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

The integral of x^2cos(wx) is 1/w x^2sin(wx)-2/w (-1/w xcos(wx)+1/(w^2)sin(wx))+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(wx)

\int x^{2} cos (w x) d x

\frac{1}{w} x^{2} sin (w x) - \frac{2}{w} (- \frac{1}{w} x cos (w x) + \frac{1}{w ^{2}} sin (w x)) + C

Solution steps

\int x^{2} cos (w x) d x

Apply Integration By Parts

: \frac{1}{w} x^{2} sin (w x) - \int \frac{2}{w} x sin (w x) d x

= \frac{1}{w} x^{2} sin (w x) - \int \frac{2}{w} x sin (w x) d x

\int \frac{2}{w} x sin (w x) d x = \frac{2}{w} (- \frac{1}{w} x cos (w x) + \frac{1}{w ^{2}} sin (w x))

= \frac{1}{w} x^{2} sin (w x) - \frac{2}{w} (- \frac{1}{w} x cos (w x) + \frac{1}{w ^{2}} sin (w x))

Add a constant to the solution

= \frac{1}{w} x^{2} sin (w x) - \frac{2}{w} (- \frac{1}{w} x cos (w x) + \frac{1}{w ^{2}} sin (w x)) + C

f (I) = \frac{110 I}{I ^{2} + I + 1}

arctan (4 t)

\int \frac{x ^{2}}{3 - x ^{3}} d x

1500 x + 3000 (5 x + 3)^{- 1} - 1000

\frac{e ^{- 4 s}}{s}

What is the integral of x^2cos(wx) ?
The integral of x^2cos(wx) is 1/w x^2sin(wx)-2/w (-1/w xcos(wx)+1/(w^2)sin(wx))+C