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

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

[Out]

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

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Rubi [A]  time = 0.0421287, 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 = {} \[ \int \frac{\sqrt{d+e x^2}}{a+b \sin ^{-1}(c x)} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

Rubi steps

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

Mathematica [A]  time = 1.2525, size = 0, normalized size = 0. \[ \int \frac{\sqrt{d+e x^2}}{a+b \sin ^{-1}(c x)} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

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Maple [A]  time = 0.253, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{a+b\arcsin \left ( cx \right ) }\sqrt{e{x}^{2}+d}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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