What is the integral of (cos((2pi)/x))/(x^2) ?

The integral of (cos((2pi)/x))/(x^2) is -1/(2pi)sin((2pi)/x)+C

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integral of (cos((2pi)/x))/(x^2)

\int \frac{cos ( \frac{2 π}{x} )}{x ^{2}} d x

- \frac{1}{2 π} sin (\frac{2 π}{x}) + C

Solution steps

\int \frac{cos ( \frac{2 π}{x} )}{x ^{2}} d x

Apply u-substitution

: \int - \frac{cos ( u )}{2 π} d u

= \int - \frac{cos ( u )}{2 π} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \frac{1}{2 π} \cdot \int cos (u) d u

Use the common integral:

\int cos (u) d u = sin (u)

= - \frac{1}{2 π} sin (u)

Substitute back

u = \frac{2 π}{x}

= - \frac{1}{2 π} sin (\frac{2 π}{x})

Add a constant to the solution

= - \frac{1}{2 π} sin (\frac{2 π}{x}) + C

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What is the integral of (cos((2pi)/x))/(x^2) ?
The integral of (cos((2pi)/x))/(x^2) is -1/(2pi)sin((2pi)/x)+C