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

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

[Out]

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

Verification is Not applicable to the result.

[In]

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

[Out]

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

Rubi steps

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

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Mathematica [A]  time = 6.68, size = 0, normalized size = 0.00 \[ \int (b x)^m \sqrt {\cos ^{-1}(a x)} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

Integrate[(b*x)^m*Sqrt[ArcCos[a*x]], 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)^(1/2),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 \[ \int \left (b x\right )^{m} \sqrt {\arccos \left (a x\right )}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate((b*x)^m*sqrt(arccos(a*x)), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

int((b*x)^m*arccos(a*x)^(1/2),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)^(1/2),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 \[ \int \sqrt {\mathrm {acos}\left (a\,x\right )}\,{\left (b\,x\right )}^m \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

int(acos(a*x)^(1/2)*(b*x)^m, x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((b*x)**m*acos(a*x)**(1/2),x)

[Out]

Integral((b*x)**m*sqrt(acos(a*x)), x)

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