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