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

The integral of 1/x cos(y/x) is sin(y/x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of 1/x cos(y/x)

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

sin (\frac{y}{x}) + C

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

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

Take the constant out:

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

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

Use the common integral:

\int cos (u) d u = sin (u)

= \frac{1}{x} x sin (u)

Substitute back

u = \frac{y}{x}

= \frac{1}{x} x sin (\frac{y}{x})

Simplify

\frac{1}{x} x sin (\frac{y}{x}) : sin (\frac{y}{x})

= sin (\frac{y}{x})

Add a constant to the solution

= sin (\frac{y}{x}) + C

What is the integral of 1/x cos(y/x) ?
The integral of 1/x cos(y/x) is sin(y/x)+C