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

The integral of (sin(pix)-pixcos(pix))/(x^2) is -(sin(pix))/x+C

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

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

- \frac{sin ( π x )}{x} + C

Solution steps

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

Expand

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

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

\int \frac{sin ( π x )}{x ^{2}} d x = - \frac{sin ( π x )}{x} + π Ci (π x)

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

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

Simplify

= - \frac{sin ( π x )}{x}

Add a constant to the solution

= - \frac{sin ( π x )}{x} + C

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