What is the integral of xsin(x/8) ?

The integral of xsin(x/8) is -8xcos(x/8)+64sin(x/8)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of xsin(x/8)

\int x sin (\frac{x}{8}) d x

- 8 x cos (\frac{x}{8}) + 64 sin (\frac{x}{8}) + C

Solution steps

\int x sin (\frac{x}{8}) d x

Apply Integration By Parts

= - 8 x cos (\frac{x}{8}) - \int - 8 cos (\frac{x}{8}) d x

\int - 8 cos (\frac{x}{8}) d x = - 64 sin (\frac{x}{8})

= - 8 x cos (\frac{x}{8}) - (- 64 sin (\frac{x}{8}))

Simplify

= - 8 x cos (\frac{x}{8}) + 64 sin (\frac{x}{8})

Add a constant to the solution

= - 8 x cos (\frac{x}{8}) + 64 sin (\frac{x}{8}) + C

What is the integral of xsin(x/8) ?
The integral of xsin(x/8) is -8xcos(x/8)+64sin(x/8)+C