3.66 \(\int \frac {1}{x^2 \cos ^{-1}(a x)^3} \, dx\)

Optimal. Leaf size=13 \[ \text {Int}\left (\frac {1}{x^2 \cos ^{-1}(a x)^3},x\right ) \]

[Out]

Unintegrable(1/x^2/arccos(a*x)^3,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 = {} \[ \int \frac {1}{x^2 \cos ^{-1}(a x)^3} \, dx \]

Verification is Not applicable to the result.

[In]

Int[1/(x^2*ArcCos[a*x]^3),x]

[Out]

Defer[Int][1/(x^2*ArcCos[a*x]^3), x]

Rubi steps

\begin {align*} \int \frac {1}{x^2 \cos ^{-1}(a x)^3} \, dx &=\int \frac {1}{x^2 \cos ^{-1}(a x)^3} \, dx\\ \end {align*}

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Mathematica [A]  time = 10.19, size = 0, normalized size = 0.00 \[ \int \frac {1}{x^2 \cos ^{-1}(a x)^3} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[1/(x^2*ArcCos[a*x]^3),x]

[Out]

Integrate[1/(x^2*ArcCos[a*x]^3), x]

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fricas [A]  time = 0.42, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {1}{x^{2} \arccos \left (a x\right )^{3}}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x^2/arccos(a*x)^3,x, algorithm="fricas")

[Out]

integral(1/(x^2*arccos(a*x)^3), x)

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giac [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{x^{2} \arccos \left (a x\right )^{3}}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x^2/arccos(a*x)^3,x, algorithm="giac")

[Out]

integrate(1/(x^2*arccos(a*x)^3), x)

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maple [A]  time = 0.33, size = 0, normalized size = 0.00 \[ \int \frac {1}{x^{2} \arccos \left (a x \right )^{3}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/x^2/arccos(a*x)^3,x)

[Out]

int(1/x^2/arccos(a*x)^3,x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x^2/arccos(a*x)^3,x, algorithm="maxima")

[Out]

-1/2*(x^3*arctan2(sqrt(a*x + 1)*sqrt(-a*x + 1), a*x)^2*integrate((a^2*x^2 - 6)/(x^4*arctan2(sqrt(a*x + 1)*sqrt
(-a*x + 1), a*x)), x) - sqrt(a*x + 1)*sqrt(-a*x + 1)*a*x + (a^2*x^2 - 2)*arctan2(sqrt(a*x + 1)*sqrt(-a*x + 1),
a*x))/(a^2*x^3*arctan2(sqrt(a*x + 1)*sqrt(-a*x + 1), a*x)^2)

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mupad [A]  time = 0.00, size = -1, normalized size = -0.08 \[ \int \frac {1}{x^2\,{\mathrm {acos}\left (a\,x\right )}^3} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(x^2*acos(a*x)^3),x)

[Out]

int(1/(x^2*acos(a*x)^3), x)

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sympy [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{x^{2} \operatorname {acos}^{3}{\left (a x \right )}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x**2/acos(a*x)**3,x)

[Out]

Integral(1/(x**2*acos(a*x)**3), x)

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