3.2.39 \(\int \frac {\text {ArcCos}(a x)^n}{(b x)^{3/2}} \, dx\) [139]

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

[Out]

Unintegrable(arccos(a*x)^n/(b*x)^(3/2),x)

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Rubi [A]
time = 0.01, 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 = {} \begin {gather*} \int \frac {\text {ArcCos}(a x)^n}{(b x)^{3/2}} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

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

Rubi steps

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

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Mathematica [A]
time = 1.38, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\text {ArcCos}(a x)^n}{(b x)^{3/2}} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Maxima [F(-2)]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: RuntimeError} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(arccos(a*x)^n/(b*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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Fricas [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integral(sqrt(b*x)*arccos(a*x)^n/(b^2*x^2), x)

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Sympy [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\operatorname {acos}^{n}{\left (a x \right )}}{\left (b x\right )^{\frac {3}{2}}}\, dx \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Giac [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Mupad [A]
time = 0.00, size = -1, normalized size = -0.06 \begin {gather*} \int \frac {{\mathrm {acos}\left (a\,x\right )}^n}{{\left (b\,x\right )}^{3/2}} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

int(acos(a*x)^n/(b*x)^(3/2), x)

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