3.73 \(\int \frac{1}{x^2 \sin ^{-1}(a x)^4} \, dx\)

Optimal. Leaf size=12 \[ \text{Unintegrable}\left (\frac{1}{x^2 \sin ^{-1}(a x)^4},x\right ) \]

[Out]

Unintegrable[1/(x^2*ArcSin[a*x]^4), x]

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Rubi [A]  time = 0.0140271, 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 = {} \[ \int \frac{1}{x^2 \sin ^{-1}(a x)^4} \, dx \]

Verification is Not applicable to the result.

[In]

Int[1/(x^2*ArcSin[a*x]^4),x]

[Out]

Defer[Int][1/(x^2*ArcSin[a*x]^4), x]

Rubi steps

\begin{align*} \int \frac{1}{x^2 \sin ^{-1}(a x)^4} \, dx &=\int \frac{1}{x^2 \sin ^{-1}(a x)^4} \, dx\\ \end{align*}

Mathematica [A]  time = 17.8693, size = 0, normalized size = 0. \[ \int \frac{1}{x^2 \sin ^{-1}(a x)^4} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[1/(x^2*ArcSin[a*x]^4),x]

[Out]

Integrate[1/(x^2*ArcSin[a*x]^4), x]

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Maple [A]  time = 0.118, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{{x}^{2} \left ( \arcsin \left ( ax \right ) \right ) ^{4}}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/x^2/arcsin(a*x)^4,x)

[Out]

int(1/x^2/arcsin(a*x)^4,x)

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Maxima [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \frac{a^{3} x^{4} \arctan \left (a x, \sqrt{a x + 1} \sqrt{-a x + 1}\right )^{3} \int \frac{{\left (a^{4} x^{4} - 20 \, a^{2} x^{2} + 24\right )} \sqrt{a x + 1} \sqrt{-a x + 1}}{{\left (a^{5} x^{7} - a^{3} x^{5}\right )} \arctan \left (a x, \sqrt{a x + 1} \sqrt{-a x + 1}\right )}\,{d x} -{\left (2 \, a^{2} x^{2} -{\left (a^{2} x^{2} - 6\right )} \arctan \left (a x, \sqrt{a x + 1} \sqrt{-a x + 1}\right )^{2}\right )} \sqrt{a x + 1} \sqrt{-a x + 1} -{\left (a^{3} x^{3} - 2 \, a x\right )} \arctan \left (a x, \sqrt{a x + 1} \sqrt{-a x + 1}\right )}{6 \, a^{3} x^{4} \arctan \left (a x, \sqrt{a x + 1} \sqrt{-a x + 1}\right )^{3}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x^2/arcsin(a*x)^4,x, algorithm="maxima")

[Out]

1/6*(6*a^3*x^4*arctan2(a*x, sqrt(a*x + 1)*sqrt(-a*x + 1))^3*integrate(1/6*(a^4*x^4 - 20*a^2*x^2 + 24)*sqrt(a*x
+ 1)*sqrt(-a*x + 1)/((a^5*x^7 - a^3*x^5)*arctan2(a*x, sqrt(a*x + 1)*sqrt(-a*x + 1))), x) - (2*a^2*x^2 - (a^2*
x^2 - 6)*arctan2(a*x, sqrt(a*x + 1)*sqrt(-a*x + 1))^2)*sqrt(a*x + 1)*sqrt(-a*x + 1) - (a^3*x^3 - 2*a*x)*arctan
2(a*x, sqrt(a*x + 1)*sqrt(-a*x + 1)))/(a^3*x^4*arctan2(a*x, sqrt(a*x + 1)*sqrt(-a*x + 1))^3)

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Fricas [A]  time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{1}{x^{2} \arcsin \left (a x\right )^{4}}, x\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x^2/arcsin(a*x)^4,x, algorithm="fricas")

[Out]

integral(1/(x^2*arcsin(a*x)^4), x)

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Sympy [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{x^{2} \operatorname{asin}^{4}{\left (a x \right )}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x**2/asin(a*x)**4,x)

[Out]

Integral(1/(x**2*asin(a*x)**4), x)

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Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{x^{2} \arcsin \left (a x\right )^{4}}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x^2/arcsin(a*x)^4,x, algorithm="giac")

[Out]

integrate(1/(x^2*arcsin(a*x)^4), x)