3.59 \(\int \frac {1}{x^2 \sinh ^{-1}(a x)^2} \, dx\)

Optimal. Leaf size=13 \[ \text {Int}\left (\frac {1}{x^2 \sinh ^{-1}(a x)^2},x\right ) \]

[Out]

Unintegrable(1/x^2/arcsinh(a*x)^2,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 = {} \[ \int \frac {1}{x^2 \sinh ^{-1}(a x)^2} \, dx \]

Verification is Not applicable to the result.

[In]

Int[1/(x^2*ArcSinh[a*x]^2),x]

[Out]

Defer[Int][1/(x^2*ArcSinh[a*x]^2), x]

Rubi steps

\begin {align*} \int \frac {1}{x^2 \sinh ^{-1}(a x)^2} \, dx &=\int \frac {1}{x^2 \sinh ^{-1}(a x)^2} \, dx\\ \end {align*}

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Mathematica [A]  time = 5.06, size = 0, normalized size = 0.00 \[ \int \frac {1}{x^2 \sinh ^{-1}(a x)^2} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[1/(x^2*ArcSinh[a*x]^2),x]

[Out]

Integrate[1/(x^2*ArcSinh[a*x]^2), x]

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fricas [A]  time = 0.43, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {1}{x^{2} \operatorname {arsinh}\left (a x\right )^{2}}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x^2/arcsinh(a*x)^2,x, algorithm="fricas")

[Out]

integral(1/(x^2*arcsinh(a*x)^2), x)

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giac [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{x^{2} \operatorname {arsinh}\left (a x\right )^{2}}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x^2/arcsinh(a*x)^2,x, algorithm="giac")

[Out]

integrate(1/(x^2*arcsinh(a*x)^2), x)

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maple [A]  time = 0.36, size = 0, normalized size = 0.00 \[ \int \frac {1}{x^{2} \arcsinh \left (a x \right )^{2}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/x^2/arcsinh(a*x)^2,x)

[Out]

int(1/x^2/arcsinh(a*x)^2,x)

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maxima [A]  time = 0.00, size = 0, normalized size = 0.00 \[ -\frac {a^{3} x^{3} + a x + {\left (a^{2} x^{2} + 1\right )}^{\frac {3}{2}}}{{\left (a^{3} x^{4} + \sqrt {a^{2} x^{2} + 1} a^{2} x^{3} + a x^{2}\right )} \log \left (a x + \sqrt {a^{2} x^{2} + 1}\right )} - \int \frac {a^{5} x^{5} + 2 \, a^{3} x^{3} + {\left (a^{3} x^{3} + 3 \, a x\right )} {\left (a^{2} x^{2} + 1\right )} + a x + {\left (2 \, a^{4} x^{4} + 5 \, a^{2} x^{2} + 2\right )} \sqrt {a^{2} x^{2} + 1}}{{\left (a^{5} x^{7} + {\left (a^{2} x^{2} + 1\right )} a^{3} x^{5} + 2 \, a^{3} x^{5} + a x^{3} + 2 \, {\left (a^{4} x^{6} + a^{2} x^{4}\right )} \sqrt {a^{2} x^{2} + 1}\right )} \log \left (a x + \sqrt {a^{2} x^{2} + 1}\right )}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x^2/arcsinh(a*x)^2,x, algorithm="maxima")

[Out]

-(a^3*x^3 + a*x + (a^2*x^2 + 1)^(3/2))/((a^3*x^4 + sqrt(a^2*x^2 + 1)*a^2*x^3 + a*x^2)*log(a*x + sqrt(a^2*x^2 +
1))) - integrate((a^5*x^5 + 2*a^3*x^3 + (a^3*x^3 + 3*a*x)*(a^2*x^2 + 1) + a*x + (2*a^4*x^4 + 5*a^2*x^2 + 2)*s
qrt(a^2*x^2 + 1))/((a^5*x^7 + (a^2*x^2 + 1)*a^3*x^5 + 2*a^3*x^5 + a*x^3 + 2*(a^4*x^6 + a^2*x^4)*sqrt(a^2*x^2 +
1))*log(a*x + sqrt(a^2*x^2 + 1))), x)

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mupad [A]  time = 0.00, size = -1, normalized size = -0.08 \[ \int \frac {1}{x^2\,{\mathrm {asinh}\left (a\,x\right )}^2} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(x^2*asinh(a*x)^2),x)

[Out]

int(1/(x^2*asinh(a*x)^2), x)

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sympy [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{x^{2} \operatorname {asinh}^{2}{\left (a x \right )}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x**2/asinh(a*x)**2,x)

[Out]

Integral(1/(x**2*asinh(a*x)**2), x)

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