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

The integral of (sin(pix))/(x^2) is -(sin(pix))/x+pi\Ci(pix)+C

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

\int \frac{sin ( π x )}{x ^{2}} d x

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

Solution steps

\int \frac{sin ( π x )}{x ^{2}} d x

Apply Integration By Parts

: - \frac{sin ( π x )}{x} - \int - \frac{π cos ( π x )}{x} d x

= - \frac{sin ( π x )}{x} - \int - \frac{π cos ( π x )}{x} d x

\int - \frac{π cos ( π x )}{x} d x = - π Ci (π x)

= - \frac{sin ( π x )}{x} - (- π Ci (π x))

Simplify

= - \frac{sin ( π x )}{x} + π Ci (π x)

Add a constant to the solution

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

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What is the integral of (sin(pix))/(x^2) ?
The integral of (sin(pix))/(x^2) is -(sin(pix))/x+pi\Ci(pix)+C