3.698 \(\int \frac{1}{(d+e x^2) \sqrt{a+b \sin ^{-1}(c x)}} \, dx\)

Optimal. Leaf size=24 \[ \text{Unintegrable}\left (\frac{1}{\left (d+e x^2\right ) \sqrt{a+b \sin ^{-1}(c x)}},x\right ) \]

[Out]

Unintegrable[1/((d + e*x^2)*Sqrt[a + b*ArcSin[c*x]]), x]

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Rubi [A]  time = 0.0567442, 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 = {} \[ \int \frac{1}{\left (d+e x^2\right ) \sqrt{a+b \sin ^{-1}(c x)}} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

Rubi steps

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

Mathematica [A]  time = 0.145486, size = 0, normalized size = 0. \[ \int \frac{1}{\left (d+e x^2\right ) \sqrt{a+b \sin ^{-1}(c x)}} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

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Maple [A]  time = 0.209, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{e{x}^{2}+d}{\frac{1}{\sqrt{a+b\arcsin \left ( cx \right ) }}}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Exception raised: ValueError

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

[Out]

Exception raised: UnboundLocalError

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Sympy [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{\sqrt{a + b \operatorname{asin}{\left (c x \right )}} \left (d + e x^{2}\right )}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Integral(1/(sqrt(a + b*asin(c*x))*(d + e*x**2)), x)

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Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{{\left (e x^{2} + d\right )} \sqrt{b \arcsin \left (c x\right ) + a}}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(1/((e*x^2 + d)*sqrt(b*arcsin(c*x) + a)), x)