3.2.27 \(\int \frac {x^m}{\sinh ^{-1}(a x)^{3/2}} \, dx\) [127]

Optimal. Leaf size=15 \[ \text {Int}\left (\frac {x^m}{\sinh ^{-1}(a x)^{3/2}},x\right ) \]

[Out]

Unintegrable(x^m/arcsinh(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 \frac {x^m}{\sinh ^{-1}(a x)^{3/2}} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[x^m/ArcSinh[a*x]^(3/2),x]

[Out]

Defer[Int][x^m/ArcSinh[a*x]^(3/2), x]

Rubi steps

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

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Mathematica [A]
time = 2.32, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {x^m}{\sinh ^{-1}(a x)^{3/2}} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[x^m/ArcSinh[a*x]^(3/2),x]

[Out]

Integrate[x^m/ArcSinh[a*x]^(3/2), x]

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Maple [A]
time = 0.98, size = 0, normalized size = 0.00 \[\int \frac {x^{m}}{\arcsinh \left (a x \right )^{\frac {3}{2}}}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Maxima [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^m/arcsinh(a*x)^(3/2),x, algorithm="maxima")

[Out]

integrate(x^m/arcsinh(a*x)^(3/2), x)

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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(x^m/arcsinh(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 \frac {x^{m}}{\operatorname {asinh}^{\frac {3}{2}}{\left (a x \right )}}\, dx \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x**m/asinh(a*x)**(3/2),x)

[Out]

Integral(x**m/asinh(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(x^m/arcsinh(a*x)^(3/2),x, algorithm="giac")

[Out]

integrate(x^m/arcsinh(a*x)^(3/2), x)

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Mupad [A]
time = 0.00, size = -1, normalized size = -0.07 \begin {gather*} \int \frac {x^m}{{\mathrm {asinh}\left (a\,x\right )}^{3/2}} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

int(x^m/asinh(a*x)^(3/2), x)

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