What is the integral of (cos(1/x))/x ?

The integral of (cos(1/x))/x is -\Ci(1/x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (cos(1/x))/x

\int \frac{cos ( \frac{1}{x} )}{x} d x

- Ci (\frac{1}{x}) + C

Solution steps

\int \frac{cos ( \frac{1}{x} )}{x} d x

Apply u-substitution

: \int - \frac{cos ( u )}{u} d u

= \int - \frac{cos ( u )}{u} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \int \frac{cos ( u )}{u} d u

Use the nonelementary integral:

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

= - Ci (u)

Substitute back

u = \frac{1}{x}

= - Ci (\frac{1}{x})

Add a constant to the solution

= - Ci (\frac{1}{x}) + C

\int \frac{4}{3} π r^{3} d r

\frac{d}{d x} ((x + 1)^{3} - x^{3})

\int_{2}^{4} \frac{2}{x ^{2} - 6 x + 10} d x

(- 2.1) (4.2)

f (x) = (x^{2} + 7) (5 - x), at x = 0

What is the integral of (cos(1/x))/x ?
The integral of (cos(1/x))/x is -\Ci(1/x)+C