3.179 \(\int \frac {1}{x \sqrt {a-a \cos (x)}} \, dx\)

Optimal. Leaf size=18 \[ \text {Int}\left (\frac {1}{x \sqrt {a-a \cos (x)}},x\right ) \]

[Out]

Unintegrable(1/x/(a-a*cos(x))^(1/2),x)

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Rubi [A]  time = 0.08, 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 = {} \[ \int \frac {1}{x \sqrt {a-a \cos (x)}} \, dx \]

Verification is Not applicable to the result.

[In]

Int[1/(x*Sqrt[a - a*Cos[x]]),x]

[Out]

Defer[Int][1/(x*Sqrt[a - a*Cos[x]]), x]

Rubi steps

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

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Mathematica [A]  time = 2.96, size = 0, normalized size = 0.00 \[ \int \frac {1}{x \sqrt {a-a \cos (x)}} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[1/(x*Sqrt[a - a*Cos[x]]),x]

[Out]

Integrate[1/(x*Sqrt[a - a*Cos[x]]), x]

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fricas [A]  time = 0.95, size = 0, normalized size = 0.00 \[ {\rm integral}\left (-\frac {\sqrt {-a \cos \relax (x) + a}}{a x \cos \relax (x) - a x}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x/(a-a*cos(x))^(1/2),x, algorithm="fricas")

[Out]

integral(-sqrt(-a*cos(x) + a)/(a*x*cos(x) - a*x), x)

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giac [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{\sqrt {-a \cos \relax (x) + a} x}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x/(a-a*cos(x))^(1/2),x, algorithm="giac")

[Out]

integrate(1/(sqrt(-a*cos(x) + a)*x), x)

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maple [A]  time = 0.06, size = 0, normalized size = 0.00 \[ \int \frac {1}{x \sqrt {a -a \cos \relax (x )}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/x/(a-a*cos(x))^(1/2),x)

[Out]

int(1/x/(a-a*cos(x))^(1/2),x)

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maxima [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{\sqrt {-a \cos \relax (x) + a} x}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x/(a-a*cos(x))^(1/2),x, algorithm="maxima")

[Out]

integrate(1/(sqrt(-a*cos(x) + a)*x), x)

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mupad [A]  time = 0.00, size = -1, normalized size = -0.06 \[ \int \frac {1}{x\,\sqrt {a-a\,\cos \relax (x)}} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(x*(a - a*cos(x))^(1/2)),x)

[Out]

int(1/(x*(a - a*cos(x))^(1/2)), x)

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sympy [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{x \sqrt {- a \left (\cos {\relax (x )} - 1\right )}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x/(a-a*cos(x))**(1/2),x)

[Out]

Integral(1/(x*sqrt(-a*(cos(x) - 1))), x)

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