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

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

[Out]

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

________________________________________________________________________________________

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

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 = 5.95, size = 0, normalized size = 0.00 \[ \int \sqrt {b x} \cos ^{-1}(a x)^n \, dx \]

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]

________________________________________________________________________________________

fricas [A]  time = 0.54, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\sqrt {b x} \arccos \left (a x\right )^{n}, x\right ) \]

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)

________________________________________________________________________________________

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

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)

________________________________________________________________________________________

maple [A]  time = 0.18, size = 0, normalized size = 0.00 \[ \int \arccos \left (a x \right )^{n} \sqrt {b x}\, dx \]

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)

________________________________________________________________________________________

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*(b*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.

________________________________________________________________________________________

mupad [A]  time = 0.00, size = -1, normalized size = -0.06 \[ \int {\mathrm {acos}\left (a\,x\right )}^n\,\sqrt {b\,x} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

int(acos(a*x)^n*(b*x)^(1/2), x)

________________________________________________________________________________________

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

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)

________________________________________________________________________________________