3.132 \(\int \frac {\cosh ^{-1}(a x)^n}{x} \, dx\)

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

[Out]

Unintegrable(arccosh(a*x)^n/x,x)

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Rubi [A]  time = 0.02, 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 = {} \[ \int \frac {\cosh ^{-1}(a x)^n}{x} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

Defer[Int][ArcCosh[a*x]^n/x, x]

Rubi steps

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

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Mathematica [A]  time = 0.35, size = 0, normalized size = 0.00 \[ \int \frac {\cosh ^{-1}(a x)^n}{x} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

Integrate[ArcCosh[a*x]^n/x, x]

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fricas [A]  time = 0.56, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\operatorname {arcosh}\left (a x\right )^{n}}{x}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integral(arccosh(a*x)^n/x, x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(arccosh(a*x)^n/x,x, algorithm="giac")

[Out]

integrate(arccosh(a*x)^n/x, x)

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maple [A]  time = 0.11, size = 0, normalized size = 0.00 \[ \int \frac {\mathrm {arccosh}\left (a x \right )^{n}}{x}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(arccosh(a*x)^n/x,x, algorithm="maxima")

[Out]

integrate(arccosh(a*x)^n/x, x)

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mupad [A]  time = 0.00, size = -1, normalized size = -0.08 \[ \int \frac {{\mathrm {acosh}\left (a\,x\right )}^n}{x} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

int(acosh(a*x)^n/x, x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Integral(acosh(a*x)**n/x, x)

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