + 4*a^2*c*d^3*f^3*x^3 + 6*a^2*c^2*d^2*f^3*x^2 + 4*a^2*c^3*d*f^3*x + a^2*c^4*f^3)*e^(3*f*x + 3*e) + (
-9*I*a^2*d^4*f^3*x^4 - 36*I*a^2*c*d^3*f^3*x^3 - 54*I*a^2*c^2*d^2*f^3*x^2 - 36*I*a^2*c^3*d*f^3*x - 9*I*a^2*c^4*
f^3)*e^(2*f*x + 2*e) - 9*(a^2*d^4*f^3*x^4 + 4*a^2*c*d^3*f^3*x^3 + 6*a^2*c^2*d^2*f^3*x^2 + 4*a^2*c^3*d*f^3*x +
a^2*c^4*f^3)*e^(f*x + e))*integral((4*I*d^3*f^2*x^2 + 8*I*c*d^2*f^2*x + 4*I*c^2*d*f^2 - 48*I*d^3)/(-3*I*a^2*d^
5*f^3*x^5 - 15*I*a^2*c*d^4*f^3*x^4 - 30*I*a^2*c^2*d^3*f^3*x^3 - 30*I*a^2*c^3*d^2*f^3*x^2 - 15*I*a^2*c^4*d*f^3*
x - 3*I*a^2*c^5*f^3 + 3*(a^2*d^5*f^3*x^5 + 5*a^2*c*d^4*f^3*x^4 + 10*a^2*c^2*d^3*f^3*x^3 + 10*a^2*c^3*d^2*f^3*x
^2 + 5*a^2*c^4*d*f^3*x + a^2*c^5*f^3)*e^(f*x + e)), x))/(3*I*a^2*d^4*f^3*x^4 + 12*I*a^2*c*d^3*f^3*x^3 + 18*I*a
^2*c^2*d^2*f^3*x^2 + 12*I*a^2*c^3*d*f^3*x + 3*I*a^2*c^4*f^3 + 3*(a^2*d^4*f^3*x^4 + 4*a^2*c*d^3*f^3*x^3 + 6*a^2
*c^2*d^2*f^3*x^2 + 4*a^2*c^3*d*f^3*x + a^2*c^4*f^3)*e^(3*f*x + 3*e) + (-9*I*a^2*d^4*f^3*x^4 - 36*I*a^2*c*d^3*f
^3*x^3 - 54*I*a^2*c^2*d^2*f^3*x^2 - 36*I*a^2*c^3*d*f^3*x - 9*I*a^2*c^4*f^3)*e^(2*f*x + 2*e) - 9*(a^2*d^4*f^3*x
^4 + 4*a^2*c*d^3*f^3*x^3 + 6*a^2*c^2*d^2*f^3*x^2 + 4*a^2*c^3*d*f^3*x + a^2*c^4*f^3)*e^(f*x + e))
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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(1/(d*x+c)**2/(a+I*a*sinh(f*x+e))**2,x)
[Out]
Timed out
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Giac [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{{\left (d x + c\right )}^{2}{\left (i \, a \sinh \left (f x + e\right ) + a\right )}^{2}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(1/(d*x+c)^2/(a+I*a*sinh(f*x+e))^2,x, algorithm="giac")
[Out]
integrate(1/((d*x + c)^2*(I*a*sinh(f*x + e) + a)^2), x)