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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

\int \frac{cos ^{2} ( 3 x )}{1 - sin ( 3 x )} d x

\int 4 x^{3} - 5 x + 5 + \frac{1}{x} + \frac{3}{x ^{2}} d x

\int \frac{x ^{4} + 7}{x ^{3} + 9 x} d x

\int \frac{2}{25 - x ^{2}} d x

\int cos (12 x) cos (3 x) d x

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