\(\int \frac {1}{x \arcsin (a x)} \, dx\) [49]

Optimal result

Integrand size = 10, antiderivative size = 10 \[ \int \frac {1}{x \arcsin (a x)} \, dx=\text {Int}\left (\frac {1}{x \arcsin (a x)},x\right ) \]

[Out]

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

Rubi [N/A]

Not integrable

Time = 0.01 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.00, number of steps used = 0, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \frac {1}{x \arcsin (a x)} \, dx=\int \frac {1}{x \arcsin (a x)} \, dx \]

[In]

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

[Out]

Defer[Int][1/(x*ArcSin[a*x]), x]

Rubi steps \begin{align*} \text {integral}& = \int \frac {1}{x \arcsin (a x)} \, dx \\ \end{align*}

Mathematica [N/A]

Not integrable

Time = 0.21 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int \frac {1}{x \arcsin (a x)} \, dx=\int \frac {1}{x \arcsin (a x)} \, dx \]

[In]

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

[Out]

Integrate[1/(x*ArcSin[a*x]), x]

Maple [N/A] (verified)

Not integrable

Time = 0.03 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.00

\[\int \frac {1}{x \arcsin \left (a x \right )}d x\]

[In]

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

[Out]

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

Fricas [N/A]

Not integrable

Time = 0.23 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int \frac {1}{x \arcsin (a x)} \, dx=\int { \frac {1}{x \arcsin \left (a x\right )} \,d x } \]

[In]

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

[Out]

integral(1/(x*arcsin(a*x)), x)

Sympy [N/A]

Not integrable

Time = 0.26 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.80 \[ \int \frac {1}{x \arcsin (a x)} \, dx=\int \frac {1}{x \operatorname {asin}{\left (a x \right )}}\, dx \]

[In]

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

[Out]

Integral(1/(x*asin(a*x)), x)

Maxima [N/A]

Not integrable

Time = 0.37 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int \frac {1}{x \arcsin (a x)} \, dx=\int { \frac {1}{x \arcsin \left (a x\right )} \,d x } \]

[In]

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

[Out]

integrate(1/(x*arcsin(a*x)), x)

Giac [N/A]

Not integrable

Time = 0.30 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int \frac {1}{x \arcsin (a x)} \, dx=\int { \frac {1}{x \arcsin \left (a x\right )} \,d x } \]

[In]

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

[Out]

integrate(1/(x*arcsin(a*x)), x)

Mupad [N/A]

Not integrable

Time = 0.04 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int \frac {1}{x \arcsin (a x)} \, dx=\int \frac {1}{x\,\mathrm {asin}\left (a\,x\right )} \,d x \]

[In]

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

[Out]

int(1/(x*asin(a*x)), x)