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

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

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

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

\frac{1}{π} cos (\frac{π}{x}) + C

Solution steps

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

Apply u-substitution

: \int - \frac{sin ( u )}{π} d u

= \int - \frac{sin ( u )}{π} d u

Take the constant out:

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

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

Use the common integral:

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

= - \frac{1}{π} (- cos (u))

Substitute back

u = \frac{π}{x}

= - \frac{1}{π} (- cos (\frac{π}{x}))

Simplify

= \frac{1}{π} cos (\frac{π}{x})

Add a constant to the solution

= \frac{1}{π} cos (\frac{π}{x}) + C

\frac{d y}{d t} = \frac{t ^{2}}{y ( 2 + t ^{3} )}

\frac{d}{d x} (sin (\frac{π}{2}))

x \to 0 lim (\frac{e ^{x} - 1}{x ^{3}})

\frac{3 x + 2}{3 x - 2}

\frac{d}{d x} (e^{\frac{x ^{2}}{2}})

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