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

Optimal. Leaf size=21 \[ \text {Int}\left (\frac {(d x)^{3/2}}{a+b \sin ^{-1}(c x)},x\right ) \]

[Out]

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

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Rubi [A]  time = 0.03, 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 = {} \[ \int \frac {(d x)^{3/2}}{a+b \sin ^{-1}(c x)} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

Rubi steps

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

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Mathematica [A]  time = 3.07, size = 0, normalized size = 0.00 \[ \int \frac {(d x)^{3/2}}{a+b \sin ^{-1}(c x)} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

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fricas [A]  time = 0.39, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\sqrt {d x} d x}{b \arcsin \left (c x\right ) + a}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integral(sqrt(d*x)*d*x/(b*arcsin(c*x) + a), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((d*x)^(3/2)/(a + b*asin(c*x)),x)

[Out]

int((d*x)^(3/2)/(a + b*asin(c*x)), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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