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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

\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

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