3.84 \(\int \frac{1}{x \sinh ^{-1}(a+b x)} \, dx\)

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

[Out]

Unintegrable[1/(x*ArcSinh[a + b*x]), x]

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Rubi [A]  time = 0.0440705, 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 = {} \[ \int \frac{1}{x \sinh ^{-1}(a+b x)} \, dx \]

Verification is Not applicable to the result.

[In]

Int[1/(x*ArcSinh[a + b*x]),x]

[Out]

Defer[Subst][Defer[Int][1/((-(a/b) + x/b)*ArcSinh[x]), x], x, a + b*x]/b

Rubi steps

\begin{align*} \int \frac{1}{x \sinh ^{-1}(a+b x)} \, dx &=\frac{\operatorname{Subst}\left (\int \frac{1}{\left (-\frac{a}{b}+\frac{x}{b}\right ) \sinh ^{-1}(x)} \, dx,x,a+b x\right )}{b}\\ \end{align*}

Mathematica [A]  time = 0.190473, size = 0, normalized size = 0. \[ \int \frac{1}{x \sinh ^{-1}(a+b x)} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[1/(x*ArcSinh[a + b*x]),x]

[Out]

Integrate[1/(x*ArcSinh[a + b*x]), x]

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Maple [A]  time = 0.091, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{x{\it Arcsinh} \left ( bx+a \right ) }}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/x/arcsinh(b*x+a),x)

[Out]

int(1/x/arcsinh(b*x+a),x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x/arcsinh(b*x+a),x, algorithm="maxima")

[Out]

integrate(1/(x*arcsinh(b*x + a)), x)

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Fricas [A]  time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{1}{x \operatorname{arsinh}\left (b x + a\right )}, x\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x/arcsinh(b*x+a),x, algorithm="fricas")

[Out]

integral(1/(x*arcsinh(b*x + a)), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x/asinh(b*x+a),x)

[Out]

Integral(1/(x*asinh(a + b*x)), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x/arcsinh(b*x+a),x, algorithm="giac")

[Out]

integrate(1/(x*arcsinh(b*x + a)), x)