3.128 \(\int \frac {(b x)^m}{\cos ^{-1}(a x)^{3/2}} \, dx\)

Optimal. Leaf size=17 \[ \text {Int}\left (\frac {(b x)^m}{\cos ^{-1}(a x)^{3/2}},x\right ) \]

[Out]

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

Verification is Not applicable to the result.

[In]

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

[Out]

Defer[Int][(b*x)^m/ArcCos[a*x]^(3/2), x]

Rubi steps

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

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Mathematica [A]  time = 3.72, size = 0, normalized size = 0.00 \[ \int \frac {(b x)^m}{\cos ^{-1}(a x)^{3/2}} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (co
nstant residues)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate((b*x)^m/arccos(a*x)^(3/2), x)

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maple [A]  time = 0.14, size = 0, normalized size = 0.00 \[ \int \frac {\left (b x \right )^{m}}{\arccos \left (a x \right )^{\frac {3}{2}}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

int((b*x)^m/arccos(a*x)^(3/2),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((b*x)^m/arccos(a*x)^(3/2),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 = -0.06 \[ \int \frac {{\left (b\,x\right )}^m}{{\mathrm {acos}\left (a\,x\right )}^{3/2}} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

int((b*x)^m/acos(a*x)^(3/2), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((b*x)**m/acos(a*x)**(3/2),x)

[Out]

Integral((b*x)**m/acos(a*x)**(3/2), x)

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