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

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

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

\int_{0}^{2 π} \frac{1}{5 - 3 cos ( x )} d x

\frac{π}{2}

Decimal

1.57079 \dots

Solution steps

\int_{0}^{2 π} \frac{1}{5 - 3 cos ( x )} d x

Evaluating using numerical calculation methods

= \frac{π}{2}

\int_{0}^{1} e^{2 x} cos (π x) d x

\int_{- 3}^{- 1} - \frac{3 x ^{2}}{5} + \frac{x}{5} + 6 d x

\int_{\frac{π}{6}}^{\frac{π}{2}} 4 cot^{2} (x) d x

\int_{- 2}^{2} (x^{5} - x^{3} + 3 x^{2} - 4) d x

\int_{0}^{1} \frac{1}{25 - x ^{2}} d x

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