3.289 \(\int \frac{e^{\cosh ^{-1}(a+b x)^2}}{x^2} \, dx\)

Optimal. Leaf size=16 \[ \text{CannotIntegrate}\left (\frac{e^{\cosh ^{-1}(a+b x)^2}}{x^2},x\right ) \]

[Out]

CannotIntegrate[E^ArcCosh[a + b*x]^2/x^2, x]

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Rubi [A]  time = 0.0388042, 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 = {} \[ \int \frac{e^{\cosh ^{-1}(a+b x)^2}}{x^2} \, dx \]

Verification is Not applicable to the result.

[In]

Int[E^ArcCosh[a + b*x]^2/x^2,x]

[Out]

Defer[Int][E^ArcCosh[a + b*x]^2/x^2, x]

Rubi steps

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

Mathematica [A]  time = 0.435765, size = 0, normalized size = 0. \[ \int \frac{e^{\cosh ^{-1}(a+b x)^2}}{x^2} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[E^ArcCosh[a + b*x]^2/x^2,x]

[Out]

Integrate[E^ArcCosh[a + b*x]^2/x^2, x]

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Maple [A]  time = 0.006, size = 0, normalized size = 0. \begin{align*} \int{\frac{{{\rm e}^{ \left ({\rm arccosh} \left (bx+a\right ) \right ) ^{2}}}}{{x}^{2}}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(arccosh(b*x+a)^2)/x^2,x)

[Out]

int(exp(arccosh(b*x+a)^2)/x^2,x)

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Maxima [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{e^{\left (\operatorname{arcosh}\left (b x + a\right )^{2}\right )}}{x^{2}}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(arccosh(b*x+a)^2)/x^2,x, algorithm="maxima")

[Out]

integrate(e^(arccosh(b*x + a)^2)/x^2, x)

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Fricas [A]  time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{e^{\left (\operatorname{arcosh}\left (b x + a\right )^{2}\right )}}{x^{2}}, x\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(arccosh(b*x+a)^2)/x^2,x, algorithm="fricas")

[Out]

integral(e^(arccosh(b*x + a)^2)/x^2, x)

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Sympy [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{e^{\operatorname{acosh}^{2}{\left (a + b x \right )}}}{x^{2}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(acosh(b*x+a)**2)/x**2,x)

[Out]

Integral(exp(acosh(a + b*x)**2)/x**2, x)

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Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{e^{\left (\operatorname{arcosh}\left (b x + a\right )^{2}\right )}}{x^{2}}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(arccosh(b*x+a)^2)/x^2,x, algorithm="giac")

[Out]

integrate(e^(arccosh(b*x + a)^2)/x^2, x)