Optimal. Leaf size=19 \[ \text {Int}\left (\frac {1}{x \sqrt {a+b \sin ^{-1}(c x)}},x\right ) \]
[Out]
________________________________________________________________________________________
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 = {} \[ \int \frac {1}{x \sqrt {a+b \sin ^{-1}(c x)}} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
Rubi steps
\begin {align*} \int \frac {1}{x \sqrt {a+b \sin ^{-1}(c x)}} \, dx &=\int \frac {1}{x \sqrt {a+b \sin ^{-1}(c x)}} \, dx\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 3.12, size = 0, normalized size = 0.00 \[ \int \frac {1}{x \sqrt {a+b \sin ^{-1}(c x)}} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [F(-2)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Exception raised: TypeError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{\sqrt {b \arcsin \left (c x\right ) + a} x}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.13, size = 0, normalized size = 0.00 \[ \int \frac {1}{x \sqrt {a +b \arcsin \left (c x \right )}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{\sqrt {b \arcsin \left (c x\right ) + a} x}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [A] time = 0.00, size = -1, normalized size = -0.05 \[ \int \frac {1}{x\,\sqrt {a+b\,\mathrm {asin}\left (c\,x\right )}} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{x \sqrt {a + b \operatorname {asin}{\left (c x \right )}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________