3.70 \(\int \frac{1}{x \cosh ^{-1}(a x)^4} \, dx\)
Optimal. Leaf size=12 \[ \text{Unintegrable}\left (\frac{1}{x \cosh ^{-1}(a x)^4},x\right ) \]
[Out]
Unintegrable[1/(x*ArcCosh[a*x]^4), x]
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Rubi [A] time = 0.0136799, 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 = {}
\[ \int \frac{1}{x \cosh ^{-1}(a x)^4} \, dx \]
Verification is Not applicable to the result.
[In]
Int[1/(x*ArcCosh[a*x]^4),x]
[Out]
Defer[Int][1/(x*ArcCosh[a*x]^4), x]
Rubi steps
\begin{align*} \int \frac{1}{x \cosh ^{-1}(a x)^4} \, dx &=\int \frac{1}{x \cosh ^{-1}(a x)^4} \, dx\\ \end{align*}
Mathematica [A] time = 9.82626, size = 0, normalized size = 0. \[ \int \frac{1}{x \cosh ^{-1}(a x)^4} \, dx \]
Verification is Not applicable to the result.
[In]
Integrate[1/(x*ArcCosh[a*x]^4),x]
[Out]
Integrate[1/(x*ArcCosh[a*x]^4), x]
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Maple [A] time = 0.069, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{x \left ({\rm arccosh} \left (ax\right ) \right ) ^{4}}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
int(1/x/arccosh(a*x)^4,x)
[Out]
int(1/x/arccosh(a*x)^4,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/x/arccosh(a*x)^4,x, algorithm="maxima")
[Out]
-1/6*(2*a^13*x^13 - 10*a^11*x^11 + 20*a^9*x^9 - 20*a^7*x^7 + 10*a^5*x^5 + 2*(a^8*x^8 - a^6*x^6)*(a*x + 1)^(5/2
)*(a*x - 1)^(5/2) - 2*a^3*x^3 + 2*(5*a^9*x^9 - 9*a^7*x^7 + 4*a^5*x^5)*(a*x + 1)^2*(a*x - 1)^2 + 4*(5*a^10*x^10
- 13*a^8*x^8 + 11*a^6*x^6 - 3*a^4*x^4)*(a*x + 1)^(3/2)*(a*x - 1)^(3/2) + 4*(5*a^11*x^11 - 17*a^9*x^9 + 21*a^7
*x^7 - 11*a^5*x^5 + 2*a^3*x^3)*(a*x + 1)*(a*x - 1) - (4*(a^6*x^6 - 3*a^4*x^4 + 2*a^2*x^2)*(a*x + 1)^(5/2)*(a*x
- 1)^(5/2) + (16*a^7*x^7 - 46*a^5*x^5 + 37*a^3*x^3 - 7*a*x)*(a*x + 1)^2*(a*x - 1)^2 + (24*a^8*x^8 - 66*a^6*x^
6 + 59*a^4*x^4 - 19*a^2*x^2 + 2)*(a*x + 1)^(3/2)*(a*x - 1)^(3/2) + (16*a^9*x^9 - 42*a^7*x^7 + 39*a^5*x^5 - 16*
a^3*x^3 + 3*a*x)*(a*x + 1)*(a*x - 1) + (4*a^10*x^10 - 10*a^8*x^8 + 9*a^6*x^6 - 4*a^4*x^4 + a^2*x^2)*sqrt(a*x +
1)*sqrt(a*x - 1))*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))^2 + 2*(5*a^12*x^12 - 21*a^10*x^10 + 34*a^8*x^8 - 26*
a^6*x^6 + 9*a^4*x^4 - a^2*x^2)*sqrt(a*x + 1)*sqrt(a*x - 1) + (2*(a^6*x^6 - a^4*x^4)*(a*x + 1)^(5/2)*(a*x - 1)^
(5/2) + (8*a^7*x^7 - 13*a^5*x^5 + 5*a^3*x^3)*(a*x + 1)^2*(a*x - 1)^2 + (12*a^8*x^8 - 27*a^6*x^6 + 19*a^4*x^4 -
4*a^2*x^2)*(a*x + 1)^(3/2)*(a*x - 1)^(3/2) + (8*a^9*x^9 - 23*a^7*x^7 + 23*a^5*x^5 - 9*a^3*x^3 + a*x)*(a*x + 1
)*(a*x - 1) + (2*a^10*x^10 - 7*a^8*x^8 + 9*a^6*x^6 - 5*a^4*x^4 + a^2*x^2)*sqrt(a*x + 1)*sqrt(a*x - 1))*log(a*x
+ sqrt(a*x + 1)*sqrt(a*x - 1)))/((a^13*x^13 - 5*a^11*x^11 + (a*x + 1)^(5/2)*(a*x - 1)^(5/2)*a^8*x^8 + 10*a^9*
x^9 - 10*a^7*x^7 + 5*a^5*x^5 - a^3*x^3 + 5*(a^9*x^9 - a^7*x^7)*(a*x + 1)^2*(a*x - 1)^2 + 10*(a^10*x^10 - 2*a^8
*x^8 + a^6*x^6)*(a*x + 1)^(3/2)*(a*x - 1)^(3/2) + 10*(a^11*x^11 - 3*a^9*x^9 + 3*a^7*x^7 - a^5*x^5)*(a*x + 1)*(
a*x - 1) + 5*(a^12*x^12 - 4*a^10*x^10 + 6*a^8*x^8 - 4*a^6*x^6 + a^4*x^4)*sqrt(a*x + 1)*sqrt(a*x - 1))*log(a*x
+ sqrt(a*x + 1)*sqrt(a*x - 1))^3) + integrate(1/6*(8*(a^7*x^7 - 6*a^5*x^5 + 6*a^3*x^3)*(a*x + 1)^3*(a*x - 1)^3
+ (40*a^8*x^8 - 204*a^6*x^6 + 228*a^4*x^4 - 57*a^2*x^2)*(a*x + 1)^(5/2)*(a*x - 1)^(5/2) + 2*(40*a^9*x^9 - 168
*a^7*x^7 + 200*a^5*x^5 - 87*a^3*x^3 + 15*a*x)*(a*x + 1)^2*(a*x - 1)^2 + 2*(40*a^10*x^10 - 132*a^8*x^8 + 156*a^
6*x^6 - 91*a^4*x^4 + 30*a^2*x^2 - 3)*(a*x + 1)^(3/2)*(a*x - 1)^(3/2) + 2*(20*a^11*x^11 - 48*a^9*x^9 + 48*a^7*x
^7 - 35*a^5*x^5 + 18*a^3*x^3 - 3*a*x)*(a*x + 1)*(a*x - 1) + (8*a^12*x^12 - 12*a^10*x^10 + 4*a^8*x^8 - 5*a^6*x^
6 + 6*a^4*x^4 - a^2*x^2)*sqrt(a*x + 1)*sqrt(a*x - 1))/((a^15*x^16 - 6*a^13*x^14 + (a*x + 1)^3*(a*x - 1)^3*a^9*
x^10 + 15*a^11*x^12 - 20*a^9*x^10 + 15*a^7*x^8 - 6*a^5*x^6 + a^3*x^4 + 6*(a^10*x^11 - a^8*x^9)*(a*x + 1)^(5/2)
*(a*x - 1)^(5/2) + 15*(a^11*x^12 - 2*a^9*x^10 + a^7*x^8)*(a*x + 1)^2*(a*x - 1)^2 + 20*(a^12*x^13 - 3*a^10*x^11
+ 3*a^8*x^9 - a^6*x^7)*(a*x + 1)^(3/2)*(a*x - 1)^(3/2) + 15*(a^13*x^14 - 4*a^11*x^12 + 6*a^9*x^10 - 4*a^7*x^8
+ a^5*x^6)*(a*x + 1)*(a*x - 1) + 6*(a^14*x^15 - 5*a^12*x^13 + 10*a^10*x^11 - 10*a^8*x^9 + 5*a^6*x^7 - a^4*x^5
)*sqrt(a*x + 1)*sqrt(a*x - 1))*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))), x)
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Fricas [A] time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{1}{x \operatorname{arcosh}\left (a x\right )^{4}}, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(1/x/arccosh(a*x)^4,x, algorithm="fricas")
[Out]
integral(1/(x*arccosh(a*x)^4), x)
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Sympy [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{x \operatorname{acosh}^{4}{\left (a x \right )}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(1/x/acosh(a*x)**4,x)
[Out]
Integral(1/(x*acosh(a*x)**4), x)
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Giac [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{x \operatorname{arcosh}\left (a x\right )^{4}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(1/x/arccosh(a*x)^4,x, algorithm="giac")
[Out]
integrate(1/(x*arccosh(a*x)^4), x)