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

Optimal. Leaf size=18 \[ \text{Unintegrable}\left (\frac{\left (a+b \sin ^{-1}(c x)\right )^{3/2}}{x},x\right ) \]

[Out]

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

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Rubi [A]  time = 0.0451535, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ \int \frac{\left (a+b \sin ^{-1}(c x)\right )^{3/2}}{x} \, dx \]

Verification is Not applicable to the result.

[In]

Int[(a + b*ArcSin[c*x])^(3/2)/x,x]

[Out]

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

Rubi steps

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

Mathematica [A]  time = 2.90078, size = 0, normalized size = 0. \[ \int \frac{\left (a+b \sin ^{-1}(c x)\right )^{3/2}}{x} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

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Maple [A]  time = 0.11, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{x} \left ( a+b\arcsin \left ( cx \right ) \right ) ^{{\frac{3}{2}}}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Maxima [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{{\left (b \arcsin \left (c x\right ) + a\right )}^{\frac{3}{2}}}{x}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Fricas [F(-2)]  time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: UnboundLocalError} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Exception raised: UnboundLocalError

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Sympy [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\left (a + b \operatorname{asin}{\left (c x \right )}\right )^{\frac{3}{2}}}{x}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{{\left (b \arcsin \left (c x\right ) + a\right )}^{\frac{3}{2}}}{x}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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