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

The integral of x(cos(x)) is xsin(x)+cos(x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of x(cos(x))

\int x (cos (x)) d x

x sin (x) + cos (x) + C

Solution steps

\int x cos (x) d x

Apply Integration By Parts

: x sin (x) - \int sin (x) d x

= x sin (x) - \int sin (x) d x

\int sin (x) d x = - cos (x)

= x sin (x) - (- cos (x))

Simplify

= x sin (x) + cos (x)

Add a constant to the solution

= x sin (x) + cos (x) + C

\frac{d}{d x} (cos^{3} (2 x))

x \to 3 lim (\frac{2}{x - 3})

\frac{d}{d x} (3 csc (x) cos^{3} (x))

\frac{d}{d x} ((1 - x)^{- 1})

y = \frac{1}{1 + x ^{2}}, (- 1, \frac{1}{2})

What is the integral of x(cos(x)) ?
The integral of x(cos(x)) is xsin(x)+cos(x)+C