3.123 \(\int \frac {(b x)^m}{\cos ^{-1}(a x)} \, dx\)

Optimal. Leaf size=15 \[ \text {Int}\left (\frac {(b x)^m}{\cos ^{-1}(a x)},x\right ) \]

[Out]

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

Verification is Not applicable to the result.

[In]

Int[(b*x)^m/ArcCos[a*x],x]

[Out]

Defer[Int][(b*x)^m/ArcCos[a*x], x]

Rubi steps

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

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Mathematica [A]  time = 0.71, size = 0, normalized size = 0.00 \[ \int \frac {(b x)^m}{\cos ^{-1}(a x)} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[(b*x)^m/ArcCos[a*x],x]

[Out]

Integrate[(b*x)^m/ArcCos[a*x], x]

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fricas [A]  time = 0.40, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\left (b x\right )^{m}}{\arccos \left (a x\right )}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((b*x)^m/arccos(a*x),x, algorithm="fricas")

[Out]

integral((b*x)^m/arccos(a*x), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((b*x)^m/arccos(a*x),x, algorithm="giac")

[Out]

integrate((b*x)^m/arccos(a*x), x)

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maple [A]  time = 0.82, size = 0, normalized size = 0.00 \[ \int \frac {\left (b x \right )^{m}}{\arccos \left (a x \right )}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((b*x)^m/arccos(a*x),x)

[Out]

int((b*x)^m/arccos(a*x),x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((b*x)^m/arccos(a*x),x, algorithm="maxima")

[Out]

integrate((b*x)^m/arccos(a*x), x)

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mupad [A]  time = 0.00, size = -1, normalized size = -0.07 \[ \int \frac {{\left (b\,x\right )}^m}{\mathrm {acos}\left (a\,x\right )} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((b*x)^m/acos(a*x),x)

[Out]

int((b*x)^m/acos(a*x), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((b*x)**m/acos(a*x),x)

[Out]

Integral((b*x)**m/acos(a*x), x)

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