What is the integral of 1/(x^2)sin(pi/x) ?

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

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integral of 1/(x^2)sin(pi/x)

\int \frac{1}{x ^{2}} sin (\frac{π}{x}) d x

\frac{1}{π} cos (\frac{π}{x}) + C

Solution steps

\int \frac{1}{x ^{2}} sin (\frac{π}{x}) d x

Simplify

\frac{1}{x ^{2}} sin (\frac{π}{x}) : \frac{sin ( \frac{π}{x} )}{x ^{2}}

= \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}{d x} (9 x e^{2 x})

y = x^{2} - 2 x - 2, (2, - 2)

\frac{1}{s ^{2} - 6 s + 9}

\int 22 arctan (x) d x

cos (x - 7 x)

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