3.1.73 \(\int \frac {1}{x^2 \sinh ^{-1}(a x)^4} \, dx\) [73]
Optimal. Leaf size=13 \[ \text {Int}\left (\frac {1}{x^2 \sinh ^{-1}(a x)^4},x\right ) \]
[Out]
Unintegrable(1/x^2/arcsinh(a*x)^4,x)
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Rubi [A]
time = 0.01, 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 = {}
\begin {gather*} \int \frac {1}{x^2 \sinh ^{-1}(a x)^4} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
Int[1/(x^2*ArcSinh[a*x]^4),x]
[Out]
Defer[Int][1/(x^2*ArcSinh[a*x]^4), x]
Rubi steps
\begin {align*} \int \frac {1}{x^2 \sinh ^{-1}(a x)^4} \, dx &=\int \frac {1}{x^2 \sinh ^{-1}(a x)^4} \, dx\\ \end {align*}
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Mathematica [A]
time = 6.35, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{x^2 \sinh ^{-1}(a x)^4} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
Integrate[1/(x^2*ArcSinh[a*x]^4),x]
[Out]
Integrate[1/(x^2*ArcSinh[a*x]^4), x]
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Maple [A]
time = 1.34, size = 0, normalized size = 0.00 \[\int \frac {1}{x^{2} \arcsinh \left (a x \right )^{4}}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
[In]
int(1/x^2/arcsinh(a*x)^4,x)
[Out]
int(1/x^2/arcsinh(a*x)^4,x)
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Maxima [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(1/x^2/arcsinh(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^3*x^3 + 2*(a^8*x^8 + a^6*x^6)*(a
^2*x^2 + 1)^(5/2) + 2*(5*a^9*x^9 + 9*a^7*x^7 + 4*a^5*x^5)*(a^2*x^2 + 1)^2 + (a^13*x^13 + 5*a^11*x^11 + 10*a^9*
x^9 + 10*a^7*x^7 + 5*a^5*x^5 + a^3*x^3 + (a^8*x^8 + 13*a^6*x^6 + 27*a^4*x^4 + 15*a^2*x^2)*(a^2*x^2 + 1)^(5/2)
+ (5*a^9*x^9 + 57*a^7*x^7 + 124*a^5*x^5 + 90*a^3*x^3 + 18*a*x)*(a^2*x^2 + 1)^2 + (10*a^10*x^10 + 98*a^8*x^8 +
220*a^6*x^6 + 189*a^4*x^4 + 63*a^2*x^2 + 6)*(a^2*x^2 + 1)^(3/2) + 2*(5*a^11*x^11 + 41*a^9*x^9 + 93*a^7*x^7 + 8
9*a^5*x^5 + 38*a^3*x^3 + 6*a*x)*(a^2*x^2 + 1) + (5*a^12*x^12 + 33*a^10*x^10 + 73*a^8*x^8 + 74*a^6*x^6 + 36*a^4
*x^4 + 7*a^2*x^2)*sqrt(a^2*x^2 + 1))*log(a*x + sqrt(a^2*x^2 + 1))^2 + 4*(5*a^10*x^10 + 13*a^8*x^8 + 11*a^6*x^6
+ 3*a^4*x^4)*(a^2*x^2 + 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^2*x^
2 + 1) - (a^13*x^13 + 5*a^11*x^11 + 10*a^9*x^9 + 10*a^7*x^7 + 5*a^5*x^5 + a^3*x^3 + (a^8*x^8 + 4*a^6*x^6 + 3*a
^4*x^4)*(a^2*x^2 + 1)^(5/2) + (5*a^9*x^9 + 21*a^7*x^7 + 24*a^5*x^5 + 8*a^3*x^3)*(a^2*x^2 + 1)^2 + (10*a^10*x^1
0 + 44*a^8*x^8 + 64*a^6*x^6 + 37*a^4*x^4 + 7*a^2*x^2)*(a^2*x^2 + 1)^(3/2) + 2*(5*a^11*x^11 + 23*a^9*x^9 + 39*a
^7*x^7 + 30*a^5*x^5 + 10*a^3*x^3 + a*x)*(a^2*x^2 + 1) + (5*a^12*x^12 + 24*a^10*x^10 + 45*a^8*x^8 + 41*a^6*x^6
+ 18*a^4*x^4 + 3*a^2*x^2)*sqrt(a^2*x^2 + 1))*log(a*x + sqrt(a^2*x^2 + 1)) + 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^2*x^2 + 1))/((a^13*x^14 + 5*a^11*x^12 + (a^2*x^2 + 1)^(5/2
)*a^8*x^9 + 10*a^9*x^10 + 10*a^7*x^8 + 5*a^5*x^6 + a^3*x^4 + 5*(a^9*x^10 + a^7*x^8)*(a^2*x^2 + 1)^2 + 10*(a^10
*x^11 + 2*a^8*x^9 + a^6*x^7)*(a^2*x^2 + 1)^(3/2) + 10*(a^11*x^12 + 3*a^9*x^10 + 3*a^7*x^8 + a^5*x^6)*(a^2*x^2
+ 1) + 5*(a^12*x^13 + 4*a^10*x^11 + 6*a^8*x^9 + 4*a^6*x^7 + a^4*x^5)*sqrt(a^2*x^2 + 1))*log(a*x + sqrt(a^2*x^2
+ 1))^3) - integrate(1/6*(a^15*x^15 + 6*a^13*x^13 + 15*a^11*x^11 + 20*a^9*x^9 + 15*a^7*x^7 + 6*a^5*x^5 + a^3*
x^3 + (a^9*x^9 + 39*a^7*x^7 + 135*a^5*x^5 + 105*a^3*x^3)*(a^2*x^2 + 1)^3 + (6*a^10*x^10 + 201*a^8*x^8 + 677*a^
6*x^6 + 663*a^4*x^4 + 174*a^2*x^2)*(a^2*x^2 + 1)^(5/2) + (15*a^11*x^11 + 420*a^9*x^9 + 1373*a^7*x^7 + 1565*a^5
*x^5 + 705*a^3*x^3 + 108*a*x)*(a^2*x^2 + 1)^2 + (20*a^12*x^12 + 450*a^10*x^10 + 1422*a^8*x^8 + 1787*a^6*x^6 +
1059*a^4*x^4 + 288*a^2*x^2 + 24)*(a^2*x^2 + 1)^(3/2) + (15*a^13*x^13 + 255*a^11*x^11 + 773*a^9*x^9 + 1026*a^7*
x^7 + 714*a^5*x^5 + 257*a^3*x^3 + 36*a*x)*(a^2*x^2 + 1) + (6*a^14*x^14 + 69*a^12*x^12 + 197*a^10*x^10 + 266*a^
8*x^8 + 201*a^6*x^6 + 83*a^4*x^4 + 14*a^2*x^2)*sqrt(a^2*x^2 + 1))/((a^15*x^17 + 6*a^13*x^15 + 15*a^11*x^13 + (
a^2*x^2 + 1)^3*a^9*x^11 + 20*a^9*x^11 + 15*a^7*x^9 + 6*a^5*x^7 + a^3*x^5 + 6*(a^10*x^12 + a^8*x^10)*(a^2*x^2 +
1)^(5/2) + 15*(a^11*x^13 + 2*a^9*x^11 + a^7*x^9)*(a^2*x^2 + 1)^2 + 20*(a^12*x^14 + 3*a^10*x^12 + 3*a^8*x^10 +
a^6*x^8)*(a^2*x^2 + 1)^(3/2) + 15*(a^13*x^15 + 4*a^11*x^13 + 6*a^9*x^11 + 4*a^7*x^9 + a^5*x^7)*(a^2*x^2 + 1)
+ 6*(a^14*x^16 + 5*a^12*x^14 + 10*a^10*x^12 + 10*a^8*x^10 + 5*a^6*x^8 + a^4*x^6)*sqrt(a^2*x^2 + 1))*log(a*x +
sqrt(a^2*x^2 + 1))), x)
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Fricas [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(1/x^2/arcsinh(a*x)^4,x, algorithm="fricas")
[Out]
integral(1/(x^2*arcsinh(a*x)^4), x)
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Sympy [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{x^{2} \operatorname {asinh}^{4}{\left (a x \right )}}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(1/x**2/asinh(a*x)**4,x)
[Out]
Integral(1/(x**2*asinh(a*x)**4), x)
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Giac [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(1/x^2/arcsinh(a*x)^4,x, algorithm="giac")
[Out]
integrate(1/(x^2*arcsinh(a*x)^4), x)
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Mupad [A]
time = 0.00, size = -1, normalized size = -0.08 \begin {gather*} \int \frac {1}{x^2\,{\mathrm {asinh}\left (a\,x\right )}^4} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
int(1/(x^2*asinh(a*x)^4),x)
[Out]
int(1/(x^2*asinh(a*x)^4), x)
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