3.2.25 \(\int (b x)^m \text {ArcCos}(a x)^{3/2} \, dx\) [125]

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

[Out]

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

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

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

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Mathematica [A]
time = 5.66, size = 0, normalized size = 0.00 \begin {gather*} \int (b x)^m \text {ArcCos}(a x)^{3/2} \, dx \end {gather*}

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

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 \begin {gather*} \text {Exception raised: RuntimeError} \end {gather*}

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

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

int(acos(a*x)^(3/2)*(b*x)^m, x)

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