What is the integral of (cos(2x))/(2x) ?

The integral of (cos(2x))/(2x) is 1/2 \Ci(2x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (cos(2x))/(2x)

\int \frac{cos ( 2 x )}{2 x} d x

\frac{1}{2} Ci (2 x) + C

Solution steps

\int \frac{cos ( 2 x )}{2 x} d x

Take the constant out:

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

= \frac{1}{2} \cdot \int \frac{cos ( 2 x )}{x} d x

Apply u-substitution

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

= \frac{1}{2} \cdot \int \frac{cos ( u )}{u} d u

Use the nonelementary integral:

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

= \frac{1}{2} Ci (u)

Substitute back

u = 2 x

= \frac{1}{2} Ci (2 x)

Add a constant to the solution

= \frac{1}{2} Ci (2 x) + C

\int x^{6} - x^{3} d x

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

\int \frac{5}{2} x 5^{- x + 6} d x

\int cot (38 x) d x

What is the integral of (cos(2x))/(2x) ?
The integral of (cos(2x))/(2x) is 1/2 \Ci(2x)+C