3.1.96 \(\int \frac {1}{x^2 \sqrt {\cosh ^{-1}(a x)}} \, dx\) [96]

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

[Out]

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

________________________________________________________________________________________

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 {1}{x^2 \sqrt {\cosh ^{-1}(a x)}} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[1/(x^2*Sqrt[ArcCosh[a*x]]),x]

[Out]

Defer[Int][1/(x^2*Sqrt[ArcCosh[a*x]]), x]

Rubi steps

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

________________________________________________________________________________________

Mathematica [A]
time = 0.51, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{x^2 \sqrt {\cosh ^{-1}(a x)}} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[1/(x^2*Sqrt[ArcCosh[a*x]]),x]

[Out]

Integrate[1/(x^2*Sqrt[ArcCosh[a*x]]), x]

________________________________________________________________________________________

Maple [A]
time = 3.45, size = 0, normalized size = 0.00 \[\int \frac {1}{x^{2} \sqrt {\mathrm {arccosh}\left (a x \right )}}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

________________________________________________________________________________________

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

[Out]

integrate(1/(x^2*sqrt(arccosh(a*x))), x)

________________________________________________________________________________________

Fricas [F(-2)]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: TypeError} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

________________________________________________________________________________________

Sympy [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{x^{2} \sqrt {\operatorname {acosh}{\left (a x \right )}}}\, dx \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Integral(1/(x**2*sqrt(acosh(a*x))), x)

________________________________________________________________________________________

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

[Out]

integrate(1/(x^2*sqrt(arccosh(a*x))), x)

________________________________________________________________________________________

Mupad [A]
time = 0.00, size = -1, normalized size = -0.07 \begin {gather*} \int \frac {1}{x^2\,\sqrt {\mathrm {acosh}\left (a\,x\right )}} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

int(1/(x^2*acosh(a*x)^(1/2)), x)

________________________________________________________________________________________