3.77 \(\int \frac{\sqrt{\cosh ^{-1}(a x)}}{x} \, dx\)

Optimal. Leaf size=14 \[ \text{Unintegrable}\left (\frac{\sqrt{\cosh ^{-1}(a x)}}{x},x\right ) \]

[Out]

Unintegrable[Sqrt[ArcCosh[a*x]]/x, x]

________________________________________________________________________________________

Rubi [A]  time = 0.0131443, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ \int \frac{\sqrt{\cosh ^{-1}(a x)}}{x} \, dx \]

Verification is Not applicable to the result.

[In]

Int[Sqrt[ArcCosh[a*x]]/x,x]

[Out]

Defer[Int][Sqrt[ArcCosh[a*x]]/x, x]

Rubi steps

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

Mathematica [A]  time = 0.283121, size = 0, normalized size = 0. \[ \int \frac{\sqrt{\cosh ^{-1}(a x)}}{x} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[Sqrt[ArcCosh[a*x]]/x,x]

[Out]

Integrate[Sqrt[ArcCosh[a*x]]/x, x]

________________________________________________________________________________________

Maple [A]  time = 0.07, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{x}\sqrt{{\rm arccosh} \left (ax\right )}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(arccosh(a*x)^(1/2)/x,x)

[Out]

int(arccosh(a*x)^(1/2)/x,x)

________________________________________________________________________________________

Maxima [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\sqrt{\operatorname{arcosh}\left (a x\right )}}{x}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(arccosh(a*x)^(1/2)/x,x, algorithm="maxima")

[Out]

integrate(sqrt(arccosh(a*x))/x, x)

________________________________________________________________________________________

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(arccosh(a*x)^(1/2)/x,x, algorithm="fricas")

[Out]

Exception raised: UnboundLocalError

________________________________________________________________________________________

Sympy [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\sqrt{\operatorname{acosh}{\left (a x \right )}}}{x}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(acosh(a*x)**(1/2)/x,x)

[Out]

Integral(sqrt(acosh(a*x))/x, x)

________________________________________________________________________________________

Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \mathit{sage}_{0} x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(arccosh(a*x)^(1/2)/x,x, algorithm="giac")

[Out]

sage0*x