3.139 \(\int \frac {\sin ^{-1}(a x)^n}{(b x)^{3/2}} \, dx\)

Optimal. Leaf size=17 \[ \text {Int}\left (\frac {\sin ^{-1}(a x)^n}{(b x)^{3/2}},x\right ) \]

[Out]

Unintegrable(arcsin(a*x)^n/(b*x)^(3/2),x)

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Rubi [A]  time = 0.02, 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 = {} \[ \int \frac {\sin ^{-1}(a x)^n}{(b x)^{3/2}} \, dx \]

Verification is Not applicable to the result.

[In]

Int[ArcSin[a*x]^n/(b*x)^(3/2),x]

[Out]

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

Rubi steps

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

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Mathematica [A]  time = 1.93, size = 0, normalized size = 0.00 \[ \int \frac {\sin ^{-1}(a x)^n}{(b x)^{3/2}} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

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fricas [A]  time = 0.45, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\sqrt {b x} \arcsin \left (a x\right )^{n}}{b^{2} x^{2}}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integral(sqrt(b*x)*arcsin(a*x)^n/(b^2*x^2), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maple [A]  time = 0.10, size = 0, normalized size = 0.00 \[ \int \frac {\arcsin \left (a x \right )^{n}}{\left (b x \right )^{\frac {3}{2}}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maxima [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(arcsin(a*x)^n/(b*x)^(3/2),x, algorithm="maxima")

[Out]

Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative e
xponent.

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mupad [A]  time = 0.00, size = -1, normalized size = -0.06 \[ \int \frac {{\mathrm {asin}\left (a\,x\right )}^n}{{\left (b\,x\right )}^{3/2}} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(asin(a*x)^n/(b*x)^(3/2),x)

[Out]

int(asin(a*x)^n/(b*x)^(3/2), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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