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

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

[Out]

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

________________________________________________________________________________________

Rubi [A]  time = 0.04, 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 = {} \[ \int \frac {1}{x \sinh ^{-1}(a+b x)} \, dx \]

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 = 0.20, size = 0, normalized size = 0.00 \[ \int \frac {1}{x \sinh ^{-1}(a+b x)} \, dx \]

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]

________________________________________________________________________________________

fricas [A]  time = 0.53, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {1}{x \operatorname {arsinh}\left (b x + a\right )}, x\right ) \]

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)

________________________________________________________________________________________

giac [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{x \operatorname {arsinh}\left (b x + a\right )}\,{d x} \]

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)

________________________________________________________________________________________

maple [A]  time = 0.17, size = 0, normalized size = 0.00 \[ \int \frac {1}{x \arcsinh \left (b x +a \right )}\, dx \]

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)

________________________________________________________________________________________

maxima [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{x \operatorname {arsinh}\left (b x + a\right )}\,{d x} \]

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)

________________________________________________________________________________________

mupad [A]  time = 0.00, size = -1, normalized size = -0.07 \[ \int \frac {1}{x\,\mathrm {asinh}\left (a+b\,x\right )} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(x*asinh(a + b*x)),x)

[Out]

int(1/(x*asinh(a + b*x)), x)

________________________________________________________________________________________

sympy [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{x \operatorname {asinh}{\left (a + b x \right )}}\, dx \]

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)

________________________________________________________________________________________