What is the integral of xcos(x/5) ?

The integral of xcos(x/5) is 5xsin(x/5)+25cos(x/5)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of xcos(x/5)

\int x cos (\frac{x}{5}) d x

5 x sin (\frac{x}{5}) + 25 cos (\frac{x}{5}) + C

Solution steps

\int x cos (\frac{x}{5}) d x

Apply Integration By Parts

= 5 x sin (\frac{x}{5}) - \int 5 sin (\frac{x}{5}) d x

\int 5 sin (\frac{x}{5}) d x = - 25 cos (\frac{x}{5})

= 5 x sin (\frac{x}{5}) - (- 25 cos (\frac{x}{5}))

Simplify

= 5 x sin (\frac{x}{5}) + 25 cos (\frac{x}{5})

Add a constant to the solution

= 5 x sin (\frac{x}{5}) + 25 cos (\frac{x}{5}) + C

What is the integral of xcos(x/5) ?
The integral of xcos(x/5) is 5xsin(x/5)+25cos(x/5)+C