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

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

[Out]

Unintegrable(arccos(a*x)^n/x^2,x)

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Rubi [A]  time = 0.02, 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 = {} \[ \int \frac {\cos ^{-1}(a x)^n}{x^2} \, dx \]

Verification is Not applicable to the result.

[In]

Int[ArcCos[a*x]^n/x^2,x]

[Out]

Defer[Int][ArcCos[a*x]^n/x^2, x]

Rubi steps

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

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Mathematica [A]  time = 0.95, size = 0, normalized size = 0.00 \[ \int \frac {\cos ^{-1}(a x)^n}{x^2} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[ArcCos[a*x]^n/x^2,x]

[Out]

Integrate[ArcCos[a*x]^n/x^2, x]

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fricas [A]  time = 0.44, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\arccos \left (a x\right )^{n}}{x^{2}}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integral(arccos(a*x)^n/x^2, x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(arccos(a*x)^n/x^2, x)

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maple [A]  time = 0.26, size = 0, normalized size = 0.00 \[ \int \frac {\arccos \left (a x \right )^{n}}{x^{2}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(arccos(a*x)^n/x^2,x)

[Out]

int(arccos(a*x)^n/x^2,x)

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maxima [F(-2)]  time = 0.00, size = 0, normalized size = 0.00 \[ \text {Exception raised: RuntimeError} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative e
xponent.

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(acos(a*x)^n/x^2,x)

[Out]

int(acos(a*x)^n/x^2, x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(acos(a*x)**n/x**2,x)

[Out]

Integral(acos(a*x)**n/x**2, x)

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