What is the integral from 0 to 2pi of 1/(5-4cos(x)) ?

The integral from 0 to 2pi of 1/(5-4cos(x)) is (2pi)/3

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integral from 0 to 2pi of 1/(5-4cos(x))

\int_{0}^{2 π} \frac{1}{5 - 4 cos ( x )} d x

\frac{2 π}{3}

Decimal Notation

2.09439 \dots

Solution steps

\int_{0}^{2 π} \frac{1}{5 - 4 cos ( x )} d x

Evaluating using numerical calculation methods

= \frac{2 π}{3}

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What is the integral from 0 to 2pi of 1/(5-4cos(x)) ?
The integral from 0 to 2pi of 1/(5-4cos(x)) is (2pi)/3