What is the integral of xsin(n)x ?

The integral of xsin(n)x is 1/3 x^3sin(n)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of xsin(n)x

\int x sin (n) x d x

\frac{1}{3} x^{3} sin (n) + C

Solution steps

\int x sin (n) x d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= sin (n) \cdot \int xx d x

Simplify

xx : x^{2}

= sin (n) \cdot \int x^{2} d x

Apply the Power Rule

: \frac{x ^{3}}{3}

= sin (n) \frac{x ^{3}}{3}

Simplify

sin (n) \frac{x ^{3}}{3} : \frac{1}{3} x^{3} sin (n)

= \frac{1}{3} x^{3} sin (n)

Add a constant to the solution

= \frac{1}{3} x^{3} sin (n) + C

n \to 2 lim (\frac{n - 1}{n ^{2} - 1})

\frac{d}{d x} (x^{3} - 3 x^{2} - 9 x + 5)

\int \frac{- 1}{4} sin (2 x) d x

x \to 0 lim (ln (x) + 1)

\frac{d}{d x} ((lo g_{e} (x))^{2})