3.2.92 \(\int \frac {1}{x^2 \sqrt {a+b \text {ArcCos}(c x)}} \, dx\) [192]

Optimal. Leaf size=19 \[ \text {Int}\left (\frac {1}{x^2 \sqrt {a+b \text {ArcCos}(c x)}},x\right ) \]

[Out]

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

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Rubi [A]
time = 0.02, 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 = {} \begin {gather*} \int \frac {1}{x^2 \sqrt {a+b \text {ArcCos}(c x)}} \, dx \end {gather*}

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*}

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Mathematica [A]
time = 8.41, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{x^2 \sqrt {a+b \text {ArcCos}(c x)}} \, dx \end {gather*}

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 = 0.88, size = 0, normalized size = 0.00 \[\int \frac {1}{x^{2} \sqrt {a +b \arccos \left (c x \right )}}\, dx\]

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 = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}

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 = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: TypeError} \end {gather*}

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: TypeError >>  Error detected within library code:   integrate: implementation incomplete (co
nstant residues)

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Sympy [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{x^{2} \sqrt {a + b \operatorname {acos}{\left (c x \right )}}}\, dx \end {gather*}

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 = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

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)

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Mupad [A]
time = 0.00, size = -1, normalized size = -0.05 \begin {gather*} \int \frac {1}{x^2\,\sqrt {a+b\,\mathrm {acos}\left (c\,x\right )}} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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