3.85 \(\int \frac {\sinh ^{-1}(a x)^{3/2}}{x} \, dx\)

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

[Out]

Unintegrable(arcsinh(a*x)^(3/2)/x,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 = {} \[ \int \frac {\sinh ^{-1}(a x)^{3/2}}{x} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

Defer[Int][ArcSinh[a*x]^(3/2)/x, x]

Rubi steps

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

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Mathematica [A]  time = 0.34, size = 0, normalized size = 0.00 \[ \int \frac {\sinh ^{-1}(a x)^{3/2}}{x} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

Integrate[ArcSinh[a*x]^(3/2)/x, x]

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fricas [F(-2)]  time = 0.00, size = 0, normalized size = 0.00 \[ \text {Exception raised: TypeError} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (co
nstant residues)

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giac [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\operatorname {arsinh}\left (a x\right )^{\frac {3}{2}}}{x}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(arcsinh(a*x)^(3/2)/x, x)

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maple [A]  time = 0.35, size = 0, normalized size = 0.00 \[ \int \frac {\arcsinh \left (a x \right )^{\frac {3}{2}}}{x}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maxima [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\operatorname {arsinh}\left (a x\right )^{\frac {3}{2}}}{x}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(arcsinh(a*x)^(3/2)/x, x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

int(asinh(a*x)^(3/2)/x, x)

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sympy [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\operatorname {asinh}^{\frac {3}{2}}{\left (a x \right )}}{x}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Integral(asinh(a*x)**(3/2)/x, x)

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