3.192 \(\int \frac{1}{x^2 \sqrt{a+b \cos ^{-1}(c x)}} \, dx\)

Optimal. Leaf size=18 \[ \text{Unintegrable}\left (\frac{1}{x^2 \sqrt{a+b \cos ^{-1}(c x)}},x\right ) \]

[Out]

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

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Rubi [A]  time = 0.0354743, 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 = {} \[ \int \frac{1}{x^2 \sqrt{a+b \cos ^{-1}(c x)}} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

Rubi steps

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

Mathematica [A]  time = 11.9607, size = 0, normalized size = 0. \[ \int \frac{1}{x^2 \sqrt{a+b \cos ^{-1}(c x)}} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/x^2/(a+b*arccos(c*x))^(1/2),x)

[Out]

int(1/x^2/(a+b*arccos(c*x))^(1/2),x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(1/(sqrt(b*arccos(c*x) + a)*x^2), x)

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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/x^2/(a+b*arccos(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}{x^{2} \sqrt{a + b \operatorname{acos}{\left (c x \right )}}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x**2/(a+b*acos(c*x))**(1/2),x)

[Out]

Integral(1/(x**2*sqrt(a + b*acos(c*x))), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(1/(sqrt(b*arccos(c*x) + a)*x^2), x)