3.196 \(\int \frac {1}{x (a+b \sin ^{-1}(c x))^{3/2}} \, dx\)

Optimal. Leaf size=19 \[ \text {Int}\left (\frac {1}{x \left (a+b \sin ^{-1}(c x)\right )^{3/2}},x\right ) \]

[Out]

Unintegrable(1/x/(a+b*arcsin(c*x))^(3/2),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 = {} \[ \int \frac {1}{x \left (a+b \sin ^{-1}(c x)\right )^{3/2}} \, dx \]

Verification is Not applicable to the result.

[In]

Int[1/(x*(a + b*ArcSin[c*x])^(3/2)),x]

[Out]

Defer[Int][1/(x*(a + b*ArcSin[c*x])^(3/2)), x]

Rubi steps

\begin {align*} \int \frac {1}{x \left (a+b \sin ^{-1}(c x)\right )^{3/2}} \, dx &=\int \frac {1}{x \left (a+b \sin ^{-1}(c x)\right )^{3/2}} \, dx\\ \end {align*}

________________________________________________________________________________________

Mathematica [A]  time = 3.81, size = 0, normalized size = 0.00 \[ \int \frac {1}{x \left (a+b \sin ^{-1}(c x)\right )^{3/2}} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[1/(x*(a + b*ArcSin[c*x])^(3/2)),x]

[Out]

Integrate[1/(x*(a + b*ArcSin[c*x])^(3/2)), x]

________________________________________________________________________________________

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]

integrate(1/x/(a+b*arcsin(c*x))^(3/2),x, algorithm="fricas")

[Out]

Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (co
nstant residues)

________________________________________________________________________________________

giac [F(-2)]  time = 0.00, size = 0, normalized size = 0.00 \[ \text {Exception raised: RuntimeError} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x/(a+b*arcsin(c*x))^(3/2),x, algorithm="giac")

[Out]

Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:sym2poly/r2sym(co
nst gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value

________________________________________________________________________________________

maple [A]  time = 0.12, size = 0, normalized size = 0.00 \[ \int \frac {1}{x \left (a +b \arcsin \left (c x \right )\right )^{\frac {3}{2}}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/x/(a+b*arcsin(c*x))^(3/2),x)

[Out]

int(1/x/(a+b*arcsin(c*x))^(3/2),x)

________________________________________________________________________________________

maxima [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{{\left (b \arcsin \left (c x\right ) + a\right )}^{\frac {3}{2}} x}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x/(a+b*arcsin(c*x))^(3/2),x, algorithm="maxima")

[Out]

integrate(1/((b*arcsin(c*x) + a)^(3/2)*x), x)

________________________________________________________________________________________

mupad [A]  time = 0.00, size = -1, normalized size = -0.05 \[ \int \frac {1}{x\,{\left (a+b\,\mathrm {asin}\left (c\,x\right )\right )}^{3/2}} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(x*(a + b*asin(c*x))^(3/2)),x)

[Out]

int(1/(x*(a + b*asin(c*x))^(3/2)), x)

________________________________________________________________________________________

sympy [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{x \left (a + b \operatorname {asin}{\left (c x \right )}\right )^{\frac {3}{2}}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x/(a+b*asin(c*x))**(3/2),x)

[Out]

Integral(1/(x*(a + b*asin(c*x))**(3/2)), x)

________________________________________________________________________________________