What is the integral of x*sin(x/2) ?

The integral of x*sin(x/2) is -2xcos(x/2)+4sin(x/2)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of x*sin(x/2)

\int x \cdot sin (\frac{x}{2}) d x

- 2 x cos (\frac{x}{2}) + 4 sin (\frac{x}{2}) + C

Solution steps

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

Apply Integration By Parts

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

\int - 2 cos (\frac{x}{2}) d x = - 4 sin (\frac{x}{2})

= - 2 x cos (\frac{x}{2}) - (- 4 sin (\frac{x}{2}))

Simplify

= - 2 x cos (\frac{x}{2}) + 4 sin (\frac{x}{2})

Add a constant to the solution

= - 2 x cos (\frac{x}{2}) + 4 sin (\frac{x}{2}) + C

What is the integral of x*sin(x/2) ?
The integral of x*sin(x/2) is -2xcos(x/2)+4sin(x/2)+C