3.1.56 \(\int \frac {1}{x \cosh ^{-1}(a x)^2} \, dx\) [56]

Optimal. Leaf size=13 \[ \text {Int}\left (\frac {1}{x \cosh ^{-1}(a x)^2},x\right ) \]

[Out]

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

Verification is not applicable to the result.

[In]

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

[Out]

Defer[Int][1/(x*ArcCosh[a*x]^2), x]

Rubi steps

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

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Mathematica [A]
time = 3.21, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{x \cosh ^{-1}(a x)^2} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

Integrate[1/(x*ArcCosh[a*x]^2), x]

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Maple [A]
time = 180.00, size = 0, normalized size = 0.00 \[\int \frac {1}{x \mathrm {arccosh}\left (a x \right )^{2}}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

[Out]

-(a^3*x^3 + (a^2*x^2 - 1)*sqrt(a*x + 1)*sqrt(a*x - 1) - a*x)/((a^3*x^3 + sqrt(a*x + 1)*sqrt(a*x - 1)*a^2*x^2 -
a*x)*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))) + integrate((2*(a*x + 1)*(a*x - 1)*a*x + (2*a^2*x^2 - 1)*sqrt(a*
x + 1)*sqrt(a*x - 1))/((a^5*x^6 + (a*x + 1)*(a*x - 1)*a^3*x^4 - 2*a^3*x^4 + a*x^2 + 2*(a^4*x^5 - a^2*x^3)*sqrt
(a*x + 1)*sqrt(a*x - 1))*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))), 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(1/x/arccosh(a*x)^2,x, algorithm="fricas")

[Out]

integral(1/(x*arccosh(a*x)^2), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

[Out]

integrate(1/(x*arccosh(a*x)^2), x)

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Mupad [A]
time = 0.00, size = -1, normalized size = -0.08 \begin {gather*} \int \frac {1}{x\,{\mathrm {acosh}\left (a\,x\right )}^2} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

int(1/(x*acosh(a*x)^2), x)

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