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

Optimal. Leaf size=16 \[ \text{Unintegrable}\left (\sqrt{b x} \cos ^{-1}(a x)^n,x\right ) \]

[Out]

Unintegrable[Sqrt[b*x]*ArcCos[a*x]^n, x]

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Rubi [A]  time = 0.0181128, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ \int \sqrt{b x} \cos ^{-1}(a x)^n \, dx \]

Verification is Not applicable to the result.

[In]

Int[Sqrt[b*x]*ArcCos[a*x]^n,x]

[Out]

Defer[Int][Sqrt[b*x]*ArcCos[a*x]^n, x]

Rubi steps

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

Mathematica [A]  time = 5.4538, size = 0, normalized size = 0. \[ \int \sqrt{b x} \cos ^{-1}(a x)^n \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[Sqrt[b*x]*ArcCos[a*x]^n,x]

[Out]

Integrate[Sqrt[b*x]*ArcCos[a*x]^n, x]

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Maple [A]  time = 0.162, size = 0, normalized size = 0. \begin{align*} \int \left ( \arccos \left ( ax \right ) \right ) ^{n}\sqrt{bx}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Maxima [F(-2)]  time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: RuntimeError} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Exception raised: RuntimeError

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Fricas [A]  time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\sqrt{b x} \arccos \left (a x\right )^{n}, x\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integral(sqrt(b*x)*arccos(a*x)^n, x)

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Sympy [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \sqrt{b x} \operatorname{acos}^{n}{\left (a x \right )}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Integral(sqrt(b*x)*acos(a*x)**n, x)

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Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \sqrt{b x} \arccos \left (a x\right )^{n}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(sqrt(b*x)*arccos(a*x)^n, x)