3.49 \(\int \frac {1}{x \sin ^{-1}(a x)} \, dx\)

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

[Out]

Unintegrable(1/x/arcsin(a*x),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 = {} \[ \int \frac {1}{x \sin ^{-1}(a x)} \, dx \]

Verification is Not applicable to the result.

[In]

Int[1/(x*ArcSin[a*x]),x]

[Out]

Defer[Int][1/(x*ArcSin[a*x]), x]

Rubi steps

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

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Mathematica [A]  time = 0.20, size = 0, normalized size = 0.00 \[ \int \frac {1}{x \sin ^{-1}(a x)} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[1/(x*ArcSin[a*x]),x]

[Out]

Integrate[1/(x*ArcSin[a*x]), x]

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fricas [A]  time = 0.60, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {1}{x \arcsin \left (a x\right )}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x/arcsin(a*x),x, algorithm="fricas")

[Out]

integral(1/(x*arcsin(a*x)), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x/arcsin(a*x),x, algorithm="giac")

[Out]

integrate(1/(x*arcsin(a*x)), x)

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maple [A]  time = 0.14, size = 0, normalized size = 0.00 \[ \int \frac {1}{x \arcsin \left (a x \right )}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/x/arcsin(a*x),x)

[Out]

int(1/x/arcsin(a*x),x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x/arcsin(a*x),x, algorithm="maxima")

[Out]

integrate(1/(x*arcsin(a*x)), x)

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mupad [A]  time = 0.00, size = -1, normalized size = -0.08 \[ \int \frac {1}{x\,\mathrm {asin}\left (a\,x\right )} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(x*asin(a*x)),x)

[Out]

int(1/(x*asin(a*x)), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x/asin(a*x),x)

[Out]

Integral(1/(x*asin(a*x)), x)

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