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

Optimal. Leaf size=25 \[ \text {Int}\left (\frac {\sqrt {d+e x^2}}{a+b \sin ^{-1}(c x)},x\right ) \]

[Out]

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

________________________________________________________________________________________

Rubi [A]  time = 0.04, 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 = {} \[ \int \frac {\sqrt {d+e x^2}}{a+b \sin ^{-1}(c x)} \, dx \]

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 = 1.34, size = 0, normalized size = 0.00 \[ \int \frac {\sqrt {d+e x^2}}{a+b \sin ^{-1}(c x)} \, dx \]

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]

________________________________________________________________________________________

fricas [A]  time = 1.03, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\sqrt {e x^{2} + d}}{b \arcsin \left (c x\right ) + a}, x\right ) \]

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)

________________________________________________________________________________________

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

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)

________________________________________________________________________________________

maple [A]  time = 0.43, size = 0, normalized size = 0.00 \[ \int \frac {\sqrt {e \,x^{2}+d}}{a +b \arcsin \left (c x \right )}\, dx \]

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)

________________________________________________________________________________________

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

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)

________________________________________________________________________________________

mupad [A]  time = 0.00, size = -1, normalized size = -0.04 \[ \int \frac {\sqrt {e\,x^2+d}}{a+b\,\mathrm {asin}\left (c\,x\right )} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

________________________________________________________________________________________

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

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)

________________________________________________________________________________________