3.1.65 \(\int \frac {1}{x \text {ArcCos}(a x)^3} \, dx\) [65]

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

[Out]

Unintegrable(1/x/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 = {} \begin {gather*} \int \frac {1}{x \text {ArcCos}(a x)^3} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

Defer[Int][1/(x*ArcCos[a*x]^3), x]

Rubi steps

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

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Mathematica [A]
time = 0.52, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{x \text {ArcCos}(a x)^3} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

Integrate[1/(x*ArcCos[a*x]^3), x]

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Maple [A]
time = 1.03, size = 0, normalized size = 0.00 \[\int \frac {1}{x \arccos \left (a x \right )^{3}}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

[Out]

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

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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/arccos(a*x)^3,x, algorithm="fricas")

[Out]

integral(1/(x*arccos(a*x)^3), x)

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Sympy [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{x \operatorname {acos}^{3}{\left (a x \right )}}\, dx \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Integral(1/(x*acos(a*x)**3), 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/arccos(a*x)^3,x, algorithm="giac")

[Out]

integrate(1/(x*arccos(a*x)^3), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

int(1/(x*acos(a*x)^3), x)

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