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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

\int t^{2} sin (θ) t d t

\int sin^{- 5} (x) cos^{7} (x) d x

\int cos (x) \cdot cos (sin (x)) d x

\int 20 x sin (7 x^{2} - 8) d x

\int \frac{2 x ^{2} - x - 4}{x ^{2} ( x + 1 )} d 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