3.2.34 \(\int \frac {\sinh ^{-1}(a x)^n}{x} \, dx\) [134]

Optimal. Leaf size=13 \[ \text {Int}\left (\frac {\sinh ^{-1}(a x)^n}{x},x\right ) \]

[Out]

Unintegrable(arcsinh(a*x)^n/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 = {} \begin {gather*} \int \frac {\sinh ^{-1}(a x)^n}{x} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[ArcSinh[a*x]^n/x,x]

[Out]

Defer[Int][ArcSinh[a*x]^n/x, x]

Rubi steps

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

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Mathematica [A]
time = 0.20, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\sinh ^{-1}(a x)^n}{x} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[ArcSinh[a*x]^n/x,x]

[Out]

Integrate[ArcSinh[a*x]^n/x, x]

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Maple [A]
time = 0.46, size = 0, normalized size = 0.00 \[\int \frac {\arcsinh \left (a x \right )^{n}}{x}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(arcsinh(a*x)^n/x,x)

[Out]

int(arcsinh(a*x)^n/x,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(arcsinh(a*x)^n/x,x, algorithm="maxima")

[Out]

integrate(arcsinh(a*x)^n/x, x)

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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(arcsinh(a*x)^n/x,x, algorithm="fricas")

[Out]

integral(arcsinh(a*x)^n/x, x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(asinh(a*x)**n/x,x)

[Out]

Integral(asinh(a*x)**n/x, 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(arcsinh(a*x)^n/x,x, algorithm="giac")

[Out]

integrate(arcsinh(a*x)^n/x, x)

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Mupad [A]
time = 0.00, size = -1, normalized size = -0.08 \begin {gather*} \int \frac {{\mathrm {asinh}\left (a\,x\right )}^n}{x} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(asinh(a*x)^n/x,x)

[Out]

int(asinh(a*x)^n/x, x)

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