What is the integral of x^2cos(x)+2xsin(x) ?

The integral of x^2cos(x)+2xsin(x) is x^2sin(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^2cos(x)+2xsin(x)

\int x^{2} cos (x) + 2 x sin (x) d x

x^{2} sin (x) + C

Solution steps

\int x^{2} cos (x) + 2 x sin (x) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int x^{2} cos (x) d x + \int 2 x sin (x) d x

\int x^{2} cos (x) d x = x^{2} sin (x) - 2 (- x cos (x) + sin (x))

\int 2 x sin (x) d x = 2 (- x cos (x) + sin (x))

= x^{2} sin (x) - 2 (- x cos (x) + sin (x)) + 2 (- x cos (x) + sin (x))

Simplify

= x^{2} sin (x)

Add a constant to the solution

= x^{2} sin (x) + C

x \to 0 lim (\frac{5 x}{x ^{2}})

\int cos^{3} (4 x) d x

\int 2 x + 8 sin (x) d x

\int (sec^{2} (x) - 2) d x

\int_{0}^{2} \frac{2}{2 - x} d x

What is the integral of x^2cos(x)+2xsin(x) ?
The integral of x^2cos(x)+2xsin(x) is x^2sin(x)+C