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

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

[Out]

Unintegrable[1/(x*Sqrt[ArcCosh[a*x]]), x]

________________________________________________________________________________________

Rubi [A]  time = 0.0142105, 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 = {} \[ \int \frac{1}{x \sqrt{\cosh ^{-1}(a x)}} \, dx \]

Verification is Not applicable to the result.

[In]

Int[1/(x*Sqrt[ArcCosh[a*x]]),x]

[Out]

Defer[Int][1/(x*Sqrt[ArcCosh[a*x]]), x]

Rubi steps

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

Mathematica [A]  time = 0.228137, size = 0, normalized size = 0. \[ \int \frac{1}{x \sqrt{\cosh ^{-1}(a x)}} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[1/(x*Sqrt[ArcCosh[a*x]]),x]

[Out]

Integrate[1/(x*Sqrt[ArcCosh[a*x]]), x]

________________________________________________________________________________________

Maple [A]  time = 0.071, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{x}{\frac{1}{\sqrt{{\rm arccosh} \left (ax\right )}}}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

________________________________________________________________________________________

Maxima [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{x \sqrt{\operatorname{arcosh}\left (a x\right )}}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

[Out]

Exception raised: UnboundLocalError

________________________________________________________________________________________

Sympy [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{x \sqrt{\operatorname{acosh}{\left (a x \right )}}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Integral(1/(x*sqrt(acosh(a*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(1/x/arccosh(a*x)^(1/2),x, algorithm="giac")

[Out]

sage0*x